PAPPI

ALEXANDRINI

MATHEMATICARVM

COLLECTIONVM

LIBER TERTIVS.

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WHOSOEVER wishes to examine more diligently those things which are investigated in geometry, O Cratiste, considers every problem to be that in which something is proposed to be done and constructed. A theorem, however, is that in which, with certain things posited, the consequence pertaining to them—and entirely contingent—is considered; although some of the ancients said that all are problems, and others that all are theorems. Therefore, he who proposes a theorem, knowing in some way its consequence, thinks it worthy of inquiry and does not propose it rightly otherwise. But he who proposes a problem, if he is unlearned and entirely rude, even if he proposes that which cannot in some way be constructed, is worthy of pardon and is free from blame. For it is the duty of the inquirer to determine both this, and what can be done, and what cannot be done at all. And if it can be done, when, and how, and in how many ways it can be done. But if someone proposes ignorantly, while professing the mathematical sciences, he is not free from blame. Recently, certain of those who profess the mathematical sciences determined some problems for us ignorantly through your propositions. Regarding these and similar things, it was necessary for us to bring forward demonstrations in the third book of the mathematical collections for your benefit and for the benefit of students. Therefore, a certain person, who seemed to be a great geometer, first determined a problem unskillfully...