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APPENDIX - Galileo Galilei, Dialogues Concerning Two New Sciences [1638]

Edition used:

Dialogues Concerning Two New Sciences by Galileo Galilei. Translated from the Italian and Latin into English by Henry Crew and Alfonso de Salvio. With an Introduction by Antonio Favaro (New York: Macmillan, 1914).

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APPENDIX

Containing some theorems, and their proofs, dealing with centers of gravity of solid bodies, written by the same Author at an earlier date.*

[finis]

[*]The reader will notice that two different problems are here involved. That which is suggested in the last remark of Sagredo is the following:

To find a beam whose maximum stress has the same value when a constant load moves from one end of the beam to the other. The second problem—the one which Salviati proceeds to solve—is the following: To find a beam in all cross-sections of which the maximum stress is the same for a constant load in a fixed position. [Trans.]

[* ]It is now well known that this curve is not a parabola but a catenary the equation of which was first given, 49 years after Galileo’s death, by James Bernoulli. [Trans.]

[* ]“Natural motion” of the author has here been translated into “free motion”—since this is the term used to-day to distinguish the “natural” from the “violent” motions of the Renaissance. [Trans.]

[† ]A theorem demonstrated on p. 175 below. [Trans.]

[* ]Following the example of the National Edition, this Appendix which covers 18 pages of the Leyden Edition of 1638 is here omitted as being of minor interest. [Trans.]