The Online Library of Liberty

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• Introduction to the House of Fame
• Introduction to the Legend of Good Women.
• Introduction to a Treatise On the Astrolabe.
• Description of the Plates.
• The Hous of Fame.
• Book I.
• Book II.
• Book III.
• The Legend of Good Women.
• The Prologe of .ix. Goode Wimmen.
• I.: The Legend of Cleopatra.
• II.: The Legend of Thisbe of Babylon.
• III.: The Legend of Dido, Queen of Carthage.
• IV.: The Legend of Hypsipyle and Medea.
• V.: The Legend of Lucretia.
• VI.: The Legend of Ariadne.
• VII.: The Legend of Philomela.
• VIII.: The Legend of Phyllis.
• IX.: The Legend of Hypermnestra.
• A Treatise On the Astrolabe.
• Prologue.
• Part I.
• Part Ii
• Supplementary Propositions.
• Critical Notes
• Notes to the House of Fame.
• Notes to the Legend of Good Women.
• Sources of the Canterbury Tales.

A TREATISE ON THE ASTROLABE.

PROLOGUE.

LITELL Lowis my sone, I have perceived wel by certeyne evidences thyn abilite to lerne sciencez touchinge noumbres and proporciouns; and as wel considere I thy bisy preyere in special to lerne the Tretis of the Astrolabie. Than, for as mechel as a philosofre seith, ‘he wrappeth him in his frend, that condescendeth5 to the rightful preyers of his frend,’ ther-for have I geven thee a suffisaunt Astrolabie as for oure orizonte, compowned after the latitude of Oxenford; up-on which, by mediacion of this litel tretis, I purpose to teche thee a certein nombre of conclusions apertening to the same instrument. I seye a certein of conclusiouns,10 for three causes. The furste cause is this: truste wel that alle the conclusiouns that han ben founde, or elles possibly mighten be founde in so noble an instrument as an Astrolabie, ben un-knowe perfitly to any mortal man in this regioun, as I suppose. A-nother cause is this; that sothly, in any tretis of the Astrolabie that I have15 seyn, there ben some conclusions that wole nat in alle thinges performen hir bihestes; and some of hem ben to harde to thy tendre age of ten yeer to conseyve. This tretis, divided in fyve parties, wole I shewe thee under ful lighte rewles and naked20 wordes in English; for Latin ne canstow yit but smal, my lyte sone. But natheles, suffyse to thee thise trewe conclusiouns in English, as wel as suffyseth to thise noble clerkes Grekes thise same conclusiouns in Greek, and to Arabiens in Arabik, and to Iewes in Ebrew, and to the Latin folk in Latin; whiche Latin folk han hem25 furst out of othre diverse langages, and writen in hir owne tonge, that is to sein, in Latin. And god wot, that in alle thise langages, and in many mo, han thise conclusiouns ben suffisantly lerned and taught, and yit by diverse rewles, right as diverse pathes leden diverse folk the righte wey to Rome. Now wol I prey meekly30 every discret persone that redeth or hereth this litel tretis, to have my rewde endyting for excused, and my superfluite of wordes, for two causes. The firste cause is, for that curious endyting and hard [ ] sentence is ful hevy atones for swich a child to lerne. And the seconde cause is this, that sothly me semeth betre to wryten un-to35 a child twyes a good sentence, than he for-gete it ones. And Lowis, yif so be that I shewe thee in my lighte English as trewe conclusiouns touching this matere, and naught only as trewe but as many and as subtil conclusiouns as ben shewed in Latin in any commune tretis of the Astrolabie, con me the more thank; and40 preye god save the king, that is lord of this langage, and alle that him feyth bereth and obeyeth, everech in his degree, the more and the lasse. But considere wel, that I ne usurpe nat to have founde this werk of my labour or of myn engin. I nam but a lewd compilatour of the labour of olde Astrologiens, and have hit translated45 in myn English only for thy doctrine; and with this swerd shal I sleen envye.

I. The firste partie of this tretis shal reherse the figures and the membres of thyn Astrolabie, bi-cause that thou shalt han the grettre knowing of thyn owne instrument.

II. The second partie shal teche thee werken the verrey50 practik of the forseide conclusiouns, as ferforth and as narwe as may be shewed in so smal an instrument portatif aboute. For wel wot every astrologien that smalest fraccions ne wol nat ben shewed in so smal an instrument, as in subtil tables calculed for a cause.55

III. The thridde partie shal contienen diverse tables of longitudes and latitudes of sterres fixe for the Astrolabie, and tables of declinacions of the sonne, and tables of longitudes of citeez and of townes; and as wel for the governance of a clokke as for to finde the altitude meridian; and many another60 notable conclusioun, after the kalendres of the reverent clerkes, frere I. Somer and frere N. Lenne.[ ]

IV. The ferthe partie shal ben a theorik to declare the moevinge of the celestial bodies with the causes. The whiche ferthe partie in special shal shewen a table of the verray65 moeving of the mone from houre to houre, every day and in every signe, after thyn almenak; upon which table ther folwith a canon, suffisant to teche as wel the maner of the wyrking of that same conclusioun, as to knowe in oure orizonte with which degree of the zodiac that the mone ariseth in any latitude;70 and the arising of any planete after his latitude fro the ecliptik lyne.

V. The fifte partie shal ben an introductorie after the statutz of oure doctours, in which thou maist lerne a gret part of the general rewles of theorik in astrologie. In which fifte partie75 shaltow finde tables of equacions of houses aftur the latitude of Oxenford; and tables of dignetes of planetes, and other noteful thinges, yif god wol vouche-sauf and his modur the mayde, mo than I be-hete, &c.

Little Lewis my son, I perceive that thou wouldst learn the Conclusions of the AStrolabe; wherefore I have given thee an instrument constructed for the latitude of Oxford, and purpose to teach thee some of these conclusions. I say some, for three reasons; (1) because some of them are unknown in this land; (2) because some are uncertain; or else (3) are too hard. This treatise, divided into five parts, I write for thee in English, just as Greeks, Arabians, Jews, and Romans were accustomed to write such things in their own tongue I pray all to excuse my shortcomings; and thou, Lewis, shouldst thank me if I teach thee as much in English as most common treatises can do in Latin. I have done no more than compile from old writers on the subject, and I have translated it into English solely for thine instruction; and with this sword shall I slay envy.

The first part gives a description of the instrument itself.

The second teaches the practical working of it.

The third shall contain tables of latitudes and longitudes of fixed stars, declinations of the sun, and the longitudes of certain towns.

The fourth shall shew the motions of the heavenly bodies, and especially of the moon.

The fifth shall teach a great part of the general rules of astronomical theory.

PART I.

Here biginneth the descripcion of the Astrolabie.

1. Thyn Astrolabie hath a ring to putten on the thoumbe of thy right hand in taking the heighte of thinges. And tak keep, for from hennes-forthward, I wol clepe the heighte of any thing that is taken by thy rewle, the altitude, with-oute mo wordes.

2. This ring renneth in a maner turet, fast to the moder of thyn Astrolabie, in so rowm a space that hit desturbeth nat the instrument to hangen after his righte centre.

3.The Moder of thyn Astrolabie is the thikkeste plate, perced with a large hole, that resseyveth in hir wombe the thinne plates compowned for diverse clymatz, and thy riet shapen in manere of a net or of a webbe of a loppe; and for the more declaracioun,5 lo here the figure.

4. This moder is devyded on the bak-half with a lyne, that cometh dessendinge fro the ring down to the nethereste bordure. The whiche lyne, fro the for-seide ring un-to the centre of the large hole amidde, is cleped the south lyne, or elles the lyne5 meridional. And the remenant of this lyne downe to the bordure is cleped the north lyne, or elles the lyne of midnight. And for the more declaracioun, lo here the figure.

5. Over-thwart this for-seide longe lyne, ther crosseth him another lyne of the same lengthe from est to west. Of the whiche lyne, from a litel croys + in the bordure un-to the centre of the large hole, is cleped the Est lyne, or elles the lyne Orientale; and the remenant of this lyne fro the forseide + un-to the bordure,5 is cleped the West lyne, or the lyne Occidentale. Now hastow here the foure quarters of thin Astrolabie, devyded after the foure principals plages or quarters of the firmament. And for the more declaracioun, lo here thy figure.

6. The est side of thyn Astrolabie is cleped the right side, and the west side is cleped the left side. Forget nat this, litel Lowis. Put the ring of thyn Astrolabie upon the thoumbe of thy right hand, and thanne wole his right syde be toward thy left syde, and his left syde wol be toward thy right syde; tak this rewle general,5 as wel on the bak as on the wombe-side. Upon the ende of this est lyne, as I first seide, is marked a litel +, wher-as evere-mo generaly is considered the entring of the first degree in which the sonne aryseth. And for the more declaracioun, lo here the figure.10

7. Fro this litel + up to the ende of the lyne meridional, under the ring, shaltow finden the bordure devyded with 90 degrees; and by that same proporcioun is every quarter of thin Astrolabie devyded. Over the whiche degrees ther ben noumbres of augrim , that devyden thilke same degrees fro fyve to fyve, as sheweth by5 longe strykes by-twene. Of whiche longe strykes the space bytwene contienith a mile-wey. And every degree of the bordure contieneth foure minutes, that is to seyn, minutes of an houre. And for more declaracioun, lo here the figure.

8. Under the compas of thilke degrees ben writen the names of the Twelve Signes, as Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces; and the nombres of the degrees of tho signes ben writen in augrim5 above, and with longe devisiouns, fro fyve to fyve; devyded fro tyme that the signe entreth un-to the laste ende. But understond wel, that thise degrees of signes ben everich of hem considered of 60 minutes, and every minute of 60 secondes, and so forth in-to smale fraccions infinit, as seith Alkabucius . And10 ther-for, know wel, that a degree of the bordure contieneth foure minutes, and a degree of a signe contieneth 60 minutes, and have this in minde. And for the more declaracioun, lo here thy figure.

9. Next this folweth the Cercle of the Dayes, that ben figured in maner of degrees, that contienen in noumbre 365; divyded also with longe strykes fro fyve to fyve, and the nombres in augrim writen under that cercle. And for more declaracioun, lo5 here thy figure.

10. Next the Cercle of the Dayes, folweth the Cercle of the names of the Monthes; that is to seyen, Ianuare, Februare, Marcius, Aprile, Mayus, Iuin, Iulius, Augustus, Septembre, October, Novembre, Decembre. The names of thise monthes5 were cleped in Arabiens , somme for hir propretees, and some by statutz of lordes, some by other lordes of Rome. Eek of thise monthes, as lyked to Iulius Cesar and to Cesar Augustus, some were compowned of diverse nombres of dayes, as Iuil and August. Thanne hath Ianuare 31 dayes, Februare 28, March10 31, Aprille 30, May 31, Iunius 30, Iulius 31, Augustus 31, September 30, Octobre 31, Novembre 30, December 31. Natheles, al-though that Iulius Cesar took 2 dayes out of Feverer and put hem in his moneth of Iuille, and Augustus Cesar cleped the moneth of August after his name, and ordeyned it of 31 dayes, yit truste wel, that the sonne dwelleth ther-for nevere the more ne15 lesse in oon signe than in another.

11. Than folwen the names of the Halidayes in the Kalender, and next hem the lettres of the Abc. on which they fallen. And for the more declaracioun, lo here thy figure.

12. Next the forseide Cercle of the Abc., under the cros-lyne, is marked the scale, in maner of two squyres, or elles in manere of laddres, that serveth by hise 12 poyntes and his devisiouns of ful many a subtil conclusioun. Of this forseide scale, fro the cross-lyne un-to the verre angle, is cleped umbra versa, and the5nether partie is cleped the umbra recta, or elles umbra extensa. And for the more declaracioun, lo here the figure.

13. Thanne hastow a brood Rewle, that hath on either ende a square plate perced with a certein holes, some more and some lesse, to resseyven the stremes of the sonne by day, and eek by mediacioun of thyn eye, to knowe the altitude of sterres by nighte. And for the more declaracioun, lo here thy figure.5

14. Thanne is ther a large Pyn, in maner of an extree, that goth thorow the hole that halt the tables of the clymates and the riet in the wombe of the Moder, thorw which Pyn ther goth a litel wegge which that is cleped ‘the hors,’ that streyneth alle5 thise parties to-hepe; this forseide grete Pyn, in maner of an extree, is imagined to be the Pol Artik in thyn Astrolabie. And for the more declaracioun, lo here the figure.

15. The wombe-side of thyn Astrolabie is also devyded with a longe croys in foure quarters from est to west, fro south to north, fro right syde to left syde, as is the bak-syde. And for the more declaracioun, lo here thy figure.

16. The bordure of which wombe-side is devyded fro the poynt of the est lyne un-to the poynt of the south lyne under the ring, in 90 degres; and by that same proporcioun is every quarter devyded as is the bak-syde, that amonteth 360 degrees. And5 understond wel, that degrees of this bordure ben answering and consentrik to the degrees of the Equinoxial, that is devyded in the same nombre as every othere cercle is in the heye hevene. This same bordure is devyded also with 23 lettres capitals and a smal croys + above the south lyne, that sheweth the 24 houres10 equals of the clokke; and, as I have said, 5 of thise degrees maken a mile-wey, and 3 mile-wey maken an houre. And every degree of this bordure conteneth 4 minutes, and every minut 60 secoundes ; now have I told thee twye. And for the more declaracioun, lo here the figure.

17. The plate under thy riet is descryved with 3 principal cercles; of whiche the leste is cleped the cercle of Cancer, by-cause that the heved of Cancer turneth evermor consentrik up-on the same cercle. In this heved of Cancer is the grettest declinacioun northward of the sonne. And ther-for is he cleped the5 Solsticioun of Somer; whiche declinacioun, aftur Ptholome , is 23 degrees and 50 minutes, as wel in Cancer as in Capricorne. This signe of Cancre is cleped the Tropik of Somer, of tropos, that is to seyn ‘agaynward’; for thanne by-ginneth the sonne to passe fro us-ward. And for the more declaracioun, lo here the figure.10

The middel cercle in wydnesse, of thise 3, is cleped the Cercle Equinoxial; up-on whiche turneth evermo the hedes of Aries and Libra. And understond wel, that evermo this Cercle Equinoxial turneth iustly fro verrey est to verrey west; as I have shewed thee in the spere solide. This same cercle is cleped also the Weyere,15equator, of the day; for whan the sonne is in the hevedes of Aries and Libra, than ben the dayes and the nightes ilyke of lengthe in al the world. And ther-fore ben thise two signes called the Equinoxies. And alle that moeveth with-in the hevedes of thise Aries and Libra, his moeving is cleped north-ward;20 and alle that moeveth with-oute thise hevedes, his moeving is cleped south-ward as fro the equinoxial. Tak keep of thise latitudes north and sowth, and forget it nat. By this Cercle Equinoxial ben considered the 24 houres of the clokke; for25 everemo the arysing of 15 degrees of the equinoxial maketh an houre equal of the clokke. This equinoxial is cleped the girdel of the firste moeving, or elles of the angulus primi motus vel primi mobilis . And nota, that firste moeving is cleped ‘moeving’ of the firste moevable of the 8 spere, whiche moeving is fro est to30 west, and eft agayn in-to est; also it is clepid ‘girdel’ of the first moeving, for it departeth the firste moevable, that is to seyn, the spere, in two ilyke parties, evene-distantz fro the poles of this world.

The wydeste of thise three principal cercles is cleped the35 Cercle of Capricorne, by-cause that the heved of Capricorne turneth evermo consentrik up-on the same cercle. In the heved of this for-seide Capricorne is the grettest declinacioun southward of the sonne, and ther-for is it cleped the Solsticioun of Winter. This signe of Capricorne is also cleped the Tropik of Winter, for40 thanne byginneth the sonne to come agayn to us-ward. And for the more declaracioun, lo here thy figure.

18. Upon this forseide plate ben compassed certein cercles that highten Almicanteras, of which som of hem semen perfit cercles, and somme semen imperfit. The centre that standith a-middes the narwest cercle is cleped the Senith; and the5 netherest cercle, or the firste cercle, is clepid the Orisonte, that is to seyn, the cercle that devydeth the two emisperies, that is, the partie of the hevene a-bove the erthe and the partie be-nethe. Thise Almicanteras ben compowned by two and two, al-be-it so that on divers Astrolabies some Almicanteras ben devyded by oon,10 and some by two, and somme by three, after the quantite of the Astrolabie. This forseide senith is imagened to ben the verrey point over the crowne of thyn heved; and also this senith is the verrey pool of the orisonte in every regioun. And for the more declaracioun, lo here thy figure.

19. From this senith, as it semeth, ther come a maner crokede strykes lyke to the clawes of a loppe, or elles like to the werk of a womanes calle, in kerving overthwart the Almikanteras. And thise same strykes or divisiouns ben cleped Azimuthz. And they devyden the orisonte of thyn Astrolabie in four and twenty5 devisiouns. And thise Azimutz serven to knowe the costes of the firmament, and to othre conclusiouns, as for to knowe the cenith of the sonne and of every sterre. And for more declaracioun, lo here thy figure.

20. Next thise azimutz, under the Cercle of Cancer, ben ther twelve devisiouns embelif, moche like to the shap of the azimutes, that shewen the spaces of the houres of planetes; and for more declaracioun, lo here thy figure .

21. The Riet of thyn Astrolabie with thy zodiak, shapen in maner of a net or of a loppe-webbe after the olde descripcioun, which thow mayst tornen up and doun as thy-self lyketh, conteneth certein nombre of sterres fixes , with hir longitudes and latitudes determinat; yif so be that the makere have nat erred. The names5 of the sterres ben writen in the margin of the riet ther as they sitte; of whiche sterres the smale poynt is cleped the Centre. [ ] And understond also that alle sterres sittinge with-in the zodiak of thyn Astrolabie ben cleped ‘sterres of the north,’ for they arysen by northe the est lyne. And alle the remenant fixed, out of the10 zodiak, ben cleped ‘sterres of the south;’ but I sey nat that they arysen alle by southe the est lyne; witnesse on Aldeberan and Algomeysa. Generally understond this rewle, that thilke sterres that ben cleped sterres of the north arysen rather than the degree15 of hir longitude, and alle the sterres of the south arysen after the degree of hir longitude; this is to seyn, sterres fixed in thyn Astrolabie. The mesure of this longitude of sterres is taken in the lyne ecliptik of hevene, under which lyne, whan that the sonne and the mone ben lyne-right or elles in the superfice of this lyne,20 than is the eclips of the sonne or of the mone; as I shal declare, and eek the cause why. But sothly the Ecliptik Lyne of thy zodiak is the outtereste bordure of thy zodiak, ther the degrees ben marked.

Thy Zodiak of thyn Astrolabie is shapen as a compas which that25 conteneth a large brede, as after the quantite of thyn Astrolabie; in ensample that the zodiak in hevene is imagened to ben a superfice contening a latitude of twelve degrees, wheras al the remenant of cercles in the hevene ben imagined verrey lynes with-oute eny latitude. Amiddes this celestial zodiak ys imagined a lyne, which30 that is cleped the Ecliptik Lyne, under which lyne is evermo the wey of the sonne. Thus ben ther six degrees of the zodiak on that on side of the lyne, and six degrees on that other. This zodiak is devided in twelve principal devisiouns, that departen the twelve signes. And, for the streitnes of thin Astrolabie, than is35 every smal devisioun in a signe departid by two degrees and two; I mene degrees contening sixty minutes. And this forseide hevenissh zodiak is cleped the Cercle of the Signes, or the Cercle of the Bestes; for zodia in langage of Greek sowneth ‘bestes’ in Latin tonge; and in the zodiak ben the twelve signes that han40 names of bestes; or elles, for whan the sonne entreth in any of the [ ] signes, he taketh the propretee of swich bestes; or elles, for that the sterres that ben there fixed ben disposed in signes of bestes, or shape like bestes; or elles, whan the planetes ben under thilke signes, they causen us by hir influence operaciouns and effectes lyk to the operaciouns of bestes. And understonde also, that whan45 an hot planete cometh in-to an hot signe, than encresseth his hete, and yif a planete be cold, thanne amenuseth his coldnesse, by-cause of the hote signe. And by this conclusioun maystow take ensample in alle the signes, be they moist or drye, or moeble or fix; rekening the qualitee of the planete as I first seide. And everich of[ ]50 thise twelve signes hath respecte to a certein parcelle of the body of a man and hath it in governance; as Aries hath thyn heved, and Taurus thy nekke and thy throte, Gemini thyn armholes and thyn armes, and so forth; as shal be shewed more pleyn in the fifte [ ] partie of this tretis. This zodiak, which that is part of the eighte55 spere, over-kerveth the equinoxial; and he over-kerveth him again in evene parties ; and that on half declineth southward, and that other northward, as pleynly declareth the tretis of the spere. And for more declaracioun, lo here thy figure.

22. Thanne hastow a label, that is schapen lyk a rewle, save that it is streit and hath no plates on either ende with holes; but, with the smale point of the forseide label, shaltow calcule thyne equaciouns in the bordure of thin Astrolabie, as by thyn almury. And for the more declaracioun, lo here thy figure.5

23. Thyn Almury is cleped the Denticle of Capricorne, or elles the Calculer. This same Almury sit fix in the hed of Capricorne, and it serveth of many a necessarie conclusioun in equaciouns of thinges, as shal be shewed; and for the more declaracioun, lo here5 thy figure.

Here endeth the descripcion of the Astrolabie.

Here begins the first part; i. e. the description of the Astrolabe itself.

1.The Ring. See figs. 1 and 2. The Latin name is Armilla suspensoria; the Arabic name is spelt alhahuacia in MS. Camb. Univ. li. 3. 3, but Stöffler says it is Alanthica, Alphantia, or Abalhantica. For the meaning of ‘rewle,’ see § 13.

2.The Turet. This answers nearly to what we call an eye or a swivel. The metal plate, or loop, to which it is fastened, or in which it turns, is called in Latin Ansa or Armilla Reflexa, in Arabic Alhabos.

3.The Moder. In Latin, Mater or Rotula. This forms the body of the instrument, the back of which is shewn in fig. 1, the front in fig. 2. The ‘large hole’ is the wide depression sunk in the front of it, into which the various discs are dropped. In the figure, the ‘Rete’ is shewn fitted into it.

4. See fig. 1; Chaucer describes the ‘bak-half’ of the instrument first. The centre of the ‘large hole amydde’ is the centre of the instrument, where a smaller hole is pierced completely through. The Southe lyne (marked Meridies in figs. 1 and 2) is also called Linea Meridiei; the North lyne is also named Linea Mediæ Noctis.

5. The Est lyne is marked with the word Oriens; the West lyne, with Occidens.

6. The rule is the same as in heraldry, the right or dexter side being towards the spectator’s left.

7. As the 360 degrees answer to 24 hours of time, 15° answer to an hour, and 5° to twenty minutes, or a Mile-way, as it is the average time for walking a mile. So also 1° answers to 4 minutes of time. See the two outermost circles in fig. 1, and the divisions of the ‘border’ in fig. 2.

8. See the third and fourth circles (reckoning inwards) in fig. 1.

9. See the fifth and sixth circles in fig. 1.

10. See the seventh, eighth, and ninth circles in fig. 1. The names of the months are all Roman. The month formerly called Quinctilis was first called Julius in 44; that called Sextilis was named Augustus in 27. It is a mistake to say that Julius and Augustus made the alterations spoken of in the text; what Julius Cæsar really did, was to add 2 days to the months of January, August (Sextilis), and December, and 1 day to April, June, September, and November. February never had more than 28 days till he introduced bissextile years.

11. See the two inmost circles in fig. 1. The names given are adopted from a comparison of the figures in the Cambridge University and Trinity MSS., neither of which are quite correct. The letters of the ‘Abc.’ are what we now call the Sunday letters. The festivals marked are those of St. Paul (Jan. 25), The Purification (Feb. 2), The Annunciation (Mar. 25), The Invention of the Holy Cross (May 3), St. John the Baptist (June 24), St. James (July 25), St. Lawrence (Aug. 10), The Nativity of the Blessed Virgin (Sept. 8), St. Luke (Oct. 18), St. Martin of Tours (Nov. 11), and St. Thomas (Dec. 21).

12. The ‘scale’ is in Latin Quadrans, or Scala Altimetra. It is certain that Chaucer has here made a slip, which cannot be fairly laid to the charge of the scribes, as the MSS. agree in transposing versa and recta. The side-parts of the scale are called Umbra versa, the lower part Umbra recta or extensa. This will appear more clearly at the end of Part II. (I here give a corrected text.)

13. See fig. 3, Plate III. Each plate turns on a hinge, just like the ‘sights’ of a gun. One is drawn flat down, the other partly elevated. Each plate (tabella vel pinnula) has two holes, the smaller one being the lower. This Rewle is named in Arabic Alhidada or Alidada in Latin Verticulum, from its turning easily on the centre; in Greek Dioptra, as carrying the sights. The straight edge, passing through the centre, is called the Linea Fiduciæ. It is pierced by a hole in the centre, of the same size as that in the Mother.

14. See fig. 4, Plate III. The Pin is also called Axis or Clavus, in Latin-Arabic Alchitot; it occupies the position of the Arctic or North Pole, passing through the centre of the plates that are required to turn round it. The Wedge is called cuneus, or equus restringens, in Arabic Alfaras or the horse, because it was sometimes cut into the shape of a horse, as shewn in fig. 7, Plate IV, which is copied from MS. Univ. Camb. Ii. 3. 3.

15. See fig. 2, Plate II. In the figure, the cross-lines are partly hidden by the Rete, which is separate and removable, and revolves within the border.

16. The Border was also called Margilabrum, Margolabrum, or Limbus. It is marked (as explained) with hour-letters and degrees. Each degree contains 4 minutes of time, and each of these minutes contains 60 seconds of time.

17. We may place under the Rete any plates we please. If only the Mother be under it, without any plate, we may suppose the Mother marked as in fig. 2. The plate or disc (tympanum) which was usually dropped in under the Rete is that shewn in fig. 5, Plate III, and which Chaucer now describes. Any number of these, marked differently for different latitudes, could be provided for the Astrolabe. The greatest declination of the sun measures the obliquity of the ecliptic, the true value of which is slightly variable, but was about 23° 31′ in Chaucer’s time, and about 23° 40′ in the time of Ptolemy, who certainly assigns to it too large a value. The value of it must be known before the three circles can be drawn. The method of finding their relative magnitudes is very simple. Let ABCD (fig. 8, Pl. IV) be the tropic of Capricorn, BO the South line, OC the West line. Make the angle EOB equal to the obliquity (say 23½°), and join EA, meeting BO in F. Then OF is the radius of the Equatorial circle, and if GH be drawn parallel to EF, OH is the radius of the Tropic of Cancer. In the phrase angulus primi motus, angulus must be taken to mean angular motion. The ‘first moving’ (primus motus) has its name of ‘moving’ (motus) from its denoting motion due to the primum mobile or ‘first moveable.’ This primum mobile (usually considered as the ninth sphere) causes the rotation of the eighth sphere, or sphæra stellarum fixarum. See the fig. in MS. Camb. Univ. Ii. 3. 3 (copied in fig. 10, PL V). Some authors make 12 heavens, viz. those of the 7 planets, the firmamentum (stellarum fixarum), the nonum cœlum, decimum cœlum, primum mobile, and cœlum empyræum.

18. See fig. 5, Pl. III. This is made upon the alt-azimuth system, and the plates are marked according to the latitude. The circles, called in Latin circuli progressionum, in Arabic Almucantarät, are circles of altitude, the largest imperfect one representing the horizon (horizon obliquus), and the central dot being the zenith, or pole of the horizon. In my figure, they are ‘compounded by’ 5 and 5, but Chaucer’s shewed every second degree, i. e. it possessed 45 such circles. For the method of drawing them, see Stöffler, leaf 5, back.

19. Some Astrolabes shew 18 of these azimuthal circles, as in my figure (fig. 5, Pl. III). See Stöffler, leaf 13, where will be found also the rules for drawing them.

20. If accurately drawn, these embelife or oblique lines should divide the portions of the three circles below the horizon obliquus into twelve equal parts. Thus each arc is determined by having to pass through three known points. They are called arcus horarum inequalium, as they shew the ‘houres inequales.’

21. In fig. 2, Pl. II, the Rete is shewn as it appears when dropped into the depression in the front of the instrument. The shape of it varied much, and another drawing of one (copied from Camb. Univ. MS. Ii. 3. 3, fol. 66 b) is given in fig. 9, Pl. IV. The positions of the stars are marked by the extreme points of the metal tongues. Fig. 2 is taken from the figures in the Cambridge MSS., but the positions of the stars have been corrected by the list of latitudes and longitudes given by Stöffler, whom I have followed, not because he is correct, but because he probably represents their positions as they were supposed to be in Chaucer’s time very nearly indeed. There was not room to inscribe the names of all the stars on the Rete, and to have written them on the plate below would have conveyed a false impression. A list of the stars marked in fig. 2 is given in the note to § 21, l. 4. The Ecliptic is the circle which crosses the Equinoctial at its East and West points (fig. 2). In Chaucer’s description of the zodiac, carefully note the distinction between the Zodiac of the Astrolabe and the Zodiac of Heaven. The former is only six degrees broad, and shews only the northern half of the heavenly zodiac, the breadth of which is imagined to be 12 degrees. Chaucer’s zodiac only shewed every other degree in the divisions round its border. This border is divided by help of a table of right ascensions of the various degrees of the ecliptic, which is by no means easily done. See Note on l. 4 of this section. I may add that the Rete is also called Aranea or Volvellum; in Arabic, Al’ancabūt (the spider).

22.The Label. See fig. 6, Pl. III. The label is more usually used on the front of the instrument, where the Rete and other plates revolve. The rule is used on the back, for taking altitudes by help of the scale.

23.The Almury; called also denticulus, ostensor, or ‘calculer.’ In fig. 2, it may be seen that the edge of the Rete is cut away near the head of Capricorn, leaving only a small pointed projecting tongue, which is the almury or denticle, or (as we should now say) pointer. As the Rete revolves, it points to the different degrees of the border. See also fig. 9, where the almury is plainly marked.

PART II

Here biginnen the Conclusions of the Astrolabie.

1.

To fynde the degree in which the sonne is day by day, after hir cours a-boute.

Rekene and knowe which is the day of thy monthe; and ley [ ] thy rewle up that same day; and thanne wol the verray point of thy rewle sitten in the bordure, up-on the degree of thy sonne. Ensample as thus; the yeer of oure lord 1391, the 12 day of5 March at midday, I wolde knowe the degree of the sonne. [ ] I soughte in the bak-half of myn Astrolabie, and fond the cercle of the dayes, the which I knowe by the names of the monthes writen under the same cercle. Tho leide I my rewle over this forseide day, and fond the point of my rewle in the bordure up-on the10 firste degree of Aries, a litel with-in the degree; and thus knowe I this conclusioun. Another day, I wolde knowe the degree of my sonne, and this was at midday in the 13 day of Decembre; I fond the day of the monthe in maner as I seide; tho leide I my rewle up-on this forseide 13 day, and fond the point of my rewle in the bordure up-on the first degree of Capricorne, a lite with-in15 the degree; and than hadde I of this conclusioun the ful experience. And for the more declaracioun, lo here thy figure.

2.

To knowe the altitude of the sonne, or of othre celestial bodies.

Put the ring of thyn Astrolabie up-on thy right thoumbe, and turne thy lift syde agayn the light of the sonne. And remeve thy rewle up and doun, til that the stremes of the sonne shyne thorgh bothe holes of thy rewle. Loke thanne how many degrees thy rewle is areised fro the litel crois up-on thyn est line, and tak5 ther the altitude of thy sonne. And in this same wyse maistow knowe by nighte the altitude of the mone, or of brighte sterres. This chapitre is so general ever in oon, that ther nedith no more declaracion; but forget it nat. And for the more declaracioun, lo here the figure.10

3.

To knowe every tyme of the day by light of the sonne, and every tyme of the night by the sterres fixe, and eke to knowe by night or by day the degree of any signe that assendeth on the Est Orisonte, which that is cleped communly the Assendent, or elles Oruscupum.

Tak the altitude of the sonne whan thee list, as I have said; and set the degree of the sonne, in cas that it be by-forn the middel of the day, among thyn almikanteras on the est side of thyn Astrolabie; and yif it be after the middel of the day, set the degree 5 of thy sonne up-on the west side; tak this manere of setting for a general rewle, ones for evere. And whan thou hast set the degree of thy sonne up as many almikanteras of heyghte as was the altitude of the sonne taken by thy rewle, ley over thy label, up-on the degree of the sonne; and thanne wol the point of thy label10 sitten in the bordure, up-on the verrey tyd of the day. Ensample as thus: the yeer of oure lord 1391, the 12 day of March, I wold knowe the tyd of the day. I took the altitude of my sonne, and fond that it was 25 degrees and 30 of minutes of heyghte in the bordure on the bak-syde. Tho turnede I myn Astrolabie, and by-cause15 that it was by-forn midday, I turnede my riet, and sette the degree of the sonne, that is to seyn, the 1 degree of Aries, on the right syde of myn Astrolabie, up-on that 25 degrees and 30 of minutes of heyghte among myn almikanteras; tho leide I my label up-on the degree of my sonne, and fond the poynte of my label in20 the bordure, up-on a capital lettre that is cleped an X; tho rekened I alle the capitalles lettres fro the lyne of midnight un-to this forseide lettre X, and fond that it was 9 of the clokke of the day. Tho loked I down up-on the est orisonte, and fond there the 20 degree of Geminis assending; which that I tok for myn assendent .25 And in this wyse hadde I the experience for ever-mo in which maner I sholde knowe the tyd of the day, and eek myn assendent. Tho wolde I wite the same night folwing the hour of the night, and wroughte in this wyse. Among an heep of sterris fixe, it lyked me for to take the altitude of the feire white sterre that is30 cleped Alhabor ; and fond hir sitting on the west side of the lyne of midday, 18 degres of heighte taken by my rewle on the bak-syde Tho sette I the centre of this Alhabor up-on 18 degrees among myn almikanteras, up-on the west syde; by-cause that she was founden on the west syde. Tho leide I my label over the degree of the sonne that was descended under the weste orisonte, and35 rikened alle the lettres capitals fro the lyne of midday un-to the point of my label in the bordure; and fond that it was passed 8 of the clokke the space of 2 degrees . Tho loked I doun up-on myn est orisonte, and fond ther 23 degrees of Libra assending, whom I tok for myn assendent; and thus lerned I to knowe ones for ever40 in which manere I shuld come to the houre of the night and to myn assendent; as verryly as may be taken by so smal an instrument. But natheles, in general, wolde I warne thee for evere, ne mak thee nevere bold to have take a iust ascendent by thyn Astrolabie, or elles to have set iustly a clokke, whan any celestial45 body by which that thow wenest governe thilke thinges ben ney the south lyne; for trust wel, whan that the sonne is ney the meridional lyne, the degree of the sonne renneth so longe consentrik up-on the almikanteras, that sothly thou shalt erre fro the iust assendent. The same conclusioun sey I by the centre of any50 sterre fix by night; and more-over, by experience, I wot wel that in oure orisonte, from 11 of the clokke un-to oon of the clokke, in taking of a iust assendent in a portatif Astrolabie, hit is to hard to knowe. I mene, from 11 of the clokke biforn the houre of noon til oon of the clok next folwing. And for the more declaracion,55 lo here thy figure.

4.

Special declaracion of the assendent.[ ]

The assendent sothly, as wel in alle nativitez as in questiouns and elecciouns of tymes, is a thing which that thise astrologiens gretly observen; wher-fore me semeth convenient, sin that I speke of the assendent, to make of it special declaracioun. The assendent sothly, to take it at the largeste , is thilke degree that5 assendeth at any of thise forseide tymes upon the est orisonte; and there-for, yif that any planet assende at that same tyme in thilke for-seide degree of his longitude , men seyn that thilke planete isin horoscopo. But sothly, the hous of the assendent,10 that is to seyn, the firste hous or the est angle, is a thing more brood and large. For after the statutz of astrologiens, what celestial body that is 5 degres above thilk degree that assendeth, or with-in that noumbre, that is to seyn, nere the degree that assendeth, yit rikne they thilke planet in the assendent. And15 what planete that is under thilke degree that assendith the space of 25 degrees , yit seyn they that thilke planete is lyk to him that is in the hous of the assendent; but sothly, yif he passe the bondes of thise forseide spaces, above or bynethe, they seyn that the planete is failling fro the assendent. Yit sein thise20 astrologiens, that the assendent, and eke the lord of the assendent, may be shapen for to be fortunat or infortunat, as thus: a fortunat [ ] assendent clepen they whan that no wykkid planete, as Saturne or Mars, or elles the Tail of the Dragoun, is in the hous of the assendent, ne that no wikked planete have non aspecte of enemite25 up-on the assendent; but they wol caste that they have a fortunat planete in hir assendent and yit in his felicitee, and than sey they that it is wel. Forther-over, they seyn that the infortuning of an assendent is the contrarie of thise forseide thinges. The lord of the assendent, sey they, that he is fortunat, whan he is in good30 place fro the assendent as in angle; or in a succedent, where-as he is in his dignitee and conforted with frendly aspectes of planetes and wel resceived, and eek that he may seen the assendent, and [ ] that he be nat retrograd ne combust , ne ioigned with no shrewe in the same signe; ne that he be nat in his descencioun, ne35 ioigned with no planete in his discencioun, ne have up-on him non aspecte infortunat; and than sey they that he is wel. Natheles, thise ben observauncez of iudicial matiere and rytes of payens, in which my spirit ne hath no feith, ne no knowing of hir horoscopum; for they seyn that every signe is departed in 3 evene40 parties by 10 degrees, and thilke porcioun they clepe a Face . And al-thogh that a planete have a latitude fro the ecliptik, yit sey some folk , so that the planete aryse in that same signe with any degree of the forseide face in which his longitude is rekned, that yit is the planete in horoscopo, be it in nativite or in eleccioun, &c. And for the more declaracioun, lo here the figure.45

5.

To knowe the verrey equacioun of the degree of the sonne, yif so be that it falle by-twixe thyn Almikanteras.

For as moche as the almikanteras in thyn Astrolabie been compouned by two and two, where-as some almikanteras in sondry Astrolabies ben compouned by on and on, or elles by two and two , it is necessarie to thy lerning to teche thee first to knowe and worke with thyn owne instrument. Wher-for, whan that the5 degree of thy sonne falleth by-twixe two almikanteras, or elles yif thyn almikanteras ben graven with over gret a point of a compas, (for bothe thise thinges may causen errour as wel in knowing of the tyd of the day as of the verrey assendent), thou most werken in this wyse. Set the degree of thy sonne up-on the heyer10 almikanteras of bothe, and waite wel wher as thin almury toucheth the bordure, and set ther a prikke of inke. Set doun agayn the degree of thy sonne up-on the nethere almikanteras of bothe, and set ther another prikke. Remewe thanne thyn almury in the bordure evene amiddes bothe prikkes, and this wol lede iustly the15 degree of thy sonne to sitte by-twixe bothe almikanteras in his right place. Ley thanne thy label over the degree of thy sonne; and find in the bordure the verrey tyde of the day or of the night. And as verreyly shaltow finde up-on thyn est orisonte thyn assendent. And for more declaracioun, lo here thy figure.20

6.

To knowe the spring of the dawing and the ende of the evening, the which ben called the two crepusculis:

Set the nadir of thy sonne up-on 18 degrees of heighte among thyn almikanteras on the west syde, and ley thy label on the degree of thy sonne, and thanne shal the poynt of thy label schewe the spring of day. Also set the nadir of thy sonne up-on 18 degrees5 of heighte a-mong thyn almikanteras on the est side, and ley over thy label up-on the degree of the sonne, and with the point of thy label find in the bordure the ende of the evening, that is, verrey night. The nadir of the sonne is thilke degree that is opposit to the degree of the sonne, in the seventhe signe , as thus:[ ]10 every degree of Aries by ordre is nadir to every degree of Libra by ordre; and Taurus to Scorpion; Gemini to Sagittare; Cancer to Capricorne; Leo to Aquarie; Virgo to Pisces; and yif any degree in thy zodiak be dirk, his nadir shal declare him. And for the more declaracioun, lo here thy figure.

7.

To knowe the arch of the day, that some folk callen the day artificial, from the sonne arysing til hit go to reste.

Set the degree of thy sonne up-on thyn est orisonte, and ley thy label on the degree of the sonne, and at the poynt of thy label in the bordure set a prikke. Turn thanne thy riet aboute til the degree of the sonne sit up-on the west orisonte, and ley5 thy label up-on the same degree of the sonne, and at the point of thy label set a-nother prikke. Rekne thanne the quantitee of tyme in the bordure by-twixe bothe prikkes, and tak ther thyn ark of the day. The remenant of the bordure under the orisonte is the ark of the night. Thus maistow rekne bothe arches, or10 every porcion, of whether that thee lyketh. And by this manere of wyrking maistow see how longe that any sterre fix dwelleth above the erthe, fro tyme that he ryseth til he go to reste. But the day natural, that is to seyn 24 houres, is the revolucioun of the equinoxial with as moche partie of the zodiak as the sonne of his propre moevinge passeth in the mene whyle. And for the15 more declaracioun, lo here thy figure.

8.

To turn the houres in-equales in houres equales.[ ]

Knowe the nombre of the degrees in the houres in-equales, and departe hem by 15, and tak ther thyn houres equales. And for the more declaracioun, lo here thy figure.

9.

To knowe the quantitee of the day vulgare, that is to seyen, from spring of the day un-to verrey night.

Know the quantitee of thy crepusculis, as I have taught in the chapitre bi-forn , and adde hem to the arch of thy day artificial; and tak ther the space of alle the hole day vulgar, un-to verrey night. The same manere maystow worke, to knowe the quantitee of the vulgar night. And for the more declaracioun, lo here the5 figure.

10.

To knowe the quantite of houres in-equales by day.

Understond wel, that thise houres in-equales ben cleped houres of planetes, and understond wel that som-tyme ben they lengere by day than by night , and som-tyme the contrarie. But understond wel, that evermo, generaly, the hour in-equal of the day with the houre in-equal of the night contenen 30 degrees of the5 bordure, whiche bordure is ever-mo answering to the degrees of the equinoxial; wher-for departe the arch of the day artificial in 12, and tak ther the quantitee of the houre in-equal by day. And yif thow abate the quantitee of the houre in-equal by daye10 out of 30, than shal the remenant that leveth performe the houre inequal by night. And for the more declaracioun, lo here the figure.

11.

To knowe the quantite of houres equales.

The quantitee of houres equales, that is to seyn, the houres of the clokke, ben departed by 15 degrees al-redy in the bordure of thyn Astrolabie, as wel by night as by day, generaly for evere. What nedeth more declaracioun? Wher-for, whan thee list to5 know how manye houres of the clokke ben passed, or any part of any of thise houres that ben passed, or elles how many houres or partie of houres ben to come, fro swich a tyme to swich a tyme, by day or by nighte, knowe the degree of thy sonne, and ley thy label on it; turne thy riet aboute ioyntly with thy label, and with10 the point of it rekne in the bordure fro the sonne aryse un-to the same place ther thou desirest, by day as by nighte. This conclusioun wol I declare in the laste chapitre of the 4 partie of this tretis so openly, that ther shal lakke no worde that nedeth to the declaracioun. And for the more declaracioun, lo here the15 figure.

12.

Special declaracioun of the houres of planetes.

Understond wel, that evere-mo, fro the arysing of the sonne til it go to reste, the nadir of the sonne shal shewe the houre of the planete, and fro that tyme forward al the night til the sonne aryse; than shal the verrey degree of the sonne shewe the houre of the planete. Ensample as thus. The 13 day of March fil5 up-on a Saterday per aventure, and, at the arising of the sonne, I fond the secounde degree of Aries sitting up-on myn est orisonte, al-be-it that it was but lite; than fond I the 2 degree of Libra, nadir of my sonne, dessending on my west orisonte, up-on which west orisonte every day generally, at the sonne ariste, entreth10 the houre of any planete, after which planete the day bereth his name; and endeth in the nexte stryk of the plate under the forseide west orisonte; and evere, as the sonne climbeth uppere and uppere, so goth his nadir dounere and dounere, teching by swich strykes the houres of planetes by ordre as they sitten in15 the hevene. The first houre inequal of every Satterday is to Saturne; and the secounde, to Iupiter; the 3, to Mars; the 4, to the Sonne; the 5, to Venus; the 6, to Mercurius; the 7, to the Mone; and thanne agayn, the 8 is to Saturne; the 9, to Iupiter; the 10, to Mars; the 11, to the Sonne; the 12, to20 Venus; and now is my sonne gon to reste as for that Setterday. Thanne sheweth the verrey degree of the sonne the houre of Mercurie entring under my west orisonte at eve; and next him succedeth the Mone; and so forth by ordre, planete after planete, in houre after houre, al the night longe til the sonne25 aryse. Now ryseth the sonne that Sonday by the morwe; and the nadir of the sonne, up-on the west orizonte, sheweth me the entring of the houre of the forseide sonne. And in this maner succedeth planete under planete, fro Saturne un-to the Mone,30 and fro the Mone up a-gayn to Saturne, houre after houre generaly. And thus knowe I this conclusion. And for the more declaracioun, lo here the figure.

13.

To knowe the altitude of the sonne in middes of the day, that is cleped the altitude meridian.

Set the degree of the sonne up-on the lyne meridional, and rikene how many degrees of almikanteras ben by-twixe thyn est orisonte and the degree of the sonne. And tak ther thyn altitude meridian; this is to seyne, the heyest of the sonne as for that day.5 So maystow knowe in the same lyne, the heyest cours that any sterre fix climbeth by night; this is to seyn, that whan any sterre fix is passed the lyne meridional, than by-ginneth it to descende, and so doth the sonne. And for the more declaracioun, lo here thy figure.

14.

To knowe the degree of the sonne by thy riet, for a maner curiositee, &c.

Sek bysily with thy rewle the heyest of the sonne in midde of the day; turne thanne thyn Astrolabie, and with a prikke of ink marke the nombre of that same altitude in the lyne meridional. Turne thanne thy riet a-boute til thou fynde a degree of thy zodiak acording with the prikke, this is to seyn, sittinge on the5 prikke; and in sooth, thou shalt finde but two degrees in al the zodiak of that condicioun; and yit thilke two degrees ben in diverse signes; than maistow lightly by the sesoun of the yere knowe the signe in whiche that is the sonne. And for the more declaracioun, lo here thy figure.[ ]10

15.

To know which day is lyk to which day as of lengthe, &c.

Loke whiche degrees ben y-lyke fer fro the hevedes of Cancer and Capricorn; and lok, whan the sonne is in any of thilke degrees, than ben the dayes y-lyke of lengthe. This is to seyn, that as long is that day in that monthe, as was swich a day in swich a month; ther varieth but lite. Also, yif thou take two5 dayes naturaly in the yer y-lyke fer fro eyther pointe of the equinoxial in the opposit parties, than as long is the day artificial of that on day as is the night of that othere, and the contrarie. And for the more declaracioun, lo here thy figure.

16.

This chapitre is a maner declaracioun to conclusiouns that folwen.

Understond wel that thy zodiak is departid in two halfe cercles, as fro the heved of Capricorne un-to the heved of Cancer; and agaynward fro the heved of Cancer un-to the heved of Capricorne. The heved of Capricorne is the lowest point, wher-as the sonne5 goth in winter; and the heved of Cancer is the heyest point, in whiche the sonne goth in somer. And ther-for understond wel, that any two degrees that ben y-lyke fer fro any of thise two hevedes, truste wel that thilke two degrees ben of y-lyke declinacioun, be it southward or northward; and the dayes of hem10 ben y-lyke of lengthe, and the nightes also; and the shadwes y-lyke, and the altitudes y-lyke at midday for evere. And for more declaracioun, lo here thy figure.

17.

To knowe the verrey degree of any maner sterre straunge or unstraunge after his longitude, though he be indeterminat in thyn Astrolabie; sothly to the trowthe, thus he shal be knowe.[ ][ ]

Tak the altitude of this sterre whan he is on the est side of the lyne meridional, as ney as thou mayst gesse; and tak an assendent a-non right by som maner sterre fix which that thou knowest; and for-get nat the altitude of the firste sterre, ne thyn5 assendent. And whan that this is don, espye diligently whan this same firste sterre passeth any-thing the south westward, and hath him a-non right in the same noumbre of altitude on the west side of this lyne meridional as he was caught on the est side; and tak a newe assendent a-non right by som maner sterre fixe which that thou knowest; and for-get nat this secounde assendent. And10 whan that this is don, rikne thanne how manye degrees ben bytwixe the firste assendent and the seconde assendent, and rikne wel the middel degree by-twene bothe assendentes, and set thilke middel degree up-on thin est orisonte; and waite thanne what degree that sit up-on the lyne meridional, and tak ther the verrey degree15 of the ecliptik in which the sterre stondeth for the tyme. For in the ecliptik is the longitude of a celestial body rekened, evene fro the heved of Aries un-to the ende of Pisces. And his latitude is rikned after the quantite of his declinacion, north or south to-warde the poles of this world; as thus. Yif it be of the sonne or of any20 fix sterre, rekene his latitude or his declinacioun fro the equinoxial cercle; and yif it be of a planete, rekne than the quantitee of his latitude fro the ecliptik lyne. Al-be-it so that fro the equinoxial may the declinacion or the latitude of any body celestial be rikned, after the site north or south, and after the quantitee of his declinacion.25 And right so may the latitude or the declinacion of any body celestial, save only of the sonne, after his site north or south, and after the quantitee of his declinacioun, be rekned fro the ecliptik lyne; fro which lyne alle planetes som tyme declynen30 north or south, save only the for-seide sonne. And for the more declaracioun, lo here thy figure.

18.

To knowe the degrees of the longitudes of fixe sterres after that they ben determinat in thin Astrolabie, yif so be that they ben trewly set.[ ]

Set the centre of the sterre up-on the lyne meridional, and tak keep of thy zodiak, and loke what degree of any signe that sit on the same lyne meridional at that same tyme, and tak the degree in which the sterre standeth; and with that same degree comth that5 same sterre un-to that same lyne fro the orisonte. And for more declaracioun, lo here thy figure.

19.

To knowe with which degree of the zodiak any sterre fixe in thyn Astrolabie aryseth up-on the est orisonte, althogh his dwelling be in a-nother signe.

Set the centre of the sterre up-on the est orisonte, and loke what degree of any signe that sit up-on the same orisonte at that same tyme. And understond wel, that with that same degree aryseth that same sterre; and this merveyllous arysing with a strange degree in another signe is by-cause that the latitude of the5 sterre fix is either north or south fro the equinoxial . But sothly the latitudes of planetes ben comunly rekned fro the ecliptik, bi-cause that non of hem declineth but fewe degrees out fro the brede of the zodiak. And tak good keep of this chapitre of arysing of the celestial bodies; for truste wel, that neyther mone ne sterre10 as in oure embelif orisonte aryseth with that same degree of his longitude, save in o cas; and that is, whan they have no latitude fro the ecliptik lyne. But natheles, som tyme is everiche of thise planetes under the same lyne. And for more declaracioun, lo here thy figure.15

20.

To knowe the declinacioun of any degree in the zodiak fro the equinoxial cercle, &c.

Set the degree of any signe up-on the lyne meridional, and rikne his altitude in almikanteras fro the est orizonte up to the same degree set in the forseide lyne, and set ther a prikke. Turne up thanne thy riet, and set the heved of Aries or Libra in the same meridional lyne, and set ther a-nother prikke. And whan that5 this is don, considere the altitudes of hem bothe; for sothly the difference of thilke altitudes is the declinacion of thilke degree fro the equinoxial. And yif so be that thilke degree be northward fro the equinoxial, than is his declinacion north; yif it be southward,10 than is it south. And for the more declaracioun, lo here thy figure.

21.

To knowe for what latitude in any regioun the almikanteras of any table ben compouned.

Rikne how manye degrees of almikanteras, in the meridional lyne, be fro the cercle equinoxial un-to the senith; or elles fro the pool artik un-to the north orisonte; and for so gret a latitude or for so smal a latitude is the table compouned. And for more5 declaracion, lo here thy figure.

22.

To knowe in special the latitude of oure countray, I mene after the latitude of Oxenford, and the heighte of oure pol.

Understond wel, that as fer is the heved of Aries or Libra in the equinoxial from oure orisonte as is the senith from the pole artik; and as hey is the pol artik fro the orisonte, as the equinoxial is fer fro the senith. I prove it thus by the latitude of Oxenford.5 Understond wel, that the heyghte of oure pool artik fro oure north orisonte is 51 degrees and 50 minutes; than is the senith from oure pool artik 38 degrees and 10 minutes; than is the equinoxial from oure senith 51 degrees and 50 minutes; than is oure south orisonte from oure equinoxial 38 degrees and 10 minutes. Understond wel this rekning. Also for-get nat that the senith is 9010 degrees of heyghte fro the orisonte, and oure equinoxial is 90 degrees from oure pool artik. Also this shorte rewle is soth, that the latitude of any place in a regioun is the distance fro the senith unto the equinoxial. And for more declaracioun, lo here thy figure.15

23.

To prove evidently the latitude of any place in a regioun, by the preve of the heyghte of the pol artik in that same place.

In some winters night, whan the firmament is clere and thikkesterred, waite a tyme til that any sterre fix sit lyne-right perpendiculer over the pol artik, and clepe that sterre A . And wayte a-nother sterre that sit lyne-right under A, and under the pol, and clepe that sterre F. And understond wel, that F is nat5 considered but only to declare that A sit evene overe the pool. Tak thanne a-non right the altitude of A from the orisonte, and forget it nat. Lat A and F go farwel til agayns the dawening a gret whyle; and come thanne agayn, and abyd til that A is evene under the pol and under F; for sothly, than wol F sitte over the pool,10 and A wol sitte under the pool. Tak than eft-sones the altitude of A from the orisonte, and note as wel his secounde altitude as his firste altitude; and whan that this is don, rikne how manye degrees that the firste altitude of A excedeth his seconde altitude, and tak15 half thilke porcioun that is exceded, and adde it to his seconde altitude; and tak ther the elevacioun of thy pool, and eke the latitude of thy regioun. For thise two ben of a nombre; this is to seyn, as many degrees as thy pool is elevat, so michel is the latitude of the regioun. Ensample as thus: par aventure, the20 altitude of A in the evening is 56 degrees of heyghte. Than wol his seconde altitude or the dawing be 48; that is 8 lasse than 56, that was his firste altitude at even. Take thanne the half of 8 , and adde it to 48, that was his seconde altitude, and than hastow 52. Now hastow the heyghte of thy pol, and the latitude25 of the regioun. But understond wel, that to prove this conclusioun and many a-nother fair conclusioun, thou most have a plomet hanging on a lyne heyer than thin heved on a perche; and thilke lyne mot hange evene perpendiculer by-twixe the pool and thyn eye; and thanne shaltow seen yif A sitte evene over the pool and30 over F at evene; and also yif F sitte evene over the pool and over A or day. And for more declaracion, lo here thy figure.

24.

Another conclusioun to prove the heyghte of the pool artik fro the orisonte.

Tak any sterre fixe that nevere dissendeth under the orisonte in thilke regioun, and considere his heyest altitude and his lowest altitude fro the orisonte; and make a nombre of bothe thise altitudes. Tak thanne and abate half that nombre, and tak ther5 the elevacioun of the pol artik in that same regioun. And for more declaracioun, lo here thy figure.

25.

A-nother conclusioun to prove the latitude of the regioun, &c.

Understond wel that the latitude of any place in a regioun is verreyly the space by-twixe the senith of hem that dwellen there and the equinoxial cerkle, north or southe, taking the mesure in the meridional lyne, as sheweth in the almikanteras of thyn Astrolabie. And thilke space is as moche as the pool artik is hey5 in the same place fro the orisonte. And than is the depressioun of the pol antartik, that is to seyn, than is the pol antartik by-nethe the orisonte, the same quantite of space, neither more ne lasse. Thanne, yif thow desire to knowe this latitude of the regioun, tak the altitude of the sonne in the middel of the day, whan the sonne10 is in the hevedes of Aries or of Libra; (for thanne moeveth the sonne in the lyne equinoxial); and abate the nombre of that same sonnes altitude out of 90, and thanne is the remenaunt of the noumbre that leveth the latitude of the regioun. As thus: I suppose that the sonne is thilke day at noon 38 degrees and 1015 minutes of heyghte. Abate thanne thise degrees and minutes out of 90; so leveth there 51 degrees and 50 minutes, the latitude. I sey nat this but for ensample; for wel I wot the latitude of Oxenforde is certein minutes lasse, as I mighte prove . Now yif [ ] so be that thee semeth to long a taryinge, to abyde til that the20 sonne be in the hevedes of Aries or of Libra, thanne waite whan the sonne is in any other degree of the zodiak, and considere the degree of his declinacion fro the equinoxial lyne; and yif it so be that the sonnes declinacion be northward fro the equinoxial, abate thanne fro the sonnes altitude at noon the nombre of his declinacion,25 and thanne hastow the heyghte of the hevedes of Aries and Libra. As thus: my sonne is, par aventure, in the firste degre of Leoun, 58 degrees and 10 minutes of heyghte at noon and his declinacion is almost 20 degrees northward fro the30 equinoxial; abate thanne thilke 20 degrees of declinacion out of the altitude at noon, than leveth thee 38 degrees and odde minutes ; lo ther the heved of Aries or Libra, and thyn equinoxial in that regioun. Also yif so be that the sonnes declinacioun be southward fro the equinoxial, adde thanne thilke declinacion to the35 altitude of the sonne at noon; and tak ther the hevedes of Aries and Libra, and thyn equinoxial. Abate thanne the heyghte of the equinoxial out of 90 degrees, and thanne leveth there the distans of the pole, 51 degrees and 50 minutes, of that regioun fro the equinoxial. Or elles, yif thee lest, take the heyest altitude40 fro the equinoxial of any sterre fix that thou knowest, and tak his nethere elongacioun lengthing fro the same equinoxial lyne, and wirke in the maner forseid. And for more declaracion, lo here thy figure.

26.

Declaracioun of the assensioun of signes, &c.

The excellence of the spere solide, amonges other noble conclusiouns, sheweth manifeste the diverse assenciouns of signes in diverse places, as wel in the righte cercle as in the embelif cercle. Thise auctours wryten that thilke signe is cleped of right5 ascensioun, with which more part of the cercle equinoxial and lasse part of the zodiak ascendeth; and thilke signe assendeth embelif, with whiche lasse part of the equinoxial and more part of the zodiak assendeth. Ferther-over they seyn, that in thilke [ ] cuntrey where as the senith of hem that dwellen there is in the equinoxial lyne, and her orisonte passing by the poles of this10 worlde, thilke folke han this right cercle and the right orisonte; and evere-mo the arch of the day and the arch of the night is ther y-like long, and the sonne twyes every yeer passinge thorow the senith of her heved; and two someres and two winteres in a yeer han this forseide poeple. And the almikanteras in her Astrolabies15 ben streighte as a lyne, so as sheweth in this figure . The utilite to knowe the assenciouns in the righte cercle is this: truste wel that by mediacioun of thilke assenciouns thise astrologiens, by hir tables and hir instrumentz, knowen verreyly the assencioun of every degree and minut in al the zodiak, as shal be shewed. And20nota, that this forseid righte orisonte, that is cleped orison rectum, divydeth the equinoxial in-to right angles; and the embelif orisonte, wher-as the pol is enhaused up-on the orisonte, overkerveth the equinoxial in embelif angles, as sheweth in the figure. And for25 the more declaracioun, lo here the figure.

27.

This is the conclusioun to knowe the assenciouns of signes in the right cercle, that is, circulus directus, &c.

Set the heved of what signe thee liste to knowe his assending in the right cercle up-on the lyne meridional; and waite wher thyn almury toucheth the bordure, and set ther a prikke. Turne thanne thy riet westward til that the ende of the forseide signe5 sitte up-on the meridional lyne; and eft-sones waite wher thyn almury toucheth the bordure, and set ther another prikke. Rikne thanne the nombre of degrees in the bordure by-twixe bothe prikkes, and tak the assencioun of the signe in the right cercle. And thus maystow wyrke with every porcioun of thy zodiak, &c.10 And for the more declaracioun, lo here thy figure.

28.

To knowe the assencions of signes in the embelif cercle in every regioun, I mene, in circulo obliquo.

Set the heved of the signe which as thee list to knowe his ascensioun up-on the est orisonte, and waite wher thyn almury toucheth the bordure, and set ther a prikke. Turne thanne thy riet upward til that the ende of the same signe sitte up-on the est orisonte, and waite eft-sones wher as thyn almury toucheth the5 bordure, and set ther a-nother prikke. Rikne thanne the noumbre of degrees in the bordure by-twixe bothe prikkes, and tak ther the assencioun of the signe in the embelif cercle. And understond wel, that alle signes in thy zodiak, fro the heved of Aries unto the ende of Virgo, ben cleped signes of the north fro the equinoxial;10 and these signes arysen by-twixe the verrey est and the verrey north in oure orisonte generaly for evere. And alle signes fro the heved of Libra un-to the ende of Pisces ben cleped signes of the south fro the equinoxial; and thise signes arysen ever-mo by-twixe the verrey est and the verrey south in oure orisonte. Also every15 signe by-twixe the heved of Capricorne un-to the ende of Geminis aryseth on oure orisonte in lasse than two houres equales; and thise same signes, fro the heved of Capricorne un-to the ende of Geminis, ben cleped ‘tortuos signes’ or ‘croked signes,’ for they arisen embelif on oure orisonte; and thise crokede signes20 ben obedient to the signes that ben of right assencioun. The signes of right assencioun ben fro the heved of Cancer to the ende of Sagittare; and thise signes arysen more upright, and they ben called eke sovereyn signes; and everich of hem aryseth in more space than in two houres. Of which signes, Gemini obeyeth25 to Cancer; and Taurus to Leo; Aries to Virgo; Pisces to Libra; Aquarius to Scorpioun; and Capricorne to Sagittare. And thus ever-mo two signes, that ben y-lyke fer fro the heved of Capricorne, obeyen everich of hem til other. And for more declaracioun, lo30 here the figure.

29.

To knowe iustly the foure quarters of the world, as est, west, north, and sowth.[ ]

Take the altitude of thy sonne whan thee list, and note wel the quarter of the world in which the sonne is for the tyme by the azimutz. Turne thanne thyn Astrolabie, and set the degree of the sonne in the almikanteras of his altitude, on thilke side that5 the sonne stant, as is the manere in taking of houres; and ley thy label on the degree of the sonne, and rikene how many degrees of the bordure ben by-twixe the lyne meridional and the point of thy label; and note wel that noumbre. Turne thanne a-gayn thyn Astrolabie, and set the point of thy gret rewle, ther thou takest10 thyne altitudes, up-on as many degrees in his bordure fro his meridional as was the point of thy label fro the lyne meridional on the wombe-syde. Tak thanne thyn Astrolabie with bothe handes sadly and slely, and lat the sonne shyne thorow bothe holes of thy rewle ; and sleyly, in thilke shyninge, lat thyn Astrolabie couch15 adoun evene up-on a smothe grond, and thanne wol the verrey lyne meridional of thyn Astrolabie lye evene south, and the est lyne wole lye est, and the west lyne west, and north lyne north, so that thou werke softly and avisely in the couching; and thus hastow the 4 quarters of the firmament. And for the more20 declaracioun, lo here the figure.

30.

To knowe the altitude of planetes fro the wey of the sonne, whether so they be north or south fro the forseide wey.

Lok whan that a planete is in the lyne meridional, yif that hir altitude be of the same heyghte that is the degree of the sonne for that day, and than is the planete in the verrey wey of the sonne , and hath no latitude. And yif the altitude of the planete be heyere than the degree of the sonne, than is the planete north fro5 the wey of the sonne swich a quantite of latitude as sheweth by thyn almikanteras. And yif the altitude of the planete be lasse than the degree of the sonne, thanne is the planete south fro the wey of the sonne swich a quantite of latitude as sheweth by thyn almikanteras. This is to seyn, fro the wey wher-as the sonne10 wente thilke day, but nat from the wey of the sonne in every place of the zodiak. And for the more declaracioun, lo here the figure.

31.

To knowe the senith of the arysing of the sonne, this is to seyn, the partie of the orisonte in which that the sonne aryseth.[ ]

Thou most first considere that the sonne aryseth nat al-wey verrey est, but some tyme by north the est, and som tyme by southe the est. Sothly, the sonne aryseth never-mo verrey est in oure orisonte, but he be in the heved of Aries or Libra. Now is thyn5 orisonte departed in 24 parties by thy azimutz, in significacion of 24 partiez of the world; al-be-it so that shipmen rikne thilke partiez in 32. Thanne is ther no more but waite in which azimut that thy sonne entreth at his arysing; and take ther the senith of the arysing of the sonne. The manere of the devisioun of thyn10 Astrolabie is this; I mene, as in this cas. First is it devided in 4 plages principalx with the lyne that goth from est to west, and than with a-nother lyne that goth fro south to north. Than is it devided in smale partiez of azimutz, as est, and est by southe, whereas is the firste azimut above the est lyne; and so forth, fro15 partie to partie, til that thou come agayn un-to the est lyne. Thus maistow understond also the senith of any sterre, in which partie he ryseth, &c. And for the more declaracion, lo here the figure.

32.

To knowe in which partie of the firmament is the coniunccioun.

Considere the tyme of the coniunccion by thy kalender, as thus; lok how many houres thilke coniunccion is fro the midday of the day precedent, as sheweth by the canoun of thy kalender. Rikne thanne thilke nombre of houres in the bordure of thyn Astrolabie, as thou art wont to do in knowing of the houres of the day or of5 the night; and ley thy label over the degree of the sonne; and thanne wol the point of thy label sitte up-on the hour of the coniunccion. Loke thanne in which azimut the degree of thy sonne sitteth, and in that partie of the firmament is the coniunccioun. And for the more declaracioun, lo here thy figure.

33.

To knowe the senith of the altitude of the sonne, &c.

This is no more to seyn but any tyme of the day tak the altitude of the sonne; and by the azimut in which he stondeth, maystou seen in which partie of the firmament he is. And in the same wyse maystou seen, by the night , of any sterre, whether the sterre sitte est or west or north , or any partie by-twene, after the5 name of the azimut in which is the sterre. And for the more declaracioun, lo here the figure.

34.

To knowe sothly the degree of the longitude of the mone, or of any planete that hath no latitude for the tyme fro the ecliptik lyne.

Tak the altitude of the mone, and rikne thyn altitude up among thyne almikanteras on which syde that the mone stande; and set there a prikke. Tak thenne anon-right, up-on the mones syde , the altitude of any sterre fix which that thou knowest, and set his5 centre up-on his altitude among thyn almikanteras ther the sterre is founde. Waite thanne which degree of the zodiak toucheth the prikke of the altitude of the mone, and tak ther the degree in which the mone standeth. This conclusioun is verrey soth, yif the sterres in thyn Astrolabie stonden after the trowthe; of10 comune, tretis of Astrolabie ne make non excepcioun whether the mone have latitude, or non; ne on whether syde of the mone the altitude of the sterre fix be taken. And nota, that yif the mone shewe himself by light of day, than maystow wyrke this same conclusioun by the sonne, as wel as by the fix sterre. And for the15 more declaracioun, lo here thy figure.

35.

This is the workinge of the conclusioun, to knowe yif that any planete be directe or retrograde.

Tak the altitude of any sterre that is cleped a planete, and note it wel. And tak eek anon the altitude of any sterre fix that thou knowest, and note it wel also. Come thanne agayn the thridde or the ferthe night next folwing; for thanne shaltow aperceyve wel the5 moeving of a planete, whether so he moeve forthward or bakward. Awaite wel thanne whan that thy sterre fix is in the same altitude that she was whan thou toke hir firste altitude; and tak than eftsones the altitude of the forseide planete, and note it wel. For trust wel, yif so be that the planete be on the right syde of the meridional lyne, so that his seconde altitude be lasse than his firste altitude10 was, thanne is the planete directe. And yif he be on the west syde in that condicion, thanne is he retrograd. And yif so be that this planete be up-on the est syde whan his altitude is taken, so that his secounde altitude be more than his firste altitude, thanne is he retrograde, and yif he be on the west syde , than is he15 directe. But the contrarie of thise parties is of the cours of the mone; for sothly , the mone moeveth the contrarie from othere planetes as in hir episicle , but in non other manere. And for [ ] the more declaracioun, lo here thy figure.

36.

The conclusiouns of equaciouns of houses, after the Astrolabie, &c.[ ]

Set the by-ginning of the degree that assendeth up-on the ende of the 8 houre inequal; thanne wol the by-ginning of the 2 hous sitte up-on the lyne of midnight. Remeve thanne the degree that assendeth, and set him on the ende of the 10 hour inequal; and thanne wol the byginning of the 3 hous sitte up-on the midnight5 lyne. Bring up agayn the same degree that assendeth first, and set him up-on the orisonte; and thanne wol the be-ginning of the 4 hous sitte up-on the lyne of midnight. Tak thanne the nadir of the degree that first assendeth, and set him on the ende of the 210 houre inequal; and thanne wol the by-ginning of the 5 hous sitte up-on the lyne of midnight; set thanne the nadir of the assendent on the ende of the 4 houre, than wol the byginning of the 6 house sitte on the midnight lyne. The byginning of the 7 hous is nadir of the assendent, and the byginning of the 8 hous is nadir of the15 2; and the by-ginning of the 9 hous is nadir of the 3; and the by-ginning of the 10 hous is the nadir of the 4; and the byginning of the 11 hous is nadir of the 5; and the byginning of the 12 hous is nadir of the 6. And for the more declaracion, lo here the figure.

37.

A-nother manere of equaciouns of houses by the Astrolabie.

Tak thyn assendent, and thanne hastow thy 4 angles; for wel thou wost that the opposit of thyn assendent, that is to seyn, thy by-ginning of the 7 hous, sit up-on the west orizonte; and the byginning of the 10 hous sit up-on the lyne meridional; and his5 opposit up-on the lyne of midnight. Thanne ley thy label over the degree that assendeth, and rekne fro the point of thy label alle the degrees in the bordure, til thou come to the meridional lyne; and departe alle thilke degrees in 3 evene parties, and take the evene equacion of 3; for ley thy label over everich of 3 parties,10 and than maistow see by thy label in which degree of the zodiak is the by-ginning of everich of thise same houses fro the assendent: that is to seyn, the beginning of the 12 house next above thyn assendent; and thanne the beginning of the 11 house; and thanne the 10, up-on the meridional lyne; as I first seide. The same wyse wirke thou fro the assendent doun to the lyne of15 midnight; and thanne thus hastow other 3 houses, that is to seyn, the byginning of the 2, and the 3, and the 4 houses; thanne is the nadir of thise 3 houses the by-ginning of the 3 houses that folwen. And for the more declaracioun, lo here thy figure.

38.

To finde the lyne merydional to dwelle fix in any certein place.

Tak a rond plate of metal; for warping , the brodere the bettre ; and make ther-upon a iust compas, a lite with-in the bordure; and ley this ronde plate up-on an evene grond, or on an evene ston, or on an evene stok fix in the gronde; and ley it even by a level. And in centre of the compas stike an evene pin or a wyr upright;5 the smallere the betere. Set thy pin by a plom-rewle evene upright; and let this pin be no lengere than a quarter of the diametre of thy compas, fro the centre . And waite bisily, aboute [ ] 10 or 11 of the clokke and whan the sonne shyneth, whan the shadwe of the pin entreth any-thing with-in the cercle of thy plate10 an heer-mele, and mark ther a prikke with inke. Abyde thanne stille waiting on the sonne after 1 of the clokke, til that the schadwe of the wyr or of the pin passe ony-thing out of the cercle of the compas, be it never so lyte; and set ther a-nother prikke of inke. Take than a compas, and mesure evene the middel15 by-twixe bothe prikkes; and set ther a prikke. Take thanne a rewle, and draw a stryke, evene a-lyne fro the pin un-to the middel prikke; and tak ther thy lyne meridional for evere-mo, as in that same place. And yif thow drawe a cros-lyne over-thwart20 the compas, iustly over the lyne meridional, than hastow est and west and south; and, par consequence, than the nadir of the south lyne is the north lyne. And for more declaracioun, lo here thy figure.

39.

Descripcion of the meridional lyne, of longitudes, and latitudes of citees and townes from on to a-nother of clymatz.[ ][ ]

This lyne meridional is but a maner descripcion of lyne imagined, that passeth upon the poles of this world and by the senith of oure heved. And hit is y-cleped the lyne meridional; for in what place that any maner man is at any tyme of the yeer,5 whan that the sonne by moeving of the firmament cometh to his verrey meridian place, than is hit verrey midday, that we clepen oure noon, as to thilke man; and therefore is it cleped the lyne of midday. And nota, for evermo, of 2 citees or of 2 tounes, of whiche that o toun aprocheth more toward the est than doth10 that other toun, truste wel that thilke tounes han diverse meridians. Nota also, that the arch of the equinoxial, that is conteyned or bounded by-twixe the 2 meridians, is cleped the longitude of the toun. And yif so be that two tounes have y-lyke meridian, or oon meridian, than is the distance of hem bothe y-lyke15 fer fro the est; and the contrarie. And in this manere they chaunge nat her meridian, but sothly they chaungen her almikanteras; for the enhausing of the pool and the distance of the sonne. The longitude of a clymat is a lyne imagined fro est to west, y-lyke distant by-twene them alle. The latitude of a clymat is a lyne imagined from north to south the space of the erthe,20 fro the byginning of the firste clymat unto the verrey ende of the same climat, evene directe agayns the pole artik . Thus seyn some auctours; and somme of hem seyn that yif men clepen the latitude, thay mene the arch meridian that is contiened or intercept by-twixe the senith and the equinoxial. Thanne sey they that25 the distaunce fro the equinoxial unto the ende of a clymat, evene agayns the pole artyk, is the latitude of a clymat for sothe. And for more declaracioun, lo here thy figure.

40.

To knowe with which degree of the zodiak that any planete assendith on the orisonte, whether so that his latitude be north or south.[ ]

Knowe by thyn almenak the degree of the ecliptik of any signe in which that the planete is rekned for to be, and that is cleped the degree of his longitude; and knowe also the degree of his latitude fro the ecliptik, north or south. And by thise samples folwinge in special, maystow wirke for sothe in every signe of the5 zodiak. The degree of the longitude , par aventure, of Venus or of another planete , was 6 of Capricorne, and the latitude of him was northward 2 degrees fro the ecliptik lyne. I tok a subtil compas, and cleped that oon poynt of my compas A, and that10 other poynt F. Than tok I the point of A, and set it in the ecliptik lyne evene in my zodiak, in the degree of the longitude of Venus, that is to seyn, in the 6 degree of Capricorne; and thanne sette I the point of F upward in the same signe, bycause [ ] that the latitude was north, up-on the latitude of Venus, that is to15 seyn, in the 6 degree fro the heved of Capricorne; and thus have I 2 degrees by-twixe my two prikkes. Than leide I doun softely my compas, and sette the degree of the longitude up-on the orisonte; tho tok I and wexede my label in maner of a peyre tables to resceyve distinctly the prikkes of my compas. Tho tok20 I this forseide label, and leide it fix over the degree of my longitude; tho tok I up my compas, and sette the point of A in the wex on my label, as evene as I coude gesse over the ecliptik lyne, in the ende of the longitude; and sette the point of F endlang in my label up-on the space of the latitude, inwarde and25 over the zodiak, that is to seyn, north-ward fro the ecliptik. Than leide I doun my compas, and lokede wel in the wey upon the prikke of A and of F; tho turned I my riet til that the prikke of F sat up-on the orisonte; than saw I wel that the body of Venus, in hir latitude of 2 degrees septentrionalis, assended, in the ende30 of the 6 degree, in the heved of Capricorne. And nota, that in the same manner maistow wirke with any latitude septentrional in alle signes; but sothly the latitude meridional of a planete in Capricorne may not be take, by-cause of the litel space by-twixe the ecliptik and the bordure of the Astrolabie; but sothly, in alle other signes35 it may.

Also the degree, par aventure, of Iuppiter or of a-nother planete, was in the first degree of Pisces in longitude, and his latitude was 3 degrees meridional; tho tok I the point of A, and sette it in the firste degree of Pisces on the ecliptik, and thanne sette I the point of F dounward in the same signe, by-cause that the latitude40 was south 3 degrees, that is to seyn, fro the heved of Pisces; and thus have I 3 degrees by-twixe bothe prikkes; thanne sette I the degree of the longitude up-on the orisonte. Tho tok I my label, and leide it fix upon the degree of the longitude; tho sette I the point of A on my label, evene over the ecliptik lyne, in the ende45evene of the degree of the longitude, and sette the point of F endlang in my label the space of 3 degrees of the latitude fro the zodiak, this is to seyn, southward fro the ecliptik, toward the bordure; and turned my riet til the prikke of F sat up-on the orisonte; thanne saw I wel that the body of Iuppiter, in his50 latitude of 3 degrees meridional, ascended with 14 degrees of Pisces in horoscopo. And in this maner maistow wirke with any latitude meridional, as I first seide, save in Capricorne. And yif thou wolt pleye this craft with the arysing of the mone, loke thou rekne wel his cours houre by houre; for she ne dwelleth nat in a degree of55hir longitude but a litel whyle, as thou wel knowest; but natheles, yif thou rekne hir verreye moeving by thy tables houre after houre,[ ] [thou shalt do wel y-now].

Explicit tractatus de Conclusionibus Astrolabii, compilatus per Galfridum Chauciers ad Filium suum Lodewicum, scolarem tunc temporis Oxonie, ac sub tutela illius nobilissimi philosophi Magistri N. Strode, etc.

* * * * * * *

Part II, § 1. [The Latin headings to the propositions are taken from the MS. in St. John’s College, Cambridge.] See fig. 1. Any straight edge laid across from the centre will shew this at once. Chaucer, reckoning by the old style, differs from us by about eight days. The first degree of Aries, which in his time answered to the 12th of March, now vibrates between the 20th and 21st of that month. This difference of eight days must be carefully borne in mind in calculating Chaucer’s dates.

2. Here ‘thy left side’ means the left side of thine own body, and therefore the right or Eastern edge of the Astrolabe. In taking the altitude of the sun, the rays are allowed to shine through the holes; but the stars are observed by looking through them. See figs. 1 and 3.

3. Drop the disc (fig. 5) within the border of the mother, and the Rete over it. Take the sun’s altitude by § 2, and let it be 25½°. As the altitude was taken by the back of the Astrolabe, turn it over, and then let the Rete revolve westward till the 1st point of Aries is just within the altitude-circle marked 25, allowing for the ½ degree by guess. This will bring the denticle near the letter C, and the first point of Aries near X, which means 9 a.m. At the same time, the 20th degree of Gemini will be on the horizon obliquus. See fig. 11, Pl. V. This result can be approximately verified by a common globe thus; elevate the pole nearly 52°; turn the small brass hour-circle so that the figure XII lies on the equinoctial colure; then turn the globe till IX lies under the brass meridian. In the next example, by the Astrolabe, let the height of Alhabor (Sirius) be about 18°. Turn the denticle Eastward till it touches the 58th degree near the letter O, and it will be found that Alhabor is about 18° high among the almicanteras, whilst the first point of Aries points to 32° near the letter H, i. e. to 8 minutes past 8 p.m.; whilst at the same time, the 23rd degree of Libra is almost on the Horizon obliquus on the Eastern side. By the globe, at about 8 minutes past 8 p.m., the altitude of Sirius is very nearly 18°, and the 23rd of Libra is very near the Eastern horizon. See fig. 12, Pl. V.

4. The ascendent at any given moment is that degree of the zodiac which is then seen upon the Eastern horizon. Chaucer says that astrologers reckoned in also 5 degrees of the zodiac above, and 25 below; the object being to extend the planet’s influence over a whole ‘house,’ which is a space of the same length as a sign, viz. 30°. See § 36 below.

5. This merely amounts to taking the mean between two results.

6. This depends upon the refraction of light by the atmosphere, owing to which light from the sun reaches us whilst he is still 18° below the horizon. The nadir of the sun being 18° high on the W. side, the sun itself is 18° below the Eastern horizon, giving the time of dawn; and if the nadir be 18° high on the E. side, we get the time of the end of the evening twilight. Thus, at the vernal equinox, the sun is 18° high soon after 8 a.m. (roughly speaking), and hence the evening twilight ends soon after 8 p.m., 12 hours later, sunset being at 6 p.m.

7. Ex. The sun being in the first point of Cancer on the longest day, its rising will be shewn by the point in fig. 5 where the horison obliquus and Tropicus Cancri intersect; this corresponds to a point between P and Q in fig. 2, or to about a quarter to 4 a.m. So too the sunset is at about a quarter past 8, and the length of the day 16½ hours; hence also, the length of the night is about 7½ hours, neglecting twilight.

8. On the same day, the number of degrees in the whole day is about 247½, that being the number through which the Rete is turned in the example to § 7. Divide by 15, and we have 16½ equal hours.

9. The ‘day vulgar’ is the length of the ‘artificial day,’ with the length of the twilight, both at morn and at eve, added to it.

10. If, as in § 7, the day be 16½ hours long, the length of each ‘hour inequal’ is 1 h. 22½ m.; and the length of each ‘hour inequal’ of the night is the 12th part of 7½ hours, or 37½ m.; and 1 h. 22½ m., added to 37½ m., will of course make up 2 hours, or 30°.

11. This merely repeats that 15° of the border answer to an hour of the clock. The ‘4 partie of this tretis’ was never written.

12. This ‘hour of the planet’ is a mere astrological supposition, involving no point of astronomy. Each hour is an ‘hour inequal,’ or the 12th part of the artificial day or night. The assumptions are so made that the first hour of every day may resemble the name of the day; the first hour of Sunday is the hour of the Sun, and so on. These hours may be easily found by the following method. Let 1 represent both Sunday and the Sun; 2, Monday and the Moon; 3, Tuesday and Mars; 4, Wednesday and Mercury; 5, Thursday and Jupiter; 6, Friday and Venus; 7, Saturday and Saturn. Next, write down the following succession of figures, which will shew the hours at once.

1642753|16427531642753164275316.

Ex. To find the planet of the 10th hour of Tuesday. Tuesday is the third day of the week; begin with 3, to the left of the upright line, and reckon 10 onwards; the 10th figure (counting 3 as the first) is 6, i. e. Venus. So also, the planet of the 24th hour of Friday is the Moon, and Saturday begins with Saturn. It may be observed that this table can be carried in the memory, by simply observing that the numbers are written, beginning with 1, in the reverse order of the spheres, i. e. Sun, Venus, Mercury, Moon; and then (beginning again at the outmost sphere) Saturn, Jupiter, Mars. This is why Chaucer takes a Saturday; that he may begin with the remotest planet, Saturn, and follow the reverse order of the spheres. See fig. 10, Pl. V. Here, too, we have the obvious reason for the succession of the names of the days of the week, viz. that the planets being reckoned in this order, we find the Moon in the 25th place or hour from the Sun, and so on.

13. The reason of this is obvious from what has gone before. The sun’s meridional altitude is at once seen by placing the sun’s degree on the South line.

14. This is the exact converse of the preceding. It furnishes a method of testing the accuracy of the drawing of the almikanteras.

15. This is best done by help of the back of the instrument, fig. 1. Thus May 13 (old style), which lies 30° to the W. of the S. line, is nearly of the same length as July 13, which lies 30° to the E. Secondly, the day of April 2 (old style), 20° above the W. line, is nearly of the same length as the night of Oct. 2, 20° below the E. line, in the opposite point of the circle. This is but an approximation, as the divisions on the instrument are rather minute.

16. This merely expresses the same thing, with the addition, that on days of the same length, the sun has the same meridional altitude, and the same declination from the equator.

17. Here passeth any-thing the south westward means, passes somewhat to the westward of the South line. The problem is, to find the degree of the zodiac which is on the meridian with the star. To do this, find the altitude of the star before it souths, and by help of problem 3, find out the ascending degree of the zodiac; secondly, find the ascending degree at an equal time after it souths, when the star has the same altitude as before, and the mean between these will be the degree that ascends when the star is on the meridian. Set this degree upon the Eastern part of the horizon obliquus, and then the degree which is upon the meridional line souths together with the star. Such is the solution given, but it is but a very rough approximation, and by no means always near to the truth. An example will shew why. Let Arcturus have the same altitude at 10 p.m. as at 2 a.m. In the first case the 4th of Sagittarius is ascending, in the second (with sufficient accuracy for our purpose) the 2nd of Aquarius; and the mean between these is the 3rd of Capricorn. Set this on the Eastern horizon upon a globe, and it will be seen that it is 20 min. past midnight, that 10° of Scorpio is on the meridian, and that Arcturus has past the meridian by 5°. At true midnight, the ascendent is the 29° of Sagittarius. The reason of the error is that right ascension and longitude are here not sufficiently distinguished. By observing the degrees of the equinoctial, instead of the ecliptic, upon the Eastern horizon, we have at the first observation 272°, at the second 332°, and the mean of these is 302°; from this subtract 90°, and the result, 212°, gives the right ascension of Arcturus very nearly, corresponding to which is the beginning of the 5° of Scorpio, which souths along with it. This latter method is correct, because it assumes the motion to take place round the axis of the equator. The error of Chaucer’s method is that it identifies the motion of the equator with that of the ecliptic. The amount of the error varies considerably, and may be rather large. But it can easily be diminished, (and no doubt was so in practice), by taking the observations as near the south line as possible. Curiously enough, the rest of the section explains the difference between the two methods of reckoning. The modern method is to call the co-ordinates right ascension and declination, if reckoned from the equator, and longitude and latitude, if from the ecliptic. Motion in longitude is not the same thing as motion in right ascension.

18. The ‘centre’ of the star is the technical name for the extremity of the metal tongue representing it. The ‘degree in which the star standeth’ is considered to be that degree of the zodiac which souths along with it. Thus Sirius or Alhabor has its true longitude nearly equal to that of 12° of Cancer, but, as it souths with the 9th degree, it would be said to stand in that degree. This may serve for an example; but it must be remembered that its longitude was different in the time of Chaucer.

19. Also it rises with the 19th degree of Leo, as it is at some distance from the zodiac in latitude. The same ‘marvellous arising in a strange sign’ is hardly because of the latitude being north or south from the equinoctial, but rather because it is north or south of the ecliptic. For example, Regulus (a Leonis) is on the ecliptic, and of course rises with that very degree in which it is. Hence the reading equinoctial leaves the case in doubt, and we find a more correct statement just below, where we have ‘whan they have no latitude fro the ecliptik lyne.’ At all places, however, upon the earth’s equator, the stars will rise with the degrees of the zodiac in which they stand.

20. Here the disc (fig. 5) is supposed to be placed beneath the Rete (fig. 2). The proposition merely tells us that the difference between the meridian altitudes of the given degree of the zodiac and of the 1st point of Aries is the declination of that degree, which follows from the very definition of the term. There is hardly any necessity for setting the second prick, as it is sufficiently marked by being the point where the equinoctial circle crosses the south line. If the given degree lie outside this circle, the declination is south; if inside, it is north.

21. In fig. 5, the almicanteras, if accurately drawn, ought to shew as many degrees between the south point of the equinoctial circle and the zenith as are equal to the latitude of the place for which they are described. The number of degrees from the pole to the northern point of the horizon obliquus is of course the same. The latitude of the place for which the disc is constructed is thus determined by inspection.

22. In the first place where ‘orisonte’ occurs, it means the South point of the horizon; in the second place, the North point. By referring to fig. 13, Plate V, it is clear that the arc ΥS, representing the distance between the equinoctial and the S. point, is equal to the arc ZP, which measures the distance from the pole to the zenith; since PO Υ and ZOS are both right angles. Hence also Chaucer’s second statement, that the arcs PN and ΥZ are equal. In his numerical example, PN is 51° 50′; and therefore ZP is the complement, or 38° 10′. So also ΥZ is 51° 50′; and ΥS is 38° 10′. Briefly, ΥZ measures the latitude.

23. Here the altitude of a star (A) is to be taken twice; firstly, when it is on the meridian in the most southern point of its course, and secondly, when on the meridian in the most northern point, which would be the case twelve hours later. The mean of these altitudes is the altitude of the pole, or the latitude of the place. In the example given, the star A is only 4° from the pole, which shews that it is the Pole-star, then farther from the Pole than it is now. The star F is, according to Chaucer, any convenient star having a right ascension differing from that of the Pole-star by 180°; though one having the same right ascension would serve as well. If then, at the first observation, the altitude of A be 56, and at the second be 48, the altitude of the pole must be 52. See fig. 13, Plate V.

24. This comes to much the same thing. The lowest or northern altitude of Dubhe (a Ursæ Majoris) may be supposed to be observed to be 25°, and his highest or southern altitude to be 79°. Add these; the sum is 104; ‘abate’ or subtract half of that number, and the result is 52°; the latitude.

25. Here, as in § 22, Chaucer says that the latitude can be measured by the arc ZΥ or PN; he adds that the depression of the Antarctic pole, viz. the arc SP′ (where P′ is the S. pole), is another measure of the latitude. He explains that an obvious way of finding the latitude is by finding the altitude of the sun at noon at the time of an equinox. If this altitude be 38° 10′, then the latitude is the complement, or 51° 50′. But this observation can only be made on two days in the year. If then this seems to be too long a tarrying, observe his midday altitude, and allow for his declination. Thus, if the sun’s altitude be 58° 10′ at noon when he is in the first degree of Leo, subtract his declination, viz. 20°, and the result is 38° 10′, the complement of the latitude. If, however, the sun’s declination be south, the amount of it must be added instead of subtracted. Or else we may find ΥA′, the highest altitude of a star A′ above the equinoctial, and also ΥA, its nether elongation extending from the same, and take the mean of the two.

26. The ‘Sphere Solid’ answers nearly to what we now call a globe. By help of a globe it is easy to find the ascensions of signs for any latitude, whereas by the astrolabe we can only tell them for those latitudes for which the plates bearing the almicanteras are constructed. The signs which Chaucer calls ‘of right (i. e. direct) ascension’ are those signs of the zodiac which rise more directly, i. e. at a greater angle to the horizon than the rest. In latitude 52°, Libra rises so directly that the whole sign takes more than 2¾ hours before it is wholly above the horizon, during which time nearly 43° of the equinoctial circle have arisen; or, in Chaucer’s words, ‘the more part’ (i. e. a larger portion) of the equinoctial ascends with it. On the other hand, the sign of Aries ascends so obliquely that the whole of it appears above the horizon in less than an hour, so that a ‘less part’ (a smaller portion) of the equinoctial ascends with it. The following is a rough table of Direct and Oblique Signs, shewing approximately how long each sign takes to ascend, and how many degrees of the equinoctial ascend with it, in lat. 52°.

These numbers are sufficiently accurate for the present purpose.

In ll. 8-11, there is a gap in the sense in nearly all the MSS., but the Bodley MS. 619 fortunately supplies what is wanting, to the effect that, at places situated on the equator, the poles are in the horizon. At such places, the days and nights are always equal. Chaucer’s next statement is true for all places within the tropics, the peculiarity of them being that they have the sun vertical twice in a year. The statement about the ‘two summer and winters’ is best explained by the following. ‘In the tropical climates, . . seasons are caused more by the effect of the winds (which are very regular, and depend mainly on the sun’s position) than by changes in the direct action of the sun’s light and heat. The seasons are not a summer and winter, so much as recurrences of wet and dry periods, two in each year.’—English Cyclopædia; Seasons, Change of. Lastly, Chaucer reverts to places on the equator, where the stars all seem to move in vertical circles, and the almicanteras are therefore straight lines. The line marked Horizon Rectus is shewn in fig. 5, where the Horizon Obliquus is also shewn, cutting the equinoctial circle obliquely.

27. The real object in this section is to find how many degrees of the equinoctial circle pass the meridian together with a given zodiacal sign. Without even turning the rete, it is clear that the sign Aries, for instance, extends through 28° of the equinoctial; for a line drawn from the centre, in fig. 2, through the end of Aries will (if the figure be correct) pass through the end of the 28th degree below the word Oriens.

28. To do this accurately requires a very carefully marked Astrolabe, on as large a scale as is convenient. It is done by observing where the ends of the given sign, estimated along the outer rim of the zodiacal circle in fig. 2, cross the horizon obliquus as the rete is turned about. Thus, the beginning of Aries lies on the horizon obliquus, and as the rete revolves to the right, the end of it, on the outer rim, will at last lie exactly on the same curved line. When this is the case, the rete ought to have moved through an angle of about 14°, as explained in § 26. By far the best way is to tabulate the results once for all, as I have there done. It is readily seen, from fig. 2, that the signs from Aries to Virgo are northern, and from Libra to Pisces are southern signs. The signs from Capricorn to Gemini are the oblique signs, or as Chaucer calls them, ‘tortuous,’ and ascend in less than 2 hours; whilst the direct signs, from Cancer to Sagittarius, take more than 2 hours to ascend; as shewn in the table on p. 209. The eastern signs in fig. 2 are said to obey to the corresponding western ones.

29. Here both sides of the Astrolabe are used, the ‘rewle’ being made to revolve at the back, and the ‘label’ in front, as usual. First, by the back of the instrument and the ‘rewle,’ take the sun’s altitude. Turn the Astrolabe round, and set the sun’s degree at the right altitude among the almicanteras, and then observe, by help of the label, how far the sun is from the meridian. Again turn the instrument round, and set the ‘rewle’ as far from the meridian as the label was. Then, holding the instrument as near the ground and as horizontal as possible, let the sun shine through the holes of the ‘rewle,’ and immediately after lay the Astrolabe down, without altering the azimuthal direction of the meridional line. It is clear that this line will then point southwards, and the other points of the compass will also be known.

30. This turns upon the definition of the phrase ‘the wey of the sonne.’ It does not mean the zodiacal circle, but the sun’s apparent path on a given day of the year. The sun’s altitude changes but little in one day, and is supposed here to remain the same throughout the time that he is, on that day, visible. Thus, if the sun’s altitude be 61½°, the way of the sun is a small circle, viz. the tropic of Cancer. If the planet be then on the zodiac, in the 1st degree of Capricorn, it is 47° S. from the way of the sun, and so on.

31. The word ‘senith’ is here used in a peculiar sense; it does not mean, as it should, the zenith point, or point directly overhead, but is made to imply the point on the horizon, (either falling upon an azimuthal line, or lying between two azimuths), which denotes the point of sunrise. In the Latin rubric, it is called signum. This point is found by actual observation of the sun at the time of rising. Chaucer’s azimuths divide the horizon into 24 parts; but it is interesting to observe his remark, that ‘shipmen’ divide the horizon into 32 parts, exactly as a compass is divided now-a-days. The reason for the division into 32 parts is obviously because this is the easiest way of reckoning the direction of the wind. For this purpose, the horizon is first divided into 4 parts; each of these is halved, and each half-part is halved again. It is easy to observe if the wind lies half-way between S. and E., or half-way between S. and S.E., or again half-way between S. and S.S.E.; but the division into 24 parts would be unsuitable, because third-parts are much more difficult to estimate.

32. The Latin rubric interprets the conjunction to mean that of the sun and moon. The time of this conjunction is to be ascertained from a calendar. If, e. g. the calendar indicates 9 a.m. as the time of conjunction on the 12th day of March, when the sun is in the first point of Aries, as in § 3, the number of hours after the preceding midday is 21, which answers to the letter X in the border (fig. 2). Turn the rete till the first point of Aries lies under the label, which is made to point to X, and the label shews at the same moment that the degree of the sun is very nearly at the point where the equinoctial circle crosses the azimuthal circle which lies 50° to the E. of the meridian. Hence the conjunction takes place at a point of which the azimuth is 50° to the E. of the S. point, or 5° to the eastward of the S.E. point. The proposition merely amounts to finding the sun’s azimuth at a given time. Fig. 11 shews the position of the rete in this case.

33. Here ‘senyth’ is again used to mean azimuth, and the proposition is, to find the sun’s azimuth by taking his altitude, and setting his degree at the right altitude on the almicanteras. Of course the two co-ordinates, altitude and azimuth, readily indicate the sun’s exact position; and the same for any star or planet.

34. The moon’s latitude is never more than 5¼° from the ecliptic, and this small distance is, ‘in common treatises of Astrolabie,’ altogether neglected; so that it is supposed to move in the ecliptic. First, then, take the moon’s altitude, say 30°. Next take the altitude of some bright star ‘on the moon’s side,’ i. e. nearly in the same azimuth as the moon, taking care to choose a star which is represented upon the Rete by a pointed tongue. Bring this tongue’s point to the right altitude among the almicanteras, and then see which degree of the ecliptic lies on the almicantera which denotes an altitude of 30°. This will give the moon’s place, ‘if the stars in the Astrolabe be set after the truth,’ i. e. if the point of the tongue is exactly where it should be.

35. The motion of a planet is called direct, when it moves in the direction of the succession of the zodiacal signs; retrograde, when in the contrary direction. When a planet is on the right or east side of the Meridional line, and is moving forward along the signs, without increase of declination, its altitude will be less on the second occasion than on the first at the moment when the altitude of the fixed star is the same as before. The same is true if the planet be retrograde, and on the western side. The contrary results occur when the second altitude is greater than the first. But the great defect of this method is that it may be rendered fallacious by a change in the planet’s declination.

36. See fig. 14, Plate VI. If the equinoctial circle in this figure be supposed to be superposed upon that in fig. 5, Plate III, and be further supposed to revolve backwards through an angle of about 60° till the point 1 (fig. 14) rests upon the point where the 8th hour-line crosses the equinoctial, the beginning of the 2nd house will then be found to be on the line of midnight. Similarly, all the other results mentioned follow. For it is easily seen that each ‘house’ occupies a space equal to 2 hours, so that the bringing of the 3rd house to the midnight line brings 1 to the 10th hour-line, and a similar placing of the 4th house brings 1 to the 12th hour-line, which is the horizon obliquus itself. Moving onward 2 more hours, the point 7 (the nadir of 1) comes to the end of the 2nd hour, whilst the 5th house comes to the north; and lastly, when 7 is at the end of the 4th hour, the 6th house is so placed. To find the nadir of a house, we have only to add 6; so that the 7th, 8th, 9th, 10th, 11th, and 12th houses are the nadirs of the 1st, 2nd, 3rd, 4th, 5th, and 6th houses respectively.

37. Again see fig. 14, Plate VI. Here the 10th house is at once seen to be on the meridional line. In the quadrant from 1 to 10, the even division of the quadrant into 3 parts shews the 12th and 11th houses. Working downwards from 1, we get the 2nd and 3rd houses, and the 4th house beginning with the north line. The rest are easily found from their nadirs.

38. This problem is discussed in arts. 144 and 145 of Hymes’s Astronomy, 2nd ed. 1840, p. 84. The words ‘for warping’ mean ‘to prevent the errors which may arise from the plate becoming warped.’ The ‘broader’ of course means ‘the larger.’ See fig. 15, Plate VI. If the shadow of the sun be observed at a time before midday when its extremity just enters within the circle, and again at a time after midday when it is just passing beyond the circle, the altitude of the sun at these two observations must be the same, and the south line must lie half-way between the two shadows. In the figure, S and S′ are the 2 positions of the sun, OT the rod, Ot and Ot′ the shadows, and OR the direction of the south line. Ott′ is the metal disc.

39. This begins with an explanation of the terms ‘meridian’ and ‘longitude.’ ‘They chaungen her Almikanteras’ means that they differ in latitude. But, when Chaucer speaks of the longitude and latitude of a ‘climate,’ he means the length and breadth of it. A ‘climate’ (clima) is a belt of the earth included between two fixed parallels of latitude. The ancients reckoned seven climates; in the sixteenth century there were nine. The ‘latitude of the climate’ is the breadth of this belt; the ‘longitude’ of it he seems to consider as measured along lines lying equidistant between the parallels of latitude of the places from which the climates are named. See Stöffler, fol. 20 b; and Petri Apiani Cosmographia, per Gemmam Phrysium restituta, ed. 1574, fol. 7 b. The seven climates were as follows:—

1. That whose central line passes through Meroë (lat. 17°); from nearly 13° to nearly 20°.

2. Central line, through Syene (lat. 24°); from 20° to 27°, nearly.

3. Central line through Alexandria (lat. 31°); from 27° to 34°, nearly.

4. Central line through Rhodes (lat. 36°); from 34° to 39°, nearly.

5. Central line through Rome (lat. 41°); from 39° to 43°, nearly.

6. Central line through Borysthenes (lat. 45°); from 43° to 47°.

7. Through the Riphæan mountains (lat. 48°); from 47° to 50°. But Chaucer must have included an eighth climate (called ultra Mæotides paludes) from 50° to 56°; and a ninth, from 56° to the pole. The part of the earth to the north of the 7th climate was considered by the ancients to be uninhabitable. A rough drawing of these climates is given in MS. Camb. Univ. Lib. Ii. 3. 3, fol. 33 b.

40. The longitude and latitude of a planet being ascertained from an almanac, we can find with what degree it ascends. For example, given that the longitude of Venus is 6° of Capricorn, and her N. latitude 2°. Set the one leg of a compass upon the degree of longitude, and extend the other till the distance between the two legs is 2° of latitude, from that point inward, i. e. northward. The 6th degree of Capricorn is now to be set on the horizon, the label (slightly coated with wax) to be made to point to the same degree, and the north latitude is set off upon the wax by help of the compass. The spot thus marking the planet’s position is, by a very slight movement of the Rete, to be brought upon the horizon, and it will be found that the planet (situated 2° N. of the 6th degree) ascends together with the head (or beginning of the sign) of Capricorn. This result, which is not quite exact, is easily tested by a globe. When the latitude of the planet is south, its place cannot well be found when in Capricorn for want of space at the edge of the Astrolabe.

As a second example, it will be found that, when Jupiter’s longitude is at the end of 1° of Pisces, and his latitude 3° south, he ascends together with the 14th of Pisces, nearly. This is easily verified by a globe, which solves all such problems very readily.

It is a singular fact that most of the best MSS. leave off at the word ‘houre,’ leaving the last sentence incomplete. I quote the last five words—‘þou shalt do wel y-now’—from the MS. in St. John’s College, Cambridge; they also occur in the old editions.

SUPPLEMENTARY PROPOSITIONS.

41.

Umbra Recta.[ ][ ]

Yif it so be that thou wilt werke by umbra recta, and thou may come to the bas of the toure, in this maner thou schalt werke. Tak the altitude of the tour by bothe holes, so that thy rewle ligge even in a poynt. Ensample as thus: I see him thorw at the5 poynt of 4; than mete I the space be-tween me and the tour, and I finde it 20 feet; than be-holde I how 4 is to 12, right so is the space betwixe thee and the tour to the altitude of the tour. For 4 is the thridde part of 12, so is the space be-tween thee and the tour the thridde part of the altitude of the tour; than thryes 20 feet is the10 heyghte of the tour, with adding of thyn owne persone to thyn eye. And this rewle is so general in umbra recta, fro the poynt of oon to 12. And yif thy rewle falle upon 5, than is 5 12-partyes of the heyght the space be-tween thee and the toure; with adding of thyn owne heyght.

42.

Umbra Versa.

Another maner of werkinge, by umbra versa. Yif so be that thou may nat come to the bas of the tour, I see him thorw the nombre of 1; I sette ther a prikke at my fote; than go I neer to the tour, and I see him thorw at the poynt of 2, and there I sette a-nother prikke; and I beholde how 1 hath him to 12, and ther5 finde I that it hath him twelfe sythes; than beholde I how 2 hath him to 12, and thou shalt finde it sexe sythes; than thou shalt finde that as 12 above 6 is the numbre of 6, right so is the space between thy two prikkes the space of 6 tymes thyn altitude. And note, that at the ferste altitude of 1, thou settest a prikke; and10 afterward, whan thou seest him at 2, ther thou settest an-other prikke; than thou findest between two prikkys 60 feet; than thou shalt finde that 10 is the 6-party of 60. And then is 10 feet the altitude of the tour. For other poyntis, yif it fille in umbra versa, as thus: I sette caas it fill upon 2 , and at the secunde upon 3;15 than schalt thou finde that 2 is 6 partyes of 12; and 3 is 4 partyes of 12; than passeth 6 4, by nombre of 2; so is the space between two prikkes twyes the heyghte of the tour. And yif the differens were thryes, than shulde it be three tymes; and thus mayst thou werke fro 2 to 12; and yif it be 4, 4 tymes; or 5, 5 tymes; et sic20de ceteris.

43.

Umbra Recta[ ] .

An-other maner of wyrking be umbra recta. Yif it so be that thou mayst nat come to the baas of the tour, in this maner thou schalt werke. Sette thy rewle upon 1 till thou see the altitude, and sette at thy foot a prikke. Than sette thy rewle upon 2, and beholde what is the differense be-tween 1 and 2, and thou shalt5 finde that it is 1. Than mete the space be-tween two prikkes, and that is the 12 partie of the altitude of the tour. And yif ther were 2, it were the 6 partye; and yif ther were 3, the 4 partye; et sic deinceps. And note, yif it were 5, it were the 5 party of 12; and 7, 7 party of 12; and note, at the altitude of thy conclusioun,10 adde the stature of thyn heyghte to thyn eye.

* * * * * * *

44.

Another maner conclusion, to knowe the mene mote and the argumentis of any planete. To know the mene mote and the argumentis of every planete fro yere to yere, from day to day, from houre to houre, and from smale fraccionis infinite.[ ][ ]

In this maner shalt thou worche: consider thy rote first, the whiche is made the beginning of the tables fro the yere of oure lord 1397, and entere hit in-to thy slate for the laste meridie of December; and than consider the yere of oure lord, what is the5 date, and be-hold whether thy date be more or lasse than the yere 1397. And yf hit so be that hit be more, loke how many yeres hit passeth, and with so many entere into thy tables in the first lyne ther-as is writen anni collecti et expansi. And loke where the same planet is writen in the hede of thy table, and than loke10 what thou findest in directe of the same yere of oure lord whiche is passid, be hit 8, or 9, or 10, or what nombre that evere it be, til the tyme that thou come to 20, or 40, or 60. And that thou findest in directe wryte in thy slate under thy rote, and adde hit to-geder , and that is thy mene mote, for the laste meridian of the15 December, for the same yere whiche that thou hast purposed. And if hit so be that hit passe 20, consider wel that fro 1 to 20 ben anni expansi, and fro 20 to 3000 ben anni collecti; and if thy nombere passe 20, than take that thou findest in directe of 20, and if hit be more, as 6 or 18, than take that thou findest in directe20 there-of, that is to sayen, signes, degrees, minutes, and secoundes, and adde to-gedere un-to thy rote; and thus to make rotes; and note, that if hit so be that the yere of oure lord be lasse than the rote, whiche is the yere of oure lord 1397, than shalt thou wryte in the same wyse furst thy rote in thy slate, and after entere in-to thy table in the same yere that be lasse, as I taught be-fore; and25 than consider how many signes, degrees, minutes, and secoundes thyn entringe conteyneth. And so be that ther be 2 entrees, than adde hem togeder, and after with-drawe hem from the rote, the yere of oure lord 1397; and the residue that leveth is thy mene mote fro the laste meridie of December, the whiche30 thou hast purposed; and if hit so be that thou wolt weten thy mene mote for any day, or for any fraccioun of day, in this maner thou shalt worche. Make thy rote fro the laste day of Decembere in the maner as I have taught , and afterward behold how many monethis, dayes, and houres ben passid from35the meridie of Decembere, and with that entere with the laste moneth that is ful passed, and take that thou findest in directe of him, and wryte hit in thy slate; and entere with as mony dayes as be more, and wryte that thou findest in directe of the same planete that thou worchest for; and in the same wyse in40 the table of houres, for houres that ben passed, and adde alle these to thy rote; and the residue is the mene mote for the same day and the same houre.

45.

Another manere to knowe the mene mote.[ ]

Whan thou wolt make the mene mote of eny planete to be by Arsechieles tables, take thy rote, the whiche is for the yere of oure lord 1397; and if so be that thy yere be passid the date, wryte that date, and than wryte the nombere of the yeres. Than withdrawe the yeres out of the yeres that ben passed that rote.5 Ensampul as thus: the yere of oure lord 1400, I wolde witen, precise, my rote; than wroot I furst 1400. And under that nombere I wrote a 1397 ; than withdrow I the laste nombere out of that, and than fond I the residue was 3 yere; I wiste10 that 3 yere was passed fro the rote, the whiche was writen in my tables. Than after-ward soghte I in my tables the annis collectis et expansis, and amonge myn expanse yeres fond I 3 yeer. Than tok I alle the signes, degrees, and minutes, that I fond directe under the same planete that I wroghte for, and15 wroot so many signes, degrees, and minutes in my slate, and afterward added I to signes, degrees, minutes, and secoundes, the whiche I fond in my rote the yere of oure lord 1397; and kepte the residue; and than had I the mene mote for the laste day of Decembere. And if thou woldest wete the20 mene mote of any planete in March, Aprile, or May, other in any other tyme or moneth of the yere, loke how many monethes and dayes ben passed from the laste day of Decembere, the yere of oure lord 1400; and so with monethes and dayes entere in-to thy table ther thou findest thy mene25 mote y-writen in monethes and dayes, and take alle the signes, degrees, minutes, and secoundes that thou findest y-write in directe of thy monethes, and adde to signes, degrees, minutes, and secoundes that thou findest with thy rote the yere of oure lord 1400, and the residue that leveth is the mene mote30 for that same day. And note, if hit so be that thou woldest wete the mene mote in ony yere that is lasse than thy rote, withdrawe the nombere of so many yeres as hit is lasse than the yere of oure lord a 1397, and kepe the residue; and so many yeres, monethes, and dayes entere in-to thy tabelis of thy mene35 mote. And take alle the signes, degrees, and minutes, and secoundes, that thou findest in directe of alle the yeris, monethes, and dayes, and wryte hem in thy slate; and above thilke nombere wryte the signes, degrees, minutes, and secoundes, the whiche thou findest with thy rote the yere of oure lord a 1397; and with-drawe alle the nethere signes and degrees fro the signes and40 degrees, minutes, and secoundes of other signes with thy rote; and thy residue that leveth is thy mene mote for that day.

46.

For to knowe at what houre of the day, or of the night, shal be flode or ebbe.

First wite thou certeinly, how that haven stondeth, that thou list to werke for; that is to say in whiche place of the firmament the mone being, maketh fulle see. Than awayte thou redily in what degree of the zodiak that the mone at that tyme is inne. Bringe furth than the labelle, and set the point therof in that5 same cost that the mone maketh flode, and set thou there the degree of the mone according with the egge of the label. Than afterward awayte where is than the degree of the sonne, at that tyme. Remeve thou than the label fro the mone, and bringe and sette it iustly upon the degree of the sonne. And the point of10 the label shal than declare to thee, at what houre of the day or of the night shal be flode. And there also maist thou wite by the same point of the label, whether it be, at that same tyme, flode or ebbe, or half flode, or quarter flode, or ebbe, or half or quarter ebbe; or ellis at what houre it was last, or shal be next by night or15 by day, thou than shalt esely knowe, &c. Furthermore, if it so be that thou happe to worke for this matere aboute the tyme of the coniunccioun, bringe furthe the degree of the mone with the labelle to that coste as it is before seyd. But than thou shalt understonde that thou may not bringe furthe the label fro the20 degree of the mone as thou dide before; for-why the sonne is than in the same degree with the mone. And so thou may at that tyme by the point of the labelle unremeved knowe the houre of the flode or of the ebbe, as it is before seyd, &c. And evermore25 as thou findest the mone passe fro the sonne, so remeve thou the labelle than fro the degree of the mone, and bringe it to the degree of the sonne. And worke thou than as thou dide before, &c. Or elles knowe thou what houre it is that thou art inne, by thyn instrument. Than bringe thou furth fro thennes the labelle30 and ley it upon the degree of the mone, and therby may thou wite also whan it was flode, or whan it wol be next, be it night or day; &c.

[The following sections are spurious; they are numbered so as to shew what propositions they repeat.]

41a.

Umbra Recta.[ ]

Yif thy rewle falle upon the 8 poynt on right schadwe, than make thy figure of 8; than loke how moche space of feet is be-tween thee and the tour, and multiplye that be 12, and whan thou hast multiplied it, than divyde it be the same nombre of 8, and kepe the residue; and5 adde therto up to thyn eye to the residue, and that shal be the verry heyght of the tour. And thus mayst thou werke on the same wyse, fro 1 to 12.

41b.

Umbra Recta.

An-other maner of werking upon the same syde. Loke upon which poynt thy rewle falleth whan thou seest the top of the tour thorow two litil holes; and mete than the space fro thy foot to the baas of the tour; and right as the nombre of thy poynt hath him-self to 12, right5 so the mesure be-tween thee and the tour hath him-self to the heighte of the same tour. Ensample: I sette caas thy rewle falle upon 8; than is 8 two-third partyes of 12; so the space is the two-third partyes of the tour.

42a.

Umbra Versa.

To knowe the heyghth by thy poyntes of umbra versa. Yif thy rewle falle upon 3, whan thou seest the top of the tour, set a prikke there-as thy foot stont; and go ner til thou mayst see the same top at the poynt of 4, and sette ther another lyk prikke. Than mete how many foot ben be-tween the two prikkes, and adde the lengthe up to5 thyn eye ther-to; and that shal be the heyght of the tour. And note, that 3 is [the] fourthe party of 12, and 4 is the thridde party of 12. Now passeth 4 the nombre of 3 be the distaunce of 1; therfore the same space, with thyn heyght to thyn eye, is the heyght of the tour. And yif it so be that ther be 2 or 3 distaunce in the nombres, so shulde10 the mesures be-tween the prikkes be twyes or thryes the heyghte of the tour.

43a.

Ad cognoscendum altitudinem alicuius rei per umbram rectam.

To knowe the heyghte of thinges, yif thou mayst nat come to the bas of a thing. Sette thy rewle upon what thou wilt, so that thou may see the top of the thing thorw the two holes, and make a marke ther thy foot standeth; and go neer or forther, til thou mayst see thorw another poynt, and marke ther a-nother marke. And loke than what5 is the differense be-twen the two poyntes in the scale; and right as that difference hath him to 12, right so the space be-tween thee and the two markes hath him to the heyghte of the thing. Ensample: I set caas thou seest it thorw a poynt of 4; after, at the poynt of 3. Now passeth the nombre of 4 the nombre of 3 be the difference of 1;10 and right as this difference 1 hath him-self to 12, right so the mesure be-tween the two markes hath him to the heyghte of the thing, putting to the heyghte of thy-self to thyn eye; and thus mayst thou werke fro 1 to 12.

42b.

Per umbram versam.

Furthermore, yif thou wilt knowe in umbra versa, by the craft of umbra recta, I suppose thou take the altitude at the poynt of 4, and makest a marke; and thou goost neer til thou hast it at the poynt of 3, and than makest thou ther a-nother mark. Than muste thou5 devyde 144 by eche of the poyntes be-fornseyd, as thus: yif thou devyde 144 be 4 , and the nombre that cometh ther-of schal be 36, and yif thou devyde 144 be 3, and the nombre that cometh ther-of schal be 48, thanne loke what is the difference be-tween 36 and 48, and ther shalt thou fynde 12; and right as 12 hath him to 12, right so the space10 be-tween two prikkes hath him to the altitude of the thing.

41. Sections 41-43 and 41a-42b are from the MS. in St. John’s College, Cambridge. For the scale of umbra recta, see fig. 1, Plate I. Observe that the umbra recta is used where the angle of elevation of an object is greater than 45°; the umbra versa, where it is less. See also fig. 16, Plate VI; where, if AC be the height of the tower, BC the same height minus the height of the observer’s eye (supposed to be placed at E), and EB the distance of the observer from the tower, then bc : Eb : : EB : BC. But Eb is reckoned as 12, and if bc be 4, we find that BC is 3 EB, i. e. 60 feet, when EB is 20. Hence AC is 60 feet, plus the height of the observer’s eye. The last sentence is to be read thus—‘And if thy “rewle” fall upon 5, then are 5-12ths of the height equivalent to the space between thee and the tower (with addition of thine own height).’ The MS. reads ‘5 12-partyes þe heyȜt of þe space,’ &c.; but the word of must be transposed, in order to make sense. It is clear that, if bc=5, then 5 : 12 : : EB : BC, which is the same as saying that EB= BC. Conversely, BC is EB=48, if EB=20.

42. See fig. 1, Plate I. See also fig. 17, Plate VI. Let Eb=12, bc =1; also E′b′=12, b′c′=2; then EB=12 BC, E′B=6 BC; therefore EE′=6 BC. If EE′=60 feet, then BC=⅙ EE′=10 feet. To get the whole height, add the height of the eye. The last part of the article, beginning ‘For other poyntis,’ is altogether corrupt in the MS.

43. Here versa (in M.) is certainly miswritten for recta, as in L. See fig. 18, Plate VI. Here Eb=E′b′=12; b′c′=1, bc=2. Hence E′B= BC, EB = BC, whence EE′ = BC. Or again, if bc become = 3, 4, 5, &c., successively, whilst b′c′ remains = 1, then EE′ is successively = or ⅙, or ¼, , &c. Afterwards, add in the height of E.

44. Sections 44 and 45 are from MS. Digby 72. This long explanation of the method of finding a planet’s place depends upon the tables which were constructed for that purpose from observation. The general idea is this. The figures shewing a planet’s position for the last day of December, 1397, give what is called the root, and afford us, in fact, a starting-point from which to measure. An ‘argument’ is the angle upon which the tabulated quantity depends; for example, a very important ‘argument’ is the planet’s longitude, upon which its declination may be made to depend, so as to admit of tabulation. The planet’s longitude for the given above-mentioned date being taken as the root, the planet’s longitude at a second date can be found from the tables. If this second date be less than 20 years afterwards, the increase of motion is set down separately for each year, viz. so much in 1 year, so much in 2 years, and so on. These separate years are called anni expansi. But when the increase during a large round number of years (such as 20, 40, or 60 years at once) is allowed for, such years are called anni collecti. For example, a period of 27 years includes 20 years taken together, and 7 separate or expanse years. The mean motion during smaller periods of time, such as months, days, and hours, is added in afterwards.

45. Here the author enters a little more into particulars. If the mean motion be required for the year 1400, 3 years later than the starting-point, look for 3 in the table of expanse years, and add the result to the number already corresponding to the ‘root,’ which is calculated for the last day of December, 1397. Allow for months and days afterwards. For a date earlier than 1397 the process is just reversed, involving subtraction instead of addition.

46. This article is probably not Chaucer’s. It is found in MS. Bodley 619, and in MS. Addit. 29250. The text is from the former of these, collated with the latter. What it asserts comes to this. Suppose it be noted, that at a given place, there is a full flood when the moon is in a certain quarter; say, e. g. when the moon is due east. And suppose that, at the time of observation, the moon’s actual longitude is such that it is in the first point of Cancer. Make the label point due east; then bring the first point of Cancer to the east by turning the Rete a quarter of the way round. Let the sun at the time be in the first point of Leo, and bring the label over this point by the motion of the label only, keeping the Rete fixed. The label then points nearly to the 32nd degree near the letter Q, or about S.E. by E.; shewing that the sun is S.E. by E. (and the moon consequently due E.) at about 4 a.m. In fact, the article merely asserts that the moon’s place in the sky is known from the sun’s place, if the difference of their longitudes be known. At the time of conjunction, the moon and sun are together, and the difference of their longitudes is zero, which much simplifies the problem. If there is a flood tide when the moon is in the E., there is another when it comes to the W., so that there is high water twice a day. It may be doubted whether this proposition is of much practical utility.

41a. This comes to precisely the same as Art. 41, but is expressed with a slight difference. See fig. 16, where, if bc = 8, then BC = EB.

41b. Merely another repetition of Art. 41. It is hard to see why it should be thus repeated in almost the same words. If bc = 8 in fig. 16, then EB = BC = ⅔ BC. The only difference is that it inverts the equation in the last article.

42a. This is only a particular case of Art. 42. If we can get bc=3, and b′c′ = 4, the equations become EB = 4BC, E′B = 3BC; whence EE′ = BC, a very convenient result. See fig. 17.

43a. The reading versam (as in the MS.) is absurd. We must also read ‘nat come,’ as, if the base were approachable, no such trouble need be taken; see Art. 41. In fact, the present article is a mere repetition of Art. 43, with different numbers, and with a slight difference in the method of expressing the result. In fig. 18, if b′c′ = 3, bc = 4, we have E′B = BC, EB = BC; or, subtracting, EE′ = BC; or BC = 12 EE′. Then add the height of E, viz. Ea, which = AB.

42b. Here, ‘by the craft of Umbra Recta’ signifies, by a method similar to that in the last article, for which purpose the numbers must be adapted for computation by the umbra recta. Moreover, it is clear, from fig. 17, that the numbers 4 and 3 (in lines 2 and 4) must be transposed. If the side parallel to bE be called nm, and mn, Ec be produced to meet in o, then mo : mE : : bE : bc; or mo : 12 : : 12 : bc; or mo=144, divided by bc (=3)=48. Similarly, m′o′=144, divided by b′c′ (=4)=36. And, as in the last article, the difference of these is to 12, as the space EE′ is to the altitude. This is nothing but Art. 42 in a rather clumsier shape.

Hence it appears that there are here but 3 independent propositions, viz. thouse in articles 41, 42, and 43, corresponding to figs. 16, 17, and 18 respectively. Arts. 41a and 41b are mere repetitions of 41; 42a and 42b, of 42; and 43a, of 43.

[Prologue. l. 26.]thise B; þese C; miswritten this A; see above, ll. 21, 22.

[32.]curious BC; miswritten curios A.

Many similar very slight alterations of spelling have been silently made in the text, and are not worth specifying here. A complete list of them is given in my edition of this treatise for the Early English Text Society. I give, however, the real variations of reading. Thus, in l. 58, A. has som for sonne; and in l. 64 omits the second the.

[Part I. § 1, l. 3.]wol B; wolde AC.

[§ 2, l. 2.]Rowm is here an adjective, meaning large, ample. It is the right reading; we find Rowm AB rowme C; rvm M.

[§ 3, l. 1.]AB omit the.

[§ 9, l. 3.]nombre AB; noumbre C; but nombres in old editions.

[§ 12, l. 5.]The MSS. all1 read—‘vmbra recta or elles vmbra extensa, & the nether partie is cleped the vmbra versa.’ This is certainly wrong.

[§ 13, l. 2.]a certein] so in AB; CM omit a. But Chaucer certainly uses the phrase ‘a certain’; cf. ‘of unces a certain,’ C. T., G 776; and see G 1024.

[§ 14, ll. 2, 5.]The word halt for holdeth, and the expression to-hepe, together, both occur in Troil. iii. 1764:— ‘And lost were al, that Love halt now to-hepe.’

[§ 17, l. 1.]principal C; tropikal AB; M om. The reading tropikal is absurd, because there are but two such; besides which, see l. 34 below.

[17.]the nyht (over an erasure) B; thee nyht (over an erasure) A; þe niȜtes C; þe nyȜtes M.

[§ 20, l. 4.]figure; here (and sometimes elsewhere) miswritten vigur A. Throughout the whole treatise, the scribe has commonly written ‘vigur’; in many places, it has been corrected to ‘figure.’

[§ 21, l. 15.]the (before sterres) supplied from BC.

[27.]where as C; wher AB.

[56.]ouerkeruyd A; ouerkerued B; ouerkerueth (the latter part of the word over an erasure) C; first time only.

[Part II. § 2, l. 8.]euer M; euere C; euery (wrongly) AB.

[§ 3, ll. 31, 32.]A has 12 degres, corrected to 18 degres; B. has 12 degrees; C has 18. The numbers in the MSS. in these propositions are somewhat uncertain; it seems probable that some alteration was made by Chaucer himself.

The readings in MS. B give one set of calculations, which are no doubt the original ones; for in MS. A the same set is again found, but altered throughout, by the scribe who drew the diagrams. The sets of readings are these:—

Ll. 31, 32. 12 degrees B; so in A, but altered to 18; C has 18.

[37.]passed 9 of the clokke the space of 10 degrees B; so in A, with 9 altered to 8, and 10 altered to 2; C has ij for 9, but agrees with A in the reading 2.

[39.]fond ther 10 degrees of taurus B; so in A originally, but 10 has been corrected to 23, and libra is written over an erasure. C agrees with neither, having 20 for 10, but agreeing with A as to libra. The later MSS. sometimes vary from all these.

[42.]an supplied from C; AB omit.

[§ 4, l. 5.]largest C; largesse AB.

[6.]upon C; vn (!) AB.

[8.]forseide degree of his longitude] forseyde same degre of hys longitude C; forseid same gre of his longitude P; forseyde latitude his longitude (sic!) AB.

[9.]planete ys C; miswritten planetes AB, but is is added in margin of A.

[16.]For ‘25 degrees,’ all the MSS. have ‘15 degrees.’ The mistake is probably Chaucer’s own; the correction was made by Mr. Brae, who remarks that it is a mere translation from the Latin version of Ptolemy’s Tetrabiblos, which has—‘Signum ascendentis, quod est a quinque gradibus qui super horizontem ante ipsum ascenderant usque ad viginti quinque qui ad ascendentem remanserint’; Lib. iii. c. 10. In fact, it is clear that 25 must be added to 5 to make up the extent of a ‘house,’ which was 30 degrees.

[16.]ys like C; is lik P; miswritten illyk AB.

[17.]in is supplied from GM; ABC omit it.

[23.]second the supplied from CP; AB omit.

[32.]wel supplied from CPM; AB omit.

[36.]than] þan CM; þenne P; AB omit.

[40.]The number 10 is supplied from C; AB omit.

[42.]some folk supplied from CPG; AB omit.

[44.]yit is] AB wrongly have yit it is; but CPGM omit it.

[§ 5, l. 3.]by 2 and 2 ACG; by 3 and 3 P; left blank in B. Either reading makes sense, but it is clear that divisions representing three degrees each must have been very awkward.

[10.]of supplied from CPGM: AB omit.

[§ 6, l. 5.]est C; west A (which is absurd); west (corrected to est) B.

[9.]signe CGP; signes ABM.

[§ 10, l. 3.]than B; þan C; A has & by nyht, which is absurd.

[4, 5.]A omits day with the howr inequal of the, which is supplied from BCP; the number 30 is also supplied from BCM, as A has a blank space here; see l. 10.

[§ 11, l. 12.]The number 4 is from CP; AB omit; old edd. fourthe.

[13.]ther supplied from PM; þere C; AB omit.

[§ 12, l. 1.]the supplied from BC; A omits.

[8.]The figure 2 is from BCP; G has secunde; A omits.

[§ 14, l. 9, 10.]The last clause supplied from B.

[§ 15, l. 6.]pointe] point P; pointes A; pointz B; poyntes C; but grammar requires the singular.

[9.]the supplied from CP; AB omit.

[§ 16, l. 5.]AB wrongly insert the before Cancer; CP omit it.

[8.]y-lyke] Ilyke G; ilik P; y-like C; ilke AB; see l. 7.

[§ 17.]Latin rubric; for latitudinem (as in M) read longitudinem. l. 18. heued B; hed ACP; see sect. 16, l. 3. The word ‘the’ (rightly placed in BCMP) is, in A, wrongly placed defore ‘Aries’ instead of before ‘ende.’

[23.]second the] þe C; AB omit.

[§ 19.]Latin Rubric; for orizon (as in M) read statio.

[§ 20.]Latin Rubric; the MS. (M) transposes the words in and a, having a zodiaco in circulo, which contradicts the sense.

[§ 22.]Latin Rubric; for centri (as in M) read regionis.

[§ 23, l. 21.]The figure ‘8’ is omitted in AB.

[23.]than] A omits; thanne inserted afterwards in B.

[§ 25, l. 3.]first the] supplied from B; AC omit.

[15.]CP om. and 10 minutes.

[16.]CP om. and minutes out. For 51 degrees and 50 minutes, C has 52, þan is 52 degrees; and P has 52. þenne is .52. grees.

[19.]CP om. as I mighte prove.

[20.]the supplied from CP; AB om.

[27.]the firste degree] 10 degrees C; 10 gree P.

[28.]58 degrees and 10 minutes] almost 56 C (meaning 56 degrees); almost .56. grees P.

[29.]almost 20] almost 18 C.

[31.]thee] C om. and odde Minutes] CP om.

It thus appears that there is a second set of readings, involving a different calculation. The second set supposes the Sun to be in the 10th degree of Leo, his altitude to be 56°, and his declination 18°; the difference, viz. 38°, is the complement of the latitude. Either set of readings suits the sense, but the one in the text agrees best with the former latitude, viz. 51°. 50′.

[37.]After there, C inserts 38 grees, þat is; and omits the words of the pole, 51 degrees and 50 Minutes. But this is a mere repetition of the ‘height of the Equinoctial,’ and is obviously wrong. After pole, in l. 38, A inserts an that, which is unmeaning, and omitted in B.

[§ 26, l. 8.]Nearly all the MSS. omit from Fertherover down to right orisonte. The missing clause appears in MS. Bodley 619; I have not found it elsewhere. It is obviously correct, and agrees sufficiently closely with the conjectural addition by Mr. Brae, in his edition of Chaucer’s Astrolabe, p. 48.

[§ 27, l. 2.]second the] supplied from BCPM; A om.

[§ 28.]Latin Rubric. MS. has in recto circulo; read oblique.

[3.]set] sett C; sete P; AB omit.

[11.]these] þese C; thise B; the A.

[23.]ende] heed A; heued C. In fact, heed, heued, or hed seems to be the reading of all the MSS. and printed copies, and may have been a slip of the pen in the first instance. The reading ende is, however, amply justified by its previous occurrence, four times over, in lines 10, 13, 16, 18. We thus have

Six Northern signs. From head of Aries to end of Virgo.

Six Southern signs. From head of Libra to end of Pisces.

Six Tortuous signs. From head of Capricorn to end of Gemini.

Six Direct signs. From head of Cancer to end of Sagittarius.

Opposite ‘sagittare’ is written ‘sagittarie’ in the margin of A, probably as a correction; but it is left uncorrected in l. 27.

[§ 29, l. 3.]Turne thanne] Turne þan C; turne the thanne AB.

[9.]thou] þou C; two AB.

[14.]rewle] rule CP; miswritten rewles AB; see l. 9.

[§ 30. l. 11.]wey A; place C. After zodiak C inserts—for on þe morowe wol þe sonne be in a-noþer degre þan þan, et cetera; P inserts—For yn þe morowe wol þe sonne be yn an oþer gree, & norþer or souþer par aventure. Nothing can be plainer than that ‘the way of the sun’ in this passage means the small circle formed by the sun’s apparent path during a day; the text says expressly—‘the wey wher as the sonne wente thilke day.’ We need not argue about the impossibility of a planet being found in ‘the way of the Sun’ at midnight at the time of the Summer solstice, because Chaucer makes no assertion whatever here about the relative positions of the sun and planet; indeed, he carefully repeats ‘if’ three times. He is only concerned with defining the phrase—‘the latitude of a planet from the way of the sun’; and in every possible case, it is clear that a planet can be either (1) situate in the small circle called in the Latin rubric cursus solis, or (2) to the north of such a circle, or (3) to the south of such a circle. About this there need be no difficulty at all. It is all copied from Messahula.

[§ 31, l. 7.]azimut] azymutz ABC; cf. sect. 32, l. 8.

[§ 33, l. 2.]Azimut] Azymutz ABC; minutis P; the same error as in sect. 31, l. 7; but see sect. 32, l. 8.

[3.]second in] yn P; ABC omit.

[4.]the night] so in AB; CP om. the.

[§ 34.]English Rubric; latitude for] so in CP; latitude and for AB.

[6.]toucheth] touchiþ P; to which (sic) ABC; see sect. 27, l. 6.

[§ 35, l. 15.]After west side, AB add & yf he be on the est syde, a mere superfluous repetition; see l. 11.

[17.]sothly] soþly CP; miswritten he settes (!) AB.

[18.]hir Episicle] so in CP; by an odd mistake, AB put hire after manere, instead of before Episicle.

[§ 37, l. 10.]than] þan C; AB omit. is] AB omit; but it is obviously wanted; C varies here.

[12.]12 house next] 12 hous next C; howses nex (sic) AB.

[13.]thanne] þan C; A omits. howse] hous C; howses AB.

[17.]AB absurdly insert fro before the byginning.

[18.]first the] þe C; AB omit.

[§ 38, l. 1.]warpyng MP; werpynge C; weripinge (sic) A.

[2.]first a CP; AB omit.

[3, 4.]an euene C; a euene AB (twice).

[8.]fro the centre; i. e. above the centre. The length of the pin, measured from the centre in which it is inserted, is to be not more than a quarter of the diameter, or half the radius. This would make the ratio of the gnomon to the shadow (or radius) to be one-half, corresponding to an altitude a, where tan a = ½: i. e. to an altitude of about 26½°. As Chaucer talks about the sun’s altitude being 25½° at about 9 o’clock, at the time of the equinoxes (sect. 3), there is nothing that is particularly absurd in the text of this section. For Mr. Brae’s conjectural emendations, see p. 56 of his edition.

[16.]tak thanne] so in P; tak me thanne AB; take me þan C. But there seems no sufficient reason for thus inserting me here.

[§ 39.]At this point MS. A, which has so far, in spite of occasional errors of the scribe, afforded a very fair text, begins to break down; probably because the corrector’s hand has not touched the two concluding sections, although section 40 is much less corrupt. The result is worth recording, as it shews what we may expect to find, even in good MSS. of the Astrolabe. The section commences thus (the obvious misreadings being printed in italics):—

‘This lyne Meridional ys but a Maner descripcion or the ymagined, that passeth vpon the pooles of þis the world And by the cenyth of owre heued / And hit is the same lyne Meridional / for in what place þat any maner man [omission] any tyme of the yer / whan that the sonne schyneth ony thing of the firmament cometh to his verrey Middel lyne of the place / than is hit verrey Midday, þat we clepen owre noon,’ &c.

It seems clear that this apparent trash was produced by a careless scribe, who had a good copy before him; it is therefore not necessary to reject it all as unworthy of consideration, but it is very necessary to correct it by collation with other copies. And this is what I have done.

MS. B has almost exactly the same words; but the section is considerably better, in general sense, in MSS. C and P, for which reason I here quote from the former the whole section.

[Rawl. MS. Misc. 1370, fol. 40 b.]

Descripcioun of þe meridional lyne, of þe longitudes and latitudes of Citees and townes, as wel as of a (sic) clymatz.

39.conclusio. This lyne meridional is but a maner discripcion or lyne ymagyned, þat passeþ upon þe pooles of þis worlde, and by þe Cenith of oure heued. ¶ And yt is cleped þe lyne meridional, for in what place þat any man ys at any time of þe Ȝere, whan þat þe sonne by meuynge of þe firmament come to his uerrey meridian place / þan is it þe uerrey mydday þat we clepe none, as to þilke man. And þerefore is yt cleped þe lyne of mydday. And nota, þat euermo of any .2. citees or of 2 townes, of which þat oo towne a-procheþ neer þe est þan doþ þe oþer towne, trust wel þat þilke townes han diuerse meridians. Nota also, þat þe arche of þe equinoxial, þat is contened or bownded by-twixe þe two meridians, is cleped þe longitude of þe towne. ¶ & Ȝif so be / þat two townes haue I-like meridian or one merydian, ¶ Than ys þe distaunce of hem boþe I-like fer from þe est, & þe contrarye. And in þis maner þei chaunge not her meridyan, but soþly, þei chaungen her almykanteras, For þe enhaunsynge of þe pool / and þe distaunce of þe sonne. ¶ The longitude of a clymate ys a lyne ymagyned fro þe est to þe west, I-like distaunte fro þe equinoxial. ¶ The latitude of a clymat may be cleped þe space of þe erþe fro þe by-gynnynge of þe first clymat unto þe ende of þe same clymat / euene-directe a-Ȝens þe pool artyke. ¶ Thus seyn somme auctours / and somme clerkes seyn / þat Ȝif men clepen þe latitude of a contrey1 , þe arche mer[i]dian þat is contened or intercept by-twixe þe Cenyth & þe equinoxial; þan sey þei þat þe distaunce fro þe equinoxial unto þe ende of a clymat, euene2 a-gaynes þe pool artik, is þe latitude off þat climat2 forsoþe.

The corrections made in this section are here fully described.

[1.]of lyne P; of a line I; or lyne C; or the AB.

[2.]this] þis the AB, absurdly; CP omit the, rightly.

[3.]ycleped the] y-clupid þe P; cleped þe C; the same (sic) AB.

[4.]is at; supplied from PCI; AB omit.

[56.]hir] his ABC. a] ABC omit.

[57.]At the word houre four of the best MSS. break off, viz. MSS. ABCE, although E adds one more section, viz. sect. 46; others come to a sudden end even sooner, viz. MSS. DFGHK. But MS. P carries us on to the end of sect. 43, and supplies the words—þu shalt do wel ynow, as in the old editions.

[§ 41. 7.]betwixe] be M (wrongly); betwixe R; by-twyx L.

M inserts & before to þe altitude; a mere slip. For; miswritten Fro M.

[8.]thridde; miswritten ridde M; þrydde R.

[13.]LM wrongly place of after the heyȜt instead of before it.

[§ 42, l. 2.]see] so in LR; miswritten sette M; see sect. 41, l. 4.

[3.]second I] so L; y R; M omits.

[8.]M omits as, above, and is þe; L has 12 passethe 6 the.

[11.]seest] so in LR; miswritten settest M.

[12.]60] so in LNR; sexe M.

[13.]M omits from 10 is to 10 feet, which is supplied from NLPR.

[14.]For] so in LNR; fro M.

[15.]For 2, M has 6; so also R. For 3, M has 4.

[16.]For 2, M has 6; for 6, M has 2; and the words and 3 is 4 partyes of 12 are omitted, though L has—& 4 is the thrid partye of 12.

[17.]betwen R] by-twene L; bitwixe P; miswritten be M; cf. sect. 41, 7.

[19.]thre R] 3 LP; miswritten þe M.

[§ 43.]Rubric in M, Umbra Versa; obviously a mistake for Recta. The error is repeated in l. 1. LPR rightly read Recta.

[3.]M omits 1, which is supplied from LPR; see l. 5.

[11.]After heythe (as in M), LNR add to thyn eye. In place of lines 9-11, P has—& so of alle oþer, &c.

[§ 44.]From MS. Digby 72 (N). Also in LMOR.

[2.]fro] so in LO; for M.

[3.]into] so in L; in M. for] so in O; fro M.

[6.]Ȝeris M; LNO omit.

[7.]tabelis NO; table M; tables L.

[8.]where L; qwere O; wheþer N.

[9.]loke LM; N omits.

[11, 2.]NM omit from or what to or; supplied from O, which has—or qwat nombre þat euere it be, tyl þe tyme þat þou come to 20, or 40, or 60. I have merely turned qwat into what, as in L, which also has this insertion.

[13.]wreten N; the alteration to wryte is my own; see l. 23.

under] so in L; vndirneþe M.

[14.]to-geder] too-geder M; miswritten to 2 degreis N; to the 2 degrees L.

[15.]hast M; miswritten laste N; last L.

[16.]that (1); supplied from M; LN omit. For 1 (as in M) LN have 10.

[21.]to-gedere M; to the degreis N; 2 grees O; to degrees L.

[22.]that (2); supplied from M; LNO omit.

lasse] passid LNO; M omits. Of course passid is wrong, and equally of course lasse is right; see ll. 5, 6 above, and l. 25 below.

[25.]that] so in L; þat MO; if hit N.

[27.]entringe] entre M; entre L. ther] so in M; miswritten the Ȝere N; the Ȝeer L.

[30.]merydie LM; merdie N.

[32.]for LM; fro N (twice).

[34.]thaȜthe N; have tauȜt M; have tawȜt O; haue tauht L.

[36.]the (1); supplied from M; LNO omit.

with the] so in M; wyche N; see l. 36.

[40.]in (2)] in-to N; yn M.

[§ 45.]From MS. Digby 72 (N); also in LOR; but not in M.

[4.]that N; the L; þe O (after wryte in l. 3).

[6.]wrytoun O; Iwyton N. But L has I wold wyttyn; read—I wolde witen precise my rote; cf. ll. 19, 30.

[8.]1397] miswritten 1391 LN; O has 1391, corrected to 1397; see l. 3.

[11.]soȜth N; sowte O; sowthe L; read soghte.

[14.]vnder N; vndyr-nethe O; vndre-nethe L.

[20, 1.]oþer in any oþer tyme or monyth N; or any oder tymys or monthys O; or in eny other moneth L.

[27.]adde] supplied from L; NO omit. There is no doubt about it, for see l. 16.

[31.]wete the] so in O; wete thi L; miswritten with thy N; see l. 19.

[35.]and (3)] supplied from LO; N omits.

[§ 46, 5, 6.]þat same E; þe same S.

[10.]it S; E omits.

[13.]þat same (om. tyme) E; þe same tyme S.

[16.]þou þan esely E; than shallt thou easly S.

[17.]tyme of E; tyme of the S.

[20.]S meve (for bringe furþe).

[§ 41a.]This and the remaining sections are certainly spurious. They occur in LMNR, the first being also found in O. The text of 41a-42b is from M.

[3.]hast] supplied from LR; M omits.

[§ 42a, 1.]heyth by þy N; heyth by the L; heythe bi þi R; M om.

[4.]lyk] lykk M; L. omits. mete] mette M; mett L.

[9.]is L; miswritten hys M.

[§ 43a, 1.]nat] not R; nott L; M omits; see the footnote. In the rubric, M has versam; but L has the rubric—Vmbra Recta.

[§ 42b, 5.]as] so in LR; miswritten & M.

[6.]4 is supplied from LR; M omits.

[Prologue, l. 1.]Lowis was at this time (1391) ten years old (see l. 18); he was therefore born in 1381, whence it is possible that his mother was the Cecilia de Chaumpaigne who, on May 1, 1380, released the poet from all liability de raptu meo. This is, of course, a mere conjecture. Probably Lowis died young, as nothing more is known concerning him.

[5.]philosofre; possibly Cicero. ‘Haec igitur prima lex amicitiae sanciatur, ut . . amicorum causâ honesta faciamus’; Lælius, cap. xiii.

[7.]suffisaunt, sufficiently good. In the best instruments, the Almicanteras, or circles of altitude, were drawn at distances of one degree only; in less-carefully made instruments, they were drawn at distances of two degrees. The one given to his son by Chaucer was one of the latter; see Part I, sect. 18, l. 8.

[10.]a certein, i. e. a certain number; but the word nombre need not be repeated; cf. a certein holes, Pt. I. sect. 13, l. 2, and see the very expression in the Milleres Tale, l. 7 (A 3193).

[21.]suffyse, let them suffice.

[32.]Repeated from Ho. Fame, 861-2, q. v.

[62.]‘Nicolaus de Lynna, i. e. of Lynn, in Norfolk, was a noted astrologer in the reign of Edward III., and was himself a writer of a treatise on the Astrolabe. See Bale—who mentions “Joannes Sombe” as the collaborateur of Nicolaus—“Istos ob eruditionem multiplicem, non vulgaribus in suo Astrolabio celebrat laudibus Galfridus Chaucer poeta lepidissimus;” Bale (edit. 1548), p. 152.’—Note by Mr. Brae, p. 21 of his edition of the Astrolabe.

Warton says that ‘John Some and Nicholas Lynne’ were both Carmelite friars, and wrote calendars constructed for the meridian of Oxford. He adds that Nicholas Lynne is said to have made several voyages to the most northerly parts of the world, charts of which he presented to Edward III. These charts are, however, lost. See Hakluyt’s Voyages, i. 121, ed. 1598; Warton, Hist. E. P. ii. 357; ed. 1871.

Tyrwhitt, in his Glossary to Chaucer, s. v. Somer, has the following. ‘The Kalendar of John Somer is extant in MS. Cotton, Vesp. E. vii. It is calculated for 140 years from 1367, the year of the birth of Richard II., and is said, in the introduction, to have been published in 1380, at the instance of Joan, mother to the king. The Kalendar of Nicholas Lenne, or Lynne, was calculated for 76 years from 1387. Tanner in v. Nicolaus Linensis. The story there quoted from Hakluit of a voyage made by this Nicholas in 1360 ad insulas septentrionales antehac Europæis incognitas, and of a book written by him to describe these countries a gradu .54. usque ad polum, is a mere fable: as appears from the very authorities which Hakluit has produced in support of it.’ It seems probable, therefore, that the ‘charts’ which Warton says are ‘lost’ were never in existence at all. The false spelling ‘Some’ no doubt arose from neglecting the curl of contraction in Somere.

[Part I. § 5, l. 5.]the remenant, &c. i.e. the rest of this line (drawn, as I said,) from the foresaid cross to the border. This appears awkward, and we should have expected ‘fro the forseide centre,’ as Mr. Brae suggests; but there is no authority for making the alteration. As the reading stands, we must put no comma after ‘this lyne,’ but read right on without a pause.

[8.]principals. It it not unusual to find adjectives of French origin retaining s in the plural; only they commonly follow their nouns when thus spelt. Cf. lettres capitals, i. 16. 8; sterres fixes, i. 21. 4. On the other hand, we find principal cercles, i. 17. 34.

[§ 7. 4.]noumbres of augrim; Arabic numerals. The degrees of the border are said to contain 4 minutes of time, whilst the degrees of the signs are divided into minutes and seconds of angular measurement, the degrees in each case being the same. There is no confusion in practice between these, because the former are used in measuring time, the latter in measuring angles.

[§ 8. 9.]Alkabucius; i. e. (says Warton, Hist. E. P. ii. 357, ed. 1871) Abdilazi Alchabitius, whose Introductiorium ad scientiam judicialem astronomiæ was printed in 1473, and afterwards. Mr. Brae quotes the very passage to which Chaucer refers, which I here quote from the edition of 1482, as described in my note to l. 119 of The Compleint of Mars (see vol. i. p. 500); viz. ‘Unumquodque istorum signorum diuiditur in 30 partes equales, que gradus vocantur. Et gradus diuiditur in 60 minuta; et minutum in 60 secunda; et secundum in 60 tertia. Similiterque sequuntur quarta, scilicet et quinta, ascendendo usque ad infinita;’ Alchabitii Differentia Prima.

These minute subdivisions were never used; it was a mere affectation of accuracy, the like of which was never attained.

[§ 10. 5.]in Arabiens, amongst the Arabians. But he goes on to speak only of the Roman names of the months. Yet I may observe that in MS. Ii. 3. 3, at fol. 97, the Arabian, Syrian, and Egyptian names of the months are given as well as the Roman.

[§ 16. 12.]& every minut 60 secoundes; i. e. every minute contains 60 seconds. The sentence, in fact, merely comes to this. ‘Every degree of the border contains four minutes (of time), and every minute (of time) contains sixty seconds (of time).’ This is consistent and intelligible. Mr. Brae proposes to read ‘four seconds’; this would mean that ‘every degree of the border contains four minutes (of time), and every minute (of the border) contains four seconds (of time).’ Both statements are true; but, in the latter case, Chaucer should have repeated the words ‘of the bordure.’ However this may be, the proposed emendation lacks authority, although the reprint of Speght changed ‘lx’ into ‘fourtie,’ which comes near to ‘four.’ But the reprint of Speght is of no value at all. See Mr. Brae’s preface, p. 4, for the defence of his proposed emendation, which is entirely needless.

[§ 17. 6.]Ptholome. The St. John’s MS. has ptolomeys almagest. ‘Almagest, a name given by the Arabs to the μεγάλη σύνταξις, or great collection, the celebrated work of Ptolemy, the astronomer of Alexandria [floruit ad 140-160]. It was translated into Arabic about the year ad 827, under the patronage of the Caliph Al Mamun, by the Jew Alhazen ben Joseph, and the Christian Sergius. The word is the Arabic article al prefixed to the Greek megistus, “greatest,” a name probably derived from the title of the work itself, or, as we may judge from the superlative adjective, partly from the estimation in which it was held.’—English Cyclopædia: Arts and Sciences, i. 223. The Almagest ‘was in thirteen books. Ptolemy wrote also four books of judicial astrology. He was an Egyptian astrologist, and flourished under Marcus Antoninus. He is mentioned in the Sompnour’s Tale [D 2289], and the Wif of Bathes Prologue, ll. 182, 324.’—Warton, Hist. E. P. ii. 356, ed. 1871. The word almagest occurs in the Milleres Tale, near the beginning (A 3208), and twice in the Wif of Bathes Prologue (D 183, 325).

Chaucer says the obliquity of the ecliptic, according to Ptolemy, was 23° 50′. The exact value, according to Ptolemy, was 23° 51′ 20″; Almagest, lib. i. c. 13. But Chaucer did not care about the odd degree, and gives it nearly enough. See note to ii. 25. 19.

8. tropos, a turning; Chaucer gives it the sense of agaynward, i. e. in a returning direction.

14. The equinoctial was supposed to revolve, because it was the ‘girdle’ of the primum mobile, and turned with it. See note below to l. 28.

14, 15. ‘As I have shewed thee in the solid sphere.’ This is interesting, as shewing that Chaucer had already given his son some lessons on the motions of the heavenly bodies, before writing this treatise.

[27.]angulus. We should rather have expected the word spera or sphera; cf. ‘the sper solide’ above, l. 15.

[28.]‘And observe, that this first moving (primus motus) is so called from the first movable (primum mobile) of the eighth sphere, which moving or motion is from East to West,’ &c. There is an apparent confusion in this, because the primum mobile was the ninth sphere see Plate V, fig. 10); but it may be called the movable of the eighth, as giving motion to it. An attempt was made to explain the movements of the heavenly bodies by imagining the earth to be in the centre, surrounded by a series of concentric spheres, or rather shells, like the coats of an onion. Of these the seven innermost, all revolving with different velocities, each carried with it a planet. Beyond these was an eighth sphere, which was at first supposed to be divided into two parts, the inner part being the firmamentum, and the outer part the primum mobile; hence the primum mobile might have been called ‘the first moving of the eighth sphere,’ as accounting for the more important part of the motion of the said sphere. It is simpler, however, to make these distinct, in which case the eighth sphere is the firmamentum or sphæra stellarum fixarum, which was supposed to have a very slow motion from West to East round the poles of the zodiac to account for the precession of the equinoxes, whilst the ninth sphere, or primum mobile, whirled round from East to West once in 24 hours, carrying all the inner spheres with it, by which means the ancients accounted for the diurnal revolution. This ninth sphere had for its poles the north and south poles of the heavens, and its ‘girdle’ (or great circle equidistant from the poles) was the equator itself. Hence the equator is here called the ‘girdle of the first moving.’ As the planetary spheres revolved in an opposite direction, thus accounting for the forward motion of the sun and planets in the ecliptic or near it, the primum mobile was considered to revolve in a backward or unnatural direction, and hence Chaucer’s apostrophe to it (Man of Lawes Tale, B 295):—

• ‘O firste moevyng cruel firmament,
• With thy diurnal sweigh that crowdest ay
• And hurlest all from Est til Occident,
• That naturelly wolde holde another way.’

That is—‘O thou primum mobile, thou cruel firmament, that with thy diurnal revolution (or revolution once in 24 hours round the axis of the equator) continually forcest along and whirlest all the celestial bodies from East to West, which naturally would wish to follow the course of the sun in the zodiac from West to East.’ This is well illustrated by a sidenote in the Ellesmere MS. to the passage in question, to this effect:—‘Vnde Ptholomeus, libro i. cap. 8. Primi motus celi duo sunt, quorum vnus est qui mouet totum semper ab Oriente in Occidentem vno modo super orbes, &c. Item aliter vero motus est qui mouet orbem stellarum currencium contra motum primum, videlicet, ab Occidente in Orientum super alios duos polos1 .’ That is, the two chief motions are that of the primum mobile, which carries everything round from East to West, and that of the fixed stars, which is a slow motion from West to East round the axis of the zodiac, to account for precession. This exactly explains the well-known passage in the Frankeleines Tale (C. T., F 1280):—

• ‘And by his eighte spere in his werking,
• He knew ful wel how fer Alnath was shove
• Fro the heed of thilke fixe Aries above
• That in the ninthe spere considered is.’

Here the eight spheres are the eight inner spheres which revolve round the axis of the zodiac in an easterly direction, whilst the ninth sphere, or primum mobile, contained both the theoretical or fixed first point of Aries from which measurements were made, and also the signs of the zodiac as distinct from the constellations. But Alnath, being an actual star, viz, α Arietis2 , was in the eighth sphere; and the distance between its position and that of the first point of Aries at any time afforded a measure of the amount of precession. Mr. Brae rightly remarks that Tyrwhitt’s readings in this passage are correct (except that eighte speres should be eightespere), and those of Mr. Wright and Dr. Morris (from the Harleian MS.) are incorrect.

It may be as well to add that a later refinement was to insert a crystalline sphere, to account for the precession; so that the order stood thus: seven spheres of planets; the eighth, of fixed stars; the ninth, or crystalline; the tenth, or primum mobile; and, beyond these, an empyræan or theological heaven, so to speak, due to no astronomical wants, but used to express the place of residence of celestial beings3 . Hence the passage in Milton, P. L. iii. 481:—

• ‘They pass the planets seven, and pass the fix’d,
• And that crystalline sphere whose balance weighs
• The trepidation talk’d, and that first mov’d.’

i. e. They pass the seven planetary spheres; then the sphere of fixed stars; then the crystalline or transparent one, whose swaying motion or libration measures the amount of the precession and nutation so often talked of; and then, the sphere of the primum mobile itself. But Milton clearly himself believed in the Copernican system; see Paradise Lost, viii. 121-140, where the primum mobile is described in the lines—

• ‘that swift
• Nocturnal and diurnal rhomb supposed,
• Invisible else above all stars, the wheel
• Of day and night.’

[§ 18. 8.]compowned by 2 & 2. This means that in the best astrolabes, every almicantarath for every degree of latitude was marked; as may be seen in Metius. In others, including the one given by Chaucer to his son, they were marked only for every other degree. See Part II. sect. 5, l. 2.

[§ 19. 7.]cenith, as here used, has a totally different meaning from that of senith, in l. 1 above. The senith in l. 1 is what we still call the zenith; but the cenith in l. 7 means the point of the horizon denoting the sun’s place in azimuth. Contrary to what one might expect, the latter is the true original meaning, as the word zenith is corrupted from the root of the word which we now spell azimuth. The Arabic as-sant is a way or path; al-samt, a point of the horizon, and, secondly, an azimuthal circle. The plural of al-samt is assumūt, whence azimuth. But zenith is a corruption of semt, from samt al-rās, the Arabic name of the vertex of heaven (rās meaning a head); and the qualifying al-rās, the most important part of the phrase, has been improperly dropped. So far from the reading cenith being wrong here, it is most entirely right, and may be found (better spelt cenit) in the same sense in Messahala. See p. 213, second footnote. For cenith, some late copies have signet, evidently taken from the Latin word signum. They make the same mistake even in l. 12 of section 18.

[§ 21. 4.]sterres fixes, fixed stars; here the s again appears in a plural adjective of French derivation; see note above, to § 5. 8. In MSS. Ii. 3. 3 and Ii. 1. 13 in the Cambridge University Library, is an interesting list of the 49 stars most usually placed upon the Astrolabe. The stars which are represented by the points of the tongues in Fig. 2 are the same as those in the diagram from which Fig. 2 is copied, the original of which is in MS. A. I have slightly altered the positions of the points of the tongues, to make them somewhat more correct. The following is the list of the stars there shewn; most of their names are written in the MS. Cf. footnote on p. 186.

Within the Zodiac. In Aries, Mirach, or β Andromedæ, shewn by a short tongue above Aries; in Taurus, Algol, or β Persei, as marked; in Libra, Aliot or Alioth, i. e. ε Ursæ Majoris (the third horse, next the cart, in Charles’s Wain), as marked; also Alramech, Arcturus, or α Boötis, shewn by the tongue projecting above Libra; in Scorpio, Alpheta, Alphecca, or α Coronæ Borealis, as marked; in Sagittarius, Raz Alhagus, or α Ophiuchi, near Alpheta; in Capricornus, Altair or α Aquilæ and Vega or α Lyræ, as marked, whilst near Vega is the unmarked Arided, or α Cygni; and in Pisces, Markab or α Pegasi.

Without the Zodiac. In Aries, under Oriens, the slight projection marks β Ceti or Deneb Kaitos, the Whale’s Tail, and the next curiously shaped projection (with side-tongues probably referring to other stars) means Batnkaitos, the Whale’s Belly, apparently ζ Ceti; next come the long tongue for Menkar or α Ceti, the Whale’s Nose; the star Aldebaran or Bull’s Eye, α Tauri; Rigel or β Orionis, Orion’s Foot; Alhabor or Sirius, the Dog-star, marked by a rude drawing of a dog’s head, the star itself being at the tip of his tongue; then Algomeisa, Procyon, or α Canis Minoris, marked by a tongue pointing to the left, whilst the long broad tongue pointing upwards is Regulus, Kalbalased, or α Leonis; the small tongue above the letter I in the border is Alphard or Cor Hydræ. Above Occidens, in Libra, the first tongue is Algorab or δ Corvi, and the next Spica Virginis or Azimech; close to the 8th degree of Scorpio is α Libræ, and close to the beginning of Sagittarius is a small head, denoting the Scorpion, at the tip of the tongue of which is the bright Kalbalacrab or Antares. The last, a projection below the letter X, is Deneb Algebi or the Goat’s Tail, i. e. δ Capricorni.

[7.]That is, the little point at the end of each tongue of metal is technically called the ‘centre’ of the star, and denotes its exact position.

[9.]The stars of the North are those to the North of the zodiac, not of the equator.

[12.]Aldeberan, &c.; the stars Aldebaran (α Tauri) and Algomeisa (α Canis Minoris) are called stars of the south, because they are to the south of the ecliptic; but as they are meanwhile (see Fig. 2) also to the north of the equator, they of course rise to the N. of the Eastern point of the horizon. The longitude of stars was always measured along the ecliptic, which is denoted in Fig. 2 by the outermost circle of the metal ring on which the names of the signs are written.

In one of the tracts in MS. G (dated ad 1486), p. 30, we find ‘Aldebaran, in the first gre of geminis (sic), of the nature of Mars and Venus’; and ‘Algomeisa, canis minor, in the xvij gre of Cancer, of the nature of Mars and Mercury.’

[29.]Amiddes, &c. Observe that the Ecliptic line in the midst of the celestial zodiac, a belt 12° broad, is on the outer edge of the zodiac as shewn in the astrolabe, which is only 6° broad and shews only the northern half of that belt. The ‘way of the sun’ is elsewhere used of the sun’s apparent diurnal path (see Part ii. sect. 30); but it here refers, as is more usual, to the annual path.

[34.]streitnes, narrowness, closeness, smallness of size. In Fig. 2, I have marked every degree in the southern half of the zodiac, but only every fifth degree in the northern, in order to avoid an appearance of crowding in so small a figure. In Chaucer’s own Astrolabe, every other degree was marked all round.

[40.]Here Chaucer gives at least three reasons for the name of ‘zodiac.’ The true one is the second, ‘for that the sterres that ben there fixed ben disposed in signes of bestes, or shape like bestes.’ But these imaginary shapes are very absurd and arbitrary.

[50.]Not only the influences here assigned to the signs, but others due to planets, may be found in ‘Porphyrii Philosophi introductio in Claudii Ptolomæi opus de affectibus astrorum,’ fol. Basileæ, n. d. p. 198. I here add a few extracts from the MS. in Trinity College, Cambridge (marked R. 15. 18), to shew the nature of the old astrology. I choose them with especial reference to Aries. The other signs are spoken of in a similar manner. ‘It is principally to be considered that the signes of hevyn haue theire strength and propre significacioun vpon the membris of eny man; as, Aries hath respect to the hed, taurus to the neck, geminis (sic) the Armys, Cancer the brest, leo the hert, virgo the bowels, &c.; as it shall shew in the Chapiters folowyng. Secundarily it is to be noted that plotholomee (sic) saith, that to touche with instrument of yroun while the mone is in the signe of the same membre, is for to be dred; let the surgen beware, and the letter of blode, let hym be aferd to touche that membre with yrene, in the which the mone shal be.’—MS. G; Tract C. p. 12.

‘Thenne Aries hath respect to the hed; And this signe is hote and dry, fiery & colerik. Saturne hath ij witnes in Ariete, a triplicitate and a terme. Jubiter also hath ij, a triplicitate and a terme. Mars hath iij testimonials or iij fortitudis in Ariete, A hows, A face, and A terme. The sonne hath iij fortitudis in Ariete, scilicet, an exaltacioun, a triplicite, and a face. Venus hath ij testimonials, A terme and a face. Mercury hath one testymony, that is to sey, a terme. And luna in Ariete hath no testimoniall. For the which it is to know, that the influens of the planetis may be fortyfied v maner of wayes. And these v maner be called v fortitudis of planetis, or testimonials, which be these: domus, exaltacio, triplicitas, terminus, and facies. Domus gevith to a planet v fortitudis; And a planet in his hows is lyke a kynge in his hall, And in the high trone of his glorie. A planet in his exaltacioun is lyke a kynge when he is crowned. A planet in his triplicite is like a kynge in honour, Amonge his sencible people. A planet in his terme is As a mann amonges his kynnesmenn And fryndis. Facies gyvith to a planet that thyng the which rowme gyvith to a maistre. Wherfore facies gyvith only on fortitude, Terminus ij, Triplicitas iij, Exaltacio iiij, And domus v. And for the more clere declaracioun, the dignytes of planettis in signes be comprehendid in this figure ensuynge, &c.1 ’—Same MS., Tract C. p. 13.

‘The dygnytes of planetis in the signes, most speciall they be to be noted in iudicials. When the mone is in Ariete, it is not gode, but vtterly to be exshewed, both for seke And disesid, for to shafe theire hede or to boist in the eris or in the nek; nor loke þou let no blode in the vayn of the hede. How-be-it, benyficiall it is to begynne euery worke that þou woldest bryng aboute sone. But that thynge that is stabill ought to be eschewed. In this signe it is necessary to dele with noble estatis And rich men, And for to go in-to A bayne [bath]1 .’—Same MS., Tract C. p. 14.

[54, 5.]See Prologue, l. 73. As the zodiak is here called a part of the eighth sphere, so we have been before told that the equinoctial is the girdle of the ninth sphere; see note above to sect. 17. l. 28.

[57.]evene parties, equal parts. That is, the equinoctial bisects the zodiac. But the northern half looks much smaller than the southern on the Astrolabe, owing to the manner in which the zodiac is there represented, viz. by projection on the plane of the equator.

[Part II. § 1.]Rubric. hir cours. The gender of the sun was feminine in Anglo-Saxon, and that of the moon masculine; but in Chaucer’s time, the gender was very variable, owing to the influence of Latin and French.

[§ 3.]Between sections 2 and 3, a section is inserted in the late copies, which merely repeats section 1, and is clearly spurious. It does not appear at all in the best MSS.; though it is found in the black-letter editions. I quote it here from MS. L.

‘To knowe the degre of thyn sonne in thyn zodiak by the days in the baksyde off the Astrolabye.

‘[T]hanne iff þou wylte wete thatt / rekyn & knowe / qwych is the day off the monyth thatt thow arte ynne, & ley thy rewle of thy astrolabye, that is to sey, the allydatha, vpon þe day in the kalendre off the Astrolabye, & he schall schewe the thy degree of the sonne.’

[26, 7.]After ‘assendent,’ the following additional paragraph occurs in MS. Bodley 619; fol. 21. It is worthy of notice, because the original of it appears in Messahala’s treatise, with the title ‘De noticia stellarum incognitarum positarum in astrolabio.’ The paragraph runs thus:—

‘Nota. þat by þis conclusioun þou may knowe also where ben at þat same tyme alle oþir sterres fixed þat ben sette in thin Astrelabie, and in what place of þe firmament; And also her arising in thy orizonte, and how longe þat thei wol ben aboue þe erthe wiþ þe Arke of þe nyght / And loke euermore hov many degrees þou fynde eny sterre at þat tyme sitting vpon þin Almycanteras, and vp-on as many degrees sette þou þe reule vpon þe altitude in þe bordere; And by the mediacioun of þy eye through þe .2. smale holes shalt thou se þe same sterre by the same altitude aforseid, And so by this conclusioun may þou redely knowe whiche is oo sterre from a-noþer in the firmament / for as many as ben in the Astrelabie. For by þat same altitude shal thou se that same sterre, & non othir / for þere ne wolle non othir altitude accorde þerto.’

[30.]Alhabor; i. e. Sirius or the Dog-star, as is evident from the fact of its being represented by a dog’s head on the Astrolabe; see also the table of stars marked on the Astrolabe (in MS. Camb. Univ. Lib. Ii. 3. 3, fol. 70, back), which gives the declination 15° S, the latitude 39° S, and places the star in Cancer. It is also plainly described in the same table as being ‘in ore canis,’ so that it is difficult to resist the conclusion of the identity of Alhabor and Sirius. Mr. Brae, following later copies that have different readings of the numbers employed, identifies Alhabor with Rigel or β Orionis. This is impossible, from the fact that Rigel and Alhabor both occur in the diagrams and tables; see, for instance, Fig. 2. It is true that Rigel was sometimes called Algebar, but Alhabor stands rather for the Arabic Al-’abūr. The Arabic name for the constellation Canis Major was Al-kalb al-akbar, ‘greater dog,’ as distinguished from Al-kalb al-asghar, or ‘lesser dog’; and the star α Canis Majoris was called Al-shi’ra al-’abūr, the former of which terms represented the Greek σείριος (Sirius), whilst from the latter (al-’abūr) we have our Alhabor. See Ideler, Über den Ursprung und die Bedeutung der Sternnamen, pp. 237, 256.

[§ 4.]‘The houses [in astrology] have different powers. The strongest of all these is the first, which contains the part of the heaven about to rise: this is called the ascendant; and the point of the ecliptic which is just rising is called the horoscope.’—English Encyclopædia; art. Astrology.

[21.]In the English Cyclopædia, art. Astrology, a quotation is given from an astrological work, in reply to the question whether the ‘querent’ should succeed as a cattle-dealer. It contains some words very similar to Chaucer’s. ‘If the lord of the sixth be in quartile, or in opposition to the dispositor of the part of Fortune, or the Moon, the querent cannot thrive by dealing in small cattle. The same if the lord of the sixth be afflicted either by Saturn, Mars, or the Dragon’s Tail; or be found either retrograde, combust, cadent, or peregrine. [See l. 33.] The Dragon’s Tail and Mars shew much loss therein by knaves and thieves, and ill bargains, &c.; and Saturn denotes much damage by the rot or murrain.’ The evil influence of the Dragon’s Tail is treated of in the last chapter of ‘Hermetis Philosophi de revolutionibus nativitatum,’ fol. Basileæ; n. d.

[32.]‘May seen the ascendant.’ Cf. ‘Cum dominator ascendens viderit, res quæ occulta est secundum ascendentis naturam erit; quod si non videt, illud erit secundum naturam loci in quo ipse est dominator’; Cl. Ptolemæi Centiloquium; sect. 90.

[33.]combust, said of a planet when its light is quenched by being too near the sun. Tyrwhitt, in his Glossary, says that it is used when the planet is not more than 8½ degrees distant from the sun. Cf. Troilus, iii. 717, and the note.

[40.]Face. See note to Part I. sect. 21. l. 50 (p. 359). The late copies are very incorrect hereabouts.

[§ 6. 9.]Mr. Brae well calls attention here to the absurd errors in the printed copies. Thynne has ‘in the 320 signe,’ and Speght ‘in the xxiii signe.’ The signs of the zodiac are only twelve, and the one opposite to the 1st is the 7th.

[§ 8.]I see no reason for supposing this proposition to be an interpolation, as Mr. Brae suggests. Though similar to § 11, it is not identical with it. Moreover, it occurs in Messahala.

[§ 9. 2.]the chapitre beforn, i. e. a previous chapter, viz. in sect. 6. The expression supplies no argument for altering the order of the ‘conclusions.’

[4.]same manere, i. e. a like manner. The ‘vulgar night’ clearly means that the quantity of the ‘crepuscules’ must be subtracted from the ‘arch of the night.’

[§ 13. 5.]cours, course; heyest cours, highest point of the path. Late copies have lyne; for which Mr. Brae suggested degre.

[§ 14. 6.]but 2 degrees. Suppose the sun’s midday altitude is 49°, in latitude 52°. Then the co-latitude is 38°, and the sun’s declination 11° North. This corresponds nearly (roughly speaking) to the 1st degrees of Taurus and Virgo. Which is right can ‘lightly’ be known by the time of year, for the sun cannot be in Virgo if the month be April. Compare sect. 15.

[§ 17.]This conclusion, as pointed out in the footnote, is not correct in theory, but can be made nearly so in practice, by taking the two altitudes very near the meridian. This is directly implied in the words ‘passeth any-thing the sowth westward,’ i. e. passes ever so little westward of the south line; cf. note below to 38. 10. Consequently, the first observation must also be taken very near the meridian.

[25.]site, situation. Late copies, sight. This proves that the word site is Chaucerian, and clears up the reading in Ho. Fame, 1114.

[§ 18.]Instead of reckoning a star’s right ascension by referring it to the equator, it was reckoned by observing the degree of the zodiac which southed along with it. This is expressed in the first ‘Table of fixed stars’ in MS. Camb. Univ. Lib. li. 3. 3 (fol. 70, back) by the phrase ‘cum gradibus, quibus celum mediant’; the other co-ordinate of position was the star’s declination from the equator, as in the modern method. The ancients also used the co-ordinates of longitude and latitude of a star, the longitude being reckoned along the ecliptic, and the latitude along great circles through the poles of the ecliptic; as appears from the second Table in the same MS.

[§ 19. 6.]equinoxial. This, as explained in the footnote, should be ‘ecliptik’; but I can find no MS. authority for the alteration, though the correction is practically made in l. 13.

[§ 22. 13.]place. Late copies and old editions, planet; absurdly. Latitudes of several places are given in old Latin MSS. They are frequently incorrect.

[§ 23. 3.]The star A is shewn by the numbers to be the Pole-star, and is obviously the one to be observed in order to find the altitude of the Pole. What the star F is, is of no consequence. The numbers used in other copies are different, and much less satisfactory. That the star A is the Pole-star or some star near the pole in this ‘conclusion’ is rendered probable also by the wording of the next ‘conclusion’; which extends the working of it to the case of any other star, provided it be a star that never sets.

[§ 25. 19.]When Chaucer says that the latitude of Oxford is ‘certain minutes less,’ he probably means no more than that the latitude of Oxford was 51 degrees and 50 minutes, as in the text. For I suspect the original reading of the passage made the sun’s altitude 38 degrees only, and the latitude 52 degrees; indeed, the passage stands so in MSS. C and P, both good authorities. But he added the statement that the latitude of Oxford was less than 52 degrees. It is probable that, on second thoughts, he put in the number of minutes, and forgot to strike out the clause ‘I sey nat this,’ &c., which was no longer necessary. Minutes were seldom reckoned otherwise than by tens; ‘a few minutes less than 50’ (say 47) is a refinement to which the ancients seldom attained. Hence the amount of 10 minutes is vaguely spoken of in l. 31 as ‘odde Minutes.’ Minutes were clearly not much considered. In the present case, we are assisted by Chaucer’s express statement in sect. 22. l. 6. The true latitude of Oxford is between 51° 45′ and 51° 46′.

[§ 26. 8-11.]It is singular that this sentence, obviously wanted, should appear only in one MS., and has, accordingly, been omitted in all previous editions. There can be no doubt about the genuineness of it, as it so exactly gives the right sense, and happily supplies the words ‘right orisonte’ in l. 11; thus enabling the author to say, as in l. 21 he does say—‘this forseid righte orisonte.’

[16.]this figure. Here occurs, in some of the MSS., a diagram representing a circle, i. e. a disc of the astrolabe, with straight lines drawn across it from left to right.

[17.]assensiouns in the righte cercle. This exactly answers to our modern ‘right ascension.’ We hence obtain the true origin of the phrase. ‘Right ascension’ was, originally, the ascension of stars at places situate on the equator, and was most conveniently measured along the equatorial circle, by observation of the times of transit of the various stars across the meridian. In other latitudes, the ascension of every degree of the zodiac could be easily tabulated by observing what degree of the equator came to the meridian with the said degree of the zodiac; see l. 20. It hence appears that, whilst persisting in using ‘longitudes’ and reckoning along the zodiac, the ancients were obliged, in practice, to refer the degrees of longitude to the equator. The modern method of recognizing this necessity, and registering right ascensions as of more importance than longitudes, is a great improvement. The ancients were restrained from it by their unnecessary reverence for the zodiac. Cf. Ptolemy’s Almagest, lib. i. c. xiii.

[§ 29.]Chaucer omits to say that the experiment should be made when the sun is very nearly on the meridian. Otherwise, the confusion of the azimuth with the hour-angle might cause a considerable error.

[§ 30. 3.]That the phrase ‘wey of the sonne’ really means the sun’s apparent diurnal course in this conclusion, may be further seen by consulting the Latin of Messahala. Cf. the Critical Note on p. 236.

[§ 31.]In my footnote, I have used the expression ‘it does not mean, as it should, the zenith point.’ I mean—‘as, according to our modern ideas, it should’;—for the derivation of zenith shews that the meaning used in this proposition is the older meaning of the two. See note above to i. 19. 7 (p. 357).

[6. 24 parties.]These 24 parts were suggested by the 24 hours of the day. The ‘32 parts’ used by ‘shipmen’ are due to the continual halving of angles. Thus, the four cardinal points have points half-way between them, making eight points; between which, we can insert eight more, making sixteen; and between these, sixteen more, making thirty-two. Hence the 32 points of the compass.

[§ 33. 5.]We should probably insert or south after the word north. Such an insertion is authorised by MSS. B. and C.

[§ 34. 3.]That ‘upon the mones syde’ means nearly in the same azimuth as the moon, is apparent from l. 11 below, where Chaucer says that some treatises make no exception even if the star is not quite in the same azimuth. This was certainly a rough mode of observation.

[§ 35. 9.]right side, East side. See i. 6. 1 (p. 179).

[18.]episicle, epicycle. To account for the planetary motions, epicycles were invented. The moon, for instance, was supposed to revolve round a moving centre, which centre itself moved round the earth in a perfect circle. This came a little nearer to the true motion in some instances, but was hopelessly wrong, and nothing could be made of it, even when a second epicycle, revolving about a centre which moved in the first epicycle, was superadded. All that Chaucer says here is, that, whilst the centre of the moon’s epicycle had a direct motion, the moon’s motion in the epicycle itself was a reverse one, unlike that of the other planetary bodies. The subject is hardly worth further discussion, so I merely refer the reader to the Almagest, lib. iv. c. 5; and lib. ix. c. 5.

[§ 36.]The ‘equations of houses’ means the dividing of the sphere into equal portions, and the right numbering of those portions or houses. The most important house was the first, or ascendent, just rising; the next in importance was the tenth, which was just coming on the meridian; then come the seventh or descendent, just about to set, and the fourth, just coming to the line of midnight. The next in importance were the succedents, or houses immediately following these, viz. the second, the eleventh, the eighth, and the fifth. The least important were the third, twelfth, ninth, and sixth. See Fig. 14.

[§ 37. 18.]thise 3 howsez. That is, the nadirs of the 2nd, 3rd, and 4th houses give the houses that ‘follow,’ i. e. the 8th, 9th, and 10th. The word ‘follow’ here seems to refer, not to position, but to the order in which the houses may most conveniently be found. Chaucer omits to add that the beginnings of the 5th and 6th houses can be found in a similar way, because it is sufficiently evident. It is all from Messahala.

[§ 38. 1.]for warping, the brodere the bettre. This may mean, either (1) to prevent warping, the thicker the better; or (2) to prevent the errors arising from warping (for fear of warping), the larger the better. I believe the latter to be the true interpretation; for it is better thus to guard against possible errors than to make the plate very thick and, at the same time, small. Besides which, the usual meaning of brodere is wider, larger, more ample. Indeed, we find the very expression ‘non sit tamen nimis parvus’ in the 4th section of the Practica Chilindri of John Hoveden, published by the Chaucer Society; which see.

[8.]fro the centre, i. e. sticking up above the centre, the length of the wire being equal to a fourth of the diameter, or half the radius, of the circle. This proportion would do for many days in the year; but in the summer time, the pin would bear to be rather longer. Still, we need not alter the text. Cf. the Critical Note on p. 237.

[10.]any-thing, i. e. ever so little; so ony-thyng in l. 13; cf. § 17. 6.

[§ 39.]Though MS. A is rather corrupt here, there is little doubt about the corrections to be made. See the Critical Notes, p. 237.

[19.]That is, the latitude, or breadth, of a climate, or belt, is measured along a line which goes from North to South as far as the earth extends; so that the latitude of the first climate, for example, is measured from the beginning of it to the end of the same, in a due northerly direction. Other authors, he explains, reckoned the latitude of a climate always from the equinoxial line, instead of from the parallel of latitude which terminated the climate immediately to the south of it. Thus the latitude of the fourth climate might mean, either the breadth of that belt itself, or the whole breadth from the equator to the Northern limit of that climate. The MS. E. 2 in St. John’s College, Cambridge, contains (besides Chaucer’s ‘Astrolabe’) a Latin treatise entitled ‘De septem climatibus expositio.’ We find mention of the ‘climates’ also in MS. Camb. li. 3. 3, fol. 33 b, where a diagram appears representing a hemisphere, divided by parallels of latitude into 9 climates or belts, which, beginning from the equator, are as follows. 1. Inhabitabile propter Calorem. 2. Primum clima dia Meroes. 3. Secundum clima dya cienes. 4. Tertium clima di’ alexandrios. 5. Quartum clima dia rodos. 6. Quintum clima dia romes. 7. Sextum clima dia boristenes. 8. Septimum clima dia rifeos. 9. Inhabitabile. This agrees with the list in the footnote on p. 221.

There is a passage in Mandeville which well illustrates Chaucer; I quote the part of it which more immediately relates to the Climates. ‘For the Superficialtee of the Erthe is departed in 7 parties, for the 7 Planetes; and the parties ben clept Clymates. And oure parties be not of the 7 Clymates: for they ben descendynge toward the West. And also these yles of Ynde, which beth evene aȜenst us, beth noght reckned in the Climates: for thei ben aȜenst us, that ben in the lowe Contree. And the 7 Clymates strecchen hem, envyrounynge the World,’ &c. Mandeville’s Voiage, ed. Halliwell, p. 186. See also Ptolemy’s Almagest, lib. ii.

As regards the longitudes of towns, it may be observed that in MS. F. 25 in St. John’s College, Cambridge, the longitudes of Rome, Cordova, London, Paris, and Malta, are said to be 34° 24′, 9° 30′, 19°, 20°, and 38° respectively. These do not well agree together, but they suggest a reckoning from a meridian situated some 20° W. from that of Greenwich. Chaucer says nothing as to what meridian was used for reckoning longitudes from; and Messahala says, vaguely enough, that longitudes were reckoned ‘a meridiano circulo ultime regionis habitabilis in occidente,’ i. e. from the most westward habitable place, which possibly once meant Madeira.

[§ 40.]It is possible that this conclusion was really intended to belong to the Fourth Part of the treatise, and was written by way of instalment. See the Prologue, ll. 67-72. It is curious that in all the best MSS. (P. excepted) the last sentence should be incomplete.

[13.]This sentence is very awkward. It seems to mean—‘and then set I the point of F upward in the same sign, because that the latitude was north, upon the latitude of Venus; that is to say, (I set it upward) keeping it in the 6th degree of Capricorn.’ Upward means inward, i. e. towards the centre or towards the north; the opposite being expressed by southward, or outward, or toward the border, as in l. 48 below. Upon the latitude of Venus means that the point F of the compass was set above the second degree of latitude, so that the space between the legs of the compass became equal to 2 degrees, as said in l. 16. Lastly, the words that is to seyn, in the 6 degree, &c., are an explanation of the vaguer expression in the same signe. The repetition of the words that is to seyn, &c. (ll. 12 and 14), is intended to draw attention to the necessity of keeping both legs of the compass in the same degree of longitude (A on the zodiac, and F to the north of it).

[57.]Possibly Chaucer left the sentence incomplete. The words thou shalt do well enough’ may easily have been added by another hand to bring the sentence to an apparent, though not wholly satisfactory, conclusion. The colophon is written (in a later hand) in MS. A. at the bottom of the page, a part of which, after the words ‘howre after howre,’ is left blank.

[41-43.]I have mended the text as well as I could by inserting words, and adopting different readings. Nearly all the emendations rest on authority; see the Critical Notes. The text is not a good one, but I do not see why these sections may not have been written by Chaucer. For a definition of the terms ‘Umbra Extensa’ and ‘Umbra Versa’ see sections 5 and 6 of the Practica Chilindri of John Hoveden, published by the Chaucer Society. The umbra extensa or recta is the shadow cast on a plain by any perfectly upright object; but the restriction is commonly introduced, that the altitude of the sun shall exceed 45°. The umbra versa is the shadow cast perpendicularly downwards along a wall by a style which projects from the wall at right angles to it; the restriction is commonly introduced, that the sun’s altitude shall be less than 45°. The umbra versa is the one which appeared on the ‘chylindre’; hence John de Hoveden explains how to calculate the altitude of an object by it.

[44.]This article and the next may possibly be Chaucer’s. It is well known that he speaks of ‘collect’ and ‘expans yeres’ and ‘rotes’ in the Frankeleines Tale; Cant. Ta., F 1275, 6, the note upon which in the glossary to Urry’s Chaucer may be found also in Tyrwhitt’s Glossary, s. v. Expans; but it is worth while to repeat it here. ‘In this and the following verses, the Poet describes the Alphonsine Astronomical Tables by the several parts of them, wherein some technical terms occur, which were used by the old astronomers, and continued by the compilers of those tables. Collect years are certain sums of years, with the motions of the heavenly bodies corresponding to them, as of 20, 40, 60, &c., disposed into tables; and Expans years are the single years, with the motions of the heavenly bodies answering to them, beginning at 1, and continued on to the smallest Collect sum, as 20. A Root, or Radix, is any certain time taken at pleasure, from which, as an era, the celestial motions are to be computed. By ‘proporcionels convenientes’ [C. T., F 1278] are meant the Tables of Proportional parts.’ To which Moxon adds, from Chamber’s Encyclopædia, with reference to C. T., F 1277, that ‘Argument in astronomy is an arc whereby we seek another unknown arc proportional to [or rather, dependent upon] the first.’

Tables of mean motions of the Sun are given in Ptolemy’s Almagest, lib. iii. c. 2; of the Moon, lib. iv. c. 3; of the Planets, lib. viii. c. 3; also in MS. Ii. 3. 3, fol. 88b, &c.

[41a-42b.]The fact that these articles are mere repetitions of sections 41-43 is almost conclusive against their genuineness. I do not suppose that sect 46 (at p. 229) is Chaucer’s either, but it is added for the sake of completeness.

[§ 12, l. 5.]The MSS. all1 read—‘vmbra recta or elles vmbra extensa, & the nether partie is cleped the vmbra versa.’ This is certainly wrong.

[§ 39.]At this point MS. A, which has so far, in spite of occasional errors of the scribe, afforded a very fair text, begins to break down; probably because the corrector’s hand has not touched the two concluding sections, although section 40 is much less corrupt. The result is worth recording, as it shews what we may expect to find, even in good MSS. of the Astrolabe. The section commences thus (the obvious misreadings being printed in italics):—

‘This lyne Meridional ys but a Maner descripcion or the ymagined, that passeth vpon the pooles of þis the world And by the cenyth of owre heued / And hit is the same lyne Meridional / for in what place þat any maner man [omission] any tyme of the yer / whan that the sonne schyneth ony thing of the firmament cometh to his verrey Middel lyne of the place / than is hit verrey Midday, þat we clepen owre noon,’ &c.

It seems clear that this apparent trash was produced by a careless scribe, who had a good copy before him; it is therefore not necessary to reject it all as unworthy of consideration, but it is very necessary to correct it by collation with other copies. And this is what I have done.

MS. B has almost exactly the same words; but the section is considerably better, in general sense, in MSS. C and P, for which reason I here quote from the former the whole section.

[Rawl. MS. Misc. 1370, fol. 40 b.]

Descripcioun of þe meridional lyne, of þe longitudes and latitudes of Citees and townes, as wel as of a (sic) clymatz.

39.conclusio. This lyne meridional is but a maner discripcion or lyne ymagyned, þat passeþ upon þe pooles of þis worlde, and by þe Cenith of oure heued. ¶ And yt is cleped þe lyne meridional, for in what place þat any man ys at any time of þe Ȝere, whan þat þe sonne by meuynge of þe firmament come to his uerrey meridian place / þan is it þe uerrey mydday þat we clepe none, as to þilke man. And þerefore is yt cleped þe lyne of mydday. And nota, þat euermo of any .2. citees or of 2 townes, of which þat oo towne a-procheþ neer þe est þan doþ þe oþer towne, trust wel þat þilke townes han diuerse meridians. Nota also, þat þe arche of þe equinoxial, þat is contened or bownded by-twixe þe two meridians, is cleped þe longitude of þe towne. ¶ & Ȝif so be / þat two townes haue I-like meridian or one merydian, ¶ Than ys þe distaunce of hem boþe I-like fer from þe est, & þe contrarye. And in þis maner þei chaunge not her meridyan, but soþly, þei chaungen her almykanteras, For þe enhaunsynge of þe pool / and þe distaunce of þe sonne. ¶ The longitude of a clymate ys a lyne ymagyned fro þe est to þe west, I-like distaunte fro þe equinoxial. ¶ The latitude of a clymat may be cleped þe space of þe erþe fro þe by-gynnynge of þe first clymat unto þe ende of þe same clymat / euene-directe a-Ȝens þe pool artyke. ¶ Thus seyn somme auctours / and somme clerkes seyn / þat Ȝif men clepen þe latitude of a contrey1 , þe arche mer[i]dian þat is contened or intercept by-twixe þe Cenyth & þe equinoxial; þan sey þei þat þe distaunce fro þe equinoxial unto þe ende of a clymat, euene2 a-gaynes þe pool artik, is þe latitude off þat climat2 forsoþe.

The corrections made in this section are here fully described.

[28.]‘And observe, that this first moving (primus motus) is so called from the first movable (primum mobile) of the eighth sphere, which moving or motion is from East to West,’ &c. There is an apparent confusion in this, because the primum mobile was the ninth sphere see Plate V, fig. 10); but it may be called the movable of the eighth, as giving motion to it. An attempt was made to explain the movements of the heavenly bodies by imagining the earth to be in the centre, surrounded by a series of concentric spheres, or rather shells, like the coats of an onion. Of these the seven innermost, all revolving with different velocities, each carried with it a planet. Beyond these was an eighth sphere, which was at first supposed to be divided into two parts, the inner part being the firmamentum, and the outer part the primum mobile; hence the primum mobile might have been called ‘the first moving of the eighth sphere,’ as accounting for the more important part of the motion of the said sphere. It is simpler, however, to make these distinct, in which case the eighth sphere is the firmamentum or sphæra stellarum fixarum, which was supposed to have a very slow motion from West to East round the poles of the zodiac to account for the precession of the equinoxes, whilst the ninth sphere, or primum mobile, whirled round from East to West once in 24 hours, carrying all the inner spheres with it, by which means the ancients accounted for the diurnal revolution. This ninth sphere had for its poles the north and south poles of the heavens, and its ‘girdle’ (or great circle equidistant from the poles) was the equator itself. Hence the equator is here called the ‘girdle of the first moving.’ As the planetary spheres revolved in an opposite direction, thus accounting for the forward motion of the sun and planets in the ecliptic or near it, the primum mobile was considered to revolve in a backward or unnatural direction, and hence Chaucer’s apostrophe to it (Man of Lawes Tale, B 295):—

• ‘O firste moevyng cruel firmament,
• With thy diurnal sweigh that crowdest ay
• And hurlest all from Est til Occident,
• That naturelly wolde holde another way.’

That is—‘O thou primum mobile, thou cruel firmament, that with thy diurnal revolution (or revolution once in 24 hours round the axis of the equator) continually forcest along and whirlest all the celestial bodies from East to West, which naturally would wish to follow the course of the sun in the zodiac from West to East.’ This is well illustrated by a sidenote in the Ellesmere MS. to the passage in question, to this effect:—‘Vnde Ptholomeus, libro i. cap. 8. Primi motus celi duo sunt, quorum vnus est qui mouet totum semper ab Oriente in Occidentem vno modo super orbes, &c. Item aliter vero motus est qui mouet orbem stellarum currencium contra motum primum, videlicet, ab Occidente in Orientum super alios duos polos1 .’ That is, the two chief motions are that of the primum mobile, which carries everything round from East to West, and that of the fixed stars, which is a slow motion from West to East round the axis of the zodiac, to account for precession. This exactly explains the well-known passage in the Frankeleines Tale (C. T., F 1280):—

• ‘And by his eighte spere in his werking,
• He knew ful wel how fer Alnath was shove
• Fro the heed of thilke fixe Aries above
• That in the ninthe spere considered is.’

Here the eight spheres are the eight inner spheres which revolve round the axis of the zodiac in an easterly direction, whilst the ninth sphere, or primum mobile, contained both the theoretical or fixed first point of Aries from which measurements were made, and also the signs of the zodiac as distinct from the constellations. But Alnath, being an actual star, viz, α Arietis2 , was in the eighth sphere; and the distance between its position and that of the first point of Aries at any time afforded a measure of the amount of precession. Mr. Brae rightly remarks that Tyrwhitt’s readings in this passage are correct (except that eighte speres should be eightespere), and those of Mr. Wright and Dr. Morris (from the Harleian MS.) are incorrect.

It may be as well to add that a later refinement was to insert a crystalline sphere, to account for the precession; so that the order stood thus: seven spheres of planets; the eighth, of fixed stars; the ninth, or crystalline; the tenth, or primum mobile; and, beyond these, an empyræan or theological heaven, so to speak, due to no astronomical wants, but used to express the place of residence of celestial beings3 . Hence the passage in Milton, P. L. iii. 481:—

• ‘They pass the planets seven, and pass the fix’d,
• And that crystalline sphere whose balance weighs
• The trepidation talk’d, and that first mov’d.’

i. e. They pass the seven planetary spheres; then the sphere of fixed stars; then the crystalline or transparent one, whose swaying motion or libration measures the amount of the precession and nutation so often talked of; and then, the sphere of the primum mobile itself. But Milton clearly himself believed in the Copernican system; see Paradise Lost, viii. 121-140, where the primum mobile is described in the lines—

• ‘that swift
• Nocturnal and diurnal rhomb supposed,
• Invisible else above all stars, the wheel
• Of day and night.’

[50.]Not only the influences here assigned to the signs, but others due to planets, may be found in ‘Porphyrii Philosophi introductio in Claudii Ptolomæi opus de affectibus astrorum,’ fol. Basileæ, n. d. p. 198. I here add a few extracts from the MS. in Trinity College, Cambridge (marked R. 15. 18), to shew the nature of the old astrology. I choose them with especial reference to Aries. The other signs are spoken of in a similar manner. ‘It is principally to be considered that the signes of hevyn haue theire strength and propre significacioun vpon the membris of eny man; as, Aries hath respect to the hed, taurus to the neck, geminis (sic) the Armys, Cancer the brest, leo the hert, virgo the bowels, &c.; as it shall shew in the Chapiters folowyng. Secundarily it is to be noted that plotholomee (sic) saith, that to touche with instrument of yroun while the mone is in the signe of the same membre, is for to be dred; let the surgen beware, and the letter of blode, let hym be aferd to touche that membre with yrene, in the which the mone shal be.’—MS. G; Tract C. p. 12.

‘Thenne Aries hath respect to the hed; And this signe is hote and dry, fiery & colerik. Saturne hath ij witnes in Ariete, a triplicitate and a terme. Jubiter also hath ij, a triplicitate and a terme. Mars hath iij testimonials or iij fortitudis in Ariete, A hows, A face, and A terme. The sonne hath iij fortitudis in Ariete, scilicet, an exaltacioun, a triplicite, and a face. Venus hath ij testimonials, A terme and a face. Mercury hath one testymony, that is to sey, a terme. And luna in Ariete hath no testimoniall. For the which it is to know, that the influens of the planetis may be fortyfied v maner of wayes. And these v maner be called v fortitudis of planetis, or testimonials, which be these: domus, exaltacio, triplicitas, terminus, and facies. Domus gevith to a planet v fortitudis; And a planet in his hows is lyke a kynge in his hall, And in the high trone of his glorie. A planet in his exaltacioun is lyke a kynge when he is crowned. A planet in his triplicite is like a kynge in honour, Amonge his sencible people. A planet in his terme is As a mann amonges his kynnesmenn And fryndis. Facies gyvith to a planet that thyng the which rowme gyvith to a maistre. Wherfore facies gyvith only on fortitude, Terminus ij, Triplicitas iij, Exaltacio iiij, And domus v. And for the more clere declaracioun, the dignytes of planettis in signes be comprehendid in this figure ensuynge, &c.1 ’—Same MS., Tract C. p. 13.

‘The dygnytes of planetis in the signes, most speciall they be to be noted in iudicials. When the mone is in Ariete, it is not gode, but vtterly to be exshewed, both for seke And disesid, for to shafe theire hede or to boist in the eris or in the nek; nor loke þou let no blode in the vayn of the hede. How-be-it, benyficiall it is to begynne euery worke that þou woldest bryng aboute sone. But that thynge that is stabill ought to be eschewed. In this signe it is necessary to dele with noble estatis And rich men, And for to go in-to A bayne [bath]1 .’—Same MS., Tract C. p. 14.

[1 ]As far as I can ascertain.

[1 ]Here insert—[they mene]—which CP omit.

[2 ]The words from euene to climat are added at the bottom of the page in the MS.

[1 ]This is doubtless quoted from some gloss upon Ptolemy, not from the work itself. The reference is right, for the ‘motus celi’ are discussed in the Almagest, lib. i. c. 8.

[2 ]This star (α Arietis) was on the supposed horn of the Ram, and hence its name; since El-nâtih signifies ‘the butter,’ and ‘El-nath’ is ‘butting’ or ‘pushing.’ See Ideler, Die Bedeutung der Sternnamen, p. 135.

[3 ]Well expressed by Dante, Parad. xxx. 38—

• ‘Noi semo usciti fuore
• Del maggior corpo al ciel ch’é pura luce.’

Dante, like Chaucer, makes the eighth sphere that of fixed stars, and the ninth the primum mobile or swiftest heaven (ciel velocissimo); Parad. xxvii. 99.

[1 ]Here follows a table, shewing that, in Aries, the value of Saturn is 5, of Jupiter 5, &c.; with the values of the planets in all the other signs. The value 5, of Saturn, is obtained by adding a triplicite (value 3) to a terme (value 2), these being the ‘witnesses’ of Saturne in Aries; and so on throughout.

[1 ]So on p. 12 of another tract (D) in the same MS., we find—

• ‘Aries calidum & sucum; bonum.
• Nill capiti noceas, Aries cum luna refulget,
• De vena minuas & balnea tutius intres,
• Non tangas Aures, nec barbam radere debes.’

Each of the signs is described in similar triplets, from the grammar of which I conclude that Aries is here put for in Ariete, in the first hexameter.