3.: Of what is just in ditribution and its rule of geometrical proportion. - Aristotle, The Nicomachean Ethics 
The Nichomachean Ethics of Aristotle, trans. F.H. Peters, M.A. 5th edition (London: Kegan Paul, Trench, Truebner & Co., 1893).
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- Preface to the Fifth Edition.
- Book I.: The End.
- 1.: In All He Does Man Seeks Same Good As End Or Means.
- 2.: The End Is the Good; Our Subject Is This and Its Science Politics.
- 3.: Exactness Not Permitted By Subject Nor to Be Expected By Student, Who Needs Experience and Training.
- 4.: Men Agree That the Good Is Happiness, But Differ As to What This Is.
- 5.: The Good Cannot Be Pleasure, Nor Honour, Nor Virtue.
- 6.: Various Arguments to Show Against the Platonists That There Cannot Be One Universal Good.
- 7.: The Good Is the Final End, and Happiness Is This.
- 8.: This View Harmonizes Various Current Views.
- 9.: It Happiness Acquired, Or the Gift of Gods Or of Chance?
- 10.: Can No Man Be Called Happy During Life?
- 11.: Cannot the Fortunes of Survivors Affect the Dead?
- 12.: Happiness As Absolute End Is Above Praise.
- 13.: Division of the Faculties and Resulting Division of the Virtues.
- Book II.: Moral Virtue.
- 1.: Moral Virtue Is Acquired By the Repetition of the Corresponding Acts.
- 2.: These Acts Must Be Such As Reason Prescribes; They Can’t Be Defined Exactly, But Must Be Neither Too Much Nor Too Little.
- 3.: Virtue Is In Various Ways Concerned With Pleasure and Pain.
- 4.: The Conditions of Virtuous Action As Distinct From Artistic Production.
- 5.: Virtue Not an Emotion, Nor a Faculty, But a Trained Faculty Or Habit.
- 6.: Viz., the Habit of Choosing the Mean.
- 7.: This Must Be Applied to the Several Virtues.
- 8.: The Two Vicious Extremes Are Opposed to One Another and to the Intermediate Virtue.
- 9.: The Mean Hard to Hit, and Is a Matter of Perception, Not of Reasoning.
- Book III.
- Chapters 1–5.: the Will.
- 1.: An Act Is Involuntary When Done (a) Under Compulsion, Or (b) Through Ignorance: (a) Means Not Originated By Doer, (b) Means Through Ignorance of the Circumstances: Voluntary Then Means Originated With Knowledge of Circumstances.
- 2.: Purpose, a Mode of Will, Means Choice After Deliberation.
- 3.: We Deliberate On What We Can Do—not On Ends, But Means.
- 4.: We Wish For
- 5.: Virtue and Vice Are Alike Voluntary, Our Acts Are Our Own; For We Are Punished For Them; If This Be Our Character, We Have Made It By Repeated Acts; Even Bodily Vices Are Blamable When Thus Formed. We Cannot Plead That Our Notion of Good Depends On Ou
- Chapters 6—12: the Several Moral Virtues and Vices.
- 6.: Of Courage and the Opposite Vices.
- 7. Of Courage (continued)
- 8. Of Courage Improperly So Called.
- 9.: How Courage Involves Both Pain and Pleasure.
- 10.: Of Temperance.
- 11. Of Temperance (continued)
- 12.: How Profligacy Is More Voluntary Than Cowardice.
- Book IV.: The Several Moral Virtues and Vices— Continued.
- 1.: Of Liberality.
- 2.: Of Magnificence.
- 3.: Of High-mindedness
- 4.: Of a Similar Virtue In Smaller Matters.
- 5.: Of Gentleness.
- 6.: Of Agreeableness.
- 7.: Of Truthfulness.
- 8.: Of Wittiness.
- 9.: Of the Feeling of Shame
- Book V.: The Several Moral Virtues and Vices— Concluded. Justice.
- 1.: Preliminary Two Senses of Justice Distinguished Justice (l) = Obedience to Law = Complete Virtue.
- 2.: Of Justice (2) = Fairness, How Related to Justice (1). What Is Just In Distribution Distinguished From What Is Just In Correction.
- 3.: Of What Is Just In Ditribution and Its Rule of Geometrical Proportion.
- 4.: Of That Which Is Just In Correction, and Its Rule of Arithmetical Proportion.
- 5.: Simple Requital Is Not Identical With What Is Just, But Proportionate Requital Is What Is Just In Exchange; and This Is Effected By Means of Money. We Can Now Give a General Definition of Justice (2).
- 6.: ( One Can Act Unjustly Without Being Unjust. ) That Which Is Just In the Strict Sense Is Between Citizens Only, For It Implies Law.
- 7.: It Is In Part Natural, In Part Conventional.
- 8.: The Internal Conditions of a Just Or Unjust Action, and of a Just Or Unjust Agent.
- 9.: Sundry Questions About Doing and Suffering Injustice
- 10.: Of Equity
- 11.: Can a Man Wrong Himself?
- Book VI.: The Intellectual Virtues.
- 1.: Must Be Studied Because (a) Reason Prescribes the Mean, (b) They Are a Part of Human Excellence. the Intellect Is (1) Scientific, (2) Calculative: We Want the Virtue of Each.
- 2.: The Function of the Intellect, Both In Practice and Speculation, Is to Attain Truth.
- 3.: Of the Five Modes of Attaining Truth: (1) of Demonstrative Science of Things Invariable.
- 4.: Of Knowledge of Things Variable, Viz. (2) of Art In What We Make;
- 5.: And (3) of Prudence In What We Do, the Virtue of the Calculative Intellect.
- 6.: (4) of Intuitive Reason As the Basis of Demonstrative Science.
- 7.: (5) of Wisdom As the Union of Science and Intuitive Reason. Comparison of the Two Intellectual Virtues, Wisdom and Prudence.
- 8.: Prudence Compared With Statesmanship and Other Forms of Knowledge.
- 9.: Of Deliberation.
- 10.: Of Intelligence
- 11.: Of Judgment of Reason Or Intuitive Perception As the Basis of the Practical Intellect.
- 12.: Of the Uses of Wisdom and Prudence. How Prudence Is Related to Cleverness.
- 13.: How Prudence Is Related to Moral Virtue
- Book VII.
- Chapters 1–10.: Characters Other Than Virtue and Vice.
- 1.: Of Continence and Incontinence, Heroic Virtue and Brutality. of Method. Statement of Opinions About Continence.
- 2.: Statement of Difficulties As to How One Can Know Right and Do Wrong.
- 3.: Solution: to Know Has Many Senses; In What Sense Such a Man Knows.
- 4.: Of Incontinence In the Strict and In the Metaphorical Sense.
- 5.: Of Incontinence In Respect of Brutal Or Morbid Appetites.
- 6.: Incontinence In Anger Less Blamed Than In Appetite.
- 7.: Incontinence Yields to Pleasure, Softness to Pain. Two Kinds of Incontinence, the Hasty and the Weak.
- 8.: Incontinence Compared With Vice and Virtue.
- 9.: Continence and Incontinence Not Identical With Keeping and Breaking a Resolution.
- 10.: Prudence Is Not, But Cleverness Is, Compatible With Incontinence.
- Chapters 11—14.: of Pleasure.
- 11.: We Must Now Discuss Pleasure. Opinions About It.
- 12.: Answers to Arguments Against Goodness of Pleasure. Ambiguity of Good and Pleasant. Pleasure Not a Transition, But Unimpeded Activity.
- 13.: Pleasure Is Good, and the Pleasure That Consists In the Highest Activity Is the Good. All Admit That Happiness Is Pleasant. Bodily Pleasures Not the Only Pleasures.
- 14.: Of the Bodily Pleasures, and the Distinction Between Naturally and Accidentally Pleasant.
- Book VIII.: Friendship Or Love.
- 1.: Uses of Friendship. Differences of Opinion About It.
- 2.: Three Motives of Friendship. Friendship Defined.
- 3.: Three Kinds of Friendship, Corresponding to the Three Motives Perfect Friendship Is That Whose Motive Is the Good.
- 4.: The Others Are Imperfect Copies of This.
- 5.: Intercourse Necessary to the Maintenance of Friendship.
- 6.: Impossible to Have Many True Friends.
- 7.: Of Friendship Between Unequal Persons and Its Rule of Proportion. Limits Within Which This Is Possible.
- 8.: Of Loving and Being Loved.
- 9.: Every Society Has Its Own Form of Friendship As of Justice. All Societies Are Summed Up In Civil Society.
- 10.: Of the Three Forms of Constitution.
- 11.: Of the Corresponding Forms of Friendship.
- 12.: Of the Friendship of Kinsmen and Comrades.
- 13.: Of the Terms of Interchange and Quarrels Hence Arising In Equal Friendships.
- 14.: Of the Same In Unequal Friendships.
- Book IX.: Friendship Or Love— Continued.
- 1.: Of the Rule of Proportion In Dissimilar Friendships.
- 2.: Of the Conflict of Duties.
- 3.: Of the Dissolution of Friendships.
- 4.: A Man’s Relation to His Friend Like His Relation to Himself.
- 5.: Friendship and Goodwill.
- 6.: Friendship and Unanimity
- 7.: Why Benefactors Love More Than They Are Loved.
- 8.: In What Sense It Is Right to Love One’s Self.
- 9.: Why a Happy Man Needs Friends.
- 10.: Of the Proper Number of Friends.
- 11.: Friends Needed Both In Prosperity and Adversity.
- 12.: Friendship Is Realized In Living Together.
- Book X.
- Chapters 1–5.: Pleasure.
- 1.: Reasons For Discussing Pleasure.
- 2.: Arguments of Eudoxus That Pleasure Is the Good.
- 3.: Argument That It Is Not a Quality; That It Is Not Determined; That It Is a Motion Or Coming Into Being. Pleasures Differ In Kind.
- 4.: Pleasure Defined: Its Relation to Activity.
- 5.: Pleasures Differ According to the Activities the Standard Is the Good Man.
- Chapters 6–9.: Conclusion.
- 6.: Happiness Not Amusement, But Life.
- 7.: Of the Speculative Life As Happiness In the Highest Sense.
- 8.: Of the Practical Life As Happiness In a Lower Sense, and of the Relation Between the Two. Prosperity, How Far Needed.
- 9.: How Is the End to Be Realized?
Of what is just in ditribution and its rule of geometrical proportion.
The unjust man [in this limited sense of the word], we say, is unfair, and that which is unjust is unfair.
Now, it is plain that there must be a mean which lies between what is unfair on this side and on that. And this is that which is fair or equal; for any act that admits of a too much and a too little admits also of that which is fair.
If then that which is unjust be unfair, that which is just will be fair, which indeed is admitted by all without further proof.
But since that which is fair or equal is a mean between two extremes, it follows that what is just will be a mean.
But equality or fairness implies two terms at least.
It follows, then, that that which is just is both a mean quantity and also a fair amount relatively to something else and to certain persons—in other words, that, on the one hand, as a mean quantity it implies certain other quantities, i.e. a more and a less; and, on the other hand, as an equal or fair amount it involves two quantities, and as a just amount it involves certain persons.
That which is just, then, implies four terms at least: two persons to whom justice is done, and two things.
And there must be the same “equality” [i.e. the same ratio] between the persons and the things: as the things are to one another, so must the persons be. For if the persons be not equal, their shares will not be equal; and this is the source of disputes and accusations, when persons who are equal do not receive equal shares, or when persons who are not equal receive equal shares.
This is also plainly indicated by the common phrase “according to merit.” For in distribution all men allow that what is just must be according to merit or worth of some kind, but they do not all adopt the same standard of worth; in democratic states they take free birth as the standard, in oligarchic states they take wealth, in others noble birth, and in the true aristocratic state virtue or personal merit.
We see, then, that that which is just is in some sort proportionate. For not abstract numbers only, but all things that can be numbered, admit of proportion; proportion meaning equality of ratios, and requiring four terms at least.
That discrete proportion requires four terms is evident at once. Continuous proportion also requires four terms: for in it one term is employed as two and is repeated; for instance, a/b = b/c. The term b then is repeated; and so, counting b twice over, we find that the terms of the proportion are four in number.
That which is just, then, requires that there be four terms at least, and that the ratio between the two pairs be the same, i.e. that the persons stand to one another in the same ratio as the things.
Let us say, then, a/b = c/d, or alternandoa/c = b/d.
The sums of these new pairs then will stand to one another in the original ratio [i.e. a + c/b + d = a/b or c/d ].
But these are the pairs which the distribution joins together; and if the things be assigned in this manner, the distribution is just.
This joining, then, of a to c and of b to d is that which is just in distribution; and that which is just in this sense is a mean quantity, while that which is unjust is that which is disproportionate; for that which is proportionate is a mean quantity, but that which is just is, as we said, proportionate.
This proportion is called by the mathematicians a geometrical proportion; for it is when four terms are in geometrical proportion that the sum [of the first and third] is to the sum [of the second and fourth] in the original ratio [of the first to the second or the third to the fourth].
But this proportion [as applied in justice] cannot be a continuous proportion; for one term cannot represent both a person and a thing.
That which is just, then, in this sense is that which is proportionate; but that which is unjust is that which is disproportionate. In the latter case one quantity becomes more or too much, the other less or too little. And this we see in practice; for he who wrongs another gets too much, and he who is wronged gets too little of the good in question: but of the evil conversely; for the lesser evil stands in the place of good when compared with the greater evil: for the lesser evil is more desirable than the greater, but that which is desirable is good, and that which is more desirable is a greater good.
This then is one form of that which is just.