Letter 131: Know that the definitions of geometry are infallibly true.

To Pylaemenes. Know that the definitions of geometry are infallibly true. Other branches of knowledge are proud when they can borrow even a little from geometry for their demonstrations. Now, there is a principle that two things equal to the same thing are equal to each other. I am bound to you by our shared education, and to the remarkable Diogenes by temperament. Both of you are friends of the same man — me. So you must be united to each other, just as you are each united to the middle term. I attach you to one another through this letter. The celebrated Diogenes will give himself to your friendship, and will receive in return my own Pylaemenes. In calling you "my own," I say nothing either of us should be ashamed of. In a few words, here is Diogenes's situation. He is a loyal young man, noble, both gentle and brave — exactly the kind of man Plato would have wanted as a guardian in his republic. He saw military service while still a youth. When he grew older, he was given command of the troops in our region, and in exposing himself to danger he earned the envy of the spectators — for that is how citizens treat success. But he rose above it. In short, he conquered his city's enemies by arms and its malicious men by virtue.

Letter 131: A Recommendation [1] To Pylaemenes Know well that the definitions of geometry are infallibly true. Moreover, the other branches of knowledge are very proud when they are able, for their demonstration, to borrow something, however slight, from geometry. [2] Now there is a certain principle, of course, that two things which are equal to a third thing are equal to each other. I am bound to you by the link of association, and to the wonderful Diogenes by temperament also. Both of you are friends of the one man. You must then be united to one another, even as you are united to the middle link, myself. I attach you, therefore, the one to the other by this letter, in virtue of which the celebrated Diogenes will also give himself up to your honor's friendship, and at the same time, I am sure, he will take in return my own Pylamenes. [3] In calling you my own, I think I am saying nothing of which we can either of us be ashamed. Thanks to you he will have, as friends, all others who love me and also such as are useful, owing to their power. It would be doing you an injustice to doubt this. More than any one at any time he stands in need of friends to come to his assistance. [4] Well, in a few words, this is his trouble. Diogenes is a loyal young man, noble and full of gentleness and courage at once, just such a man as Plato would have wished to make a guardian in his state. Further, he saw military service while still a stripling. When he had passed out of youth he was given the command of the troops in our country, and in exposing himself to dangers he incurred the obloquy of the spectators. For so do the citizens regard whatever is successful. But this man rose superior to envy. Another might have much to say on this subject, but we resemble each other too much, he and I, in our attitude towards praising and being praised, for further comment. In a word, he has conquered the enemies of his city by his feats of arms, and all evil-minded men in it by his virtue. Although stepping into power while still young, he was not ashamed of his relationship with a philosopher. [5] Diogenes, such as I describe him to you, has some troublesome affairs to deal with, precisely, because he is a virtuous man, for every honest man is a gold-mine for scoundrels, and the wicked get their revenues from the other part of mankind.  [6] An informer is trying to extort money from Diogenes, and now, having failed in that attempt, he has brought an action against him in the courts. As he has not succeeded by this means in getting any of his ill-founded claims, for we have the law upon our side, he has turned to another plan; he is changing the civil suit into a criminal charge by trying to impute to him a misdemeanor, committed before the accused was born. [7] Diogenes will not wait to be brought before justice, for we must not give way to a murderous blackmailer, nor can he abandon to this fellow the possessions he has inherited from his fathers and from his ancestors, with the appearance of disgrace in addition. Diogenes, therefore, is in want of sincere, incorruptible, able friends, like yourself, and he shall have, by the grace of God, yourself through me, and the friends who are mine and yours through you. In doing a service to Diogenes every one will acquire a claim to my personal gratitude.