Commentary on the First Book of Euclid's Elements

grammar; for it seems to me that the diligently prepared codex has faithfully retained the spelling system of Proclus, and I think that those times felt the elegance of the Greek language better than any man can feel it in our times; nor was the usage of the school to be considered in a book that those learning the elements of the Greek language would scarcely touch. I therefore transmit what was transmitted, lest I be more Greek than Proclus, as I feared.

Another peculiar usage must also be mentioned, whether it is unique to Proclus or to his age, namely that the same letter signifies two things. In the figure described on page 290, epsilon marks both the circle with center gamma and radius gamma-delta, and a point beyond its circumference; in a similar way, in the figure described on page 346, epsilon marks both the triangle and the point of the circle drawn with center delta and radius delta-zeta. Finally, it is worthy of note that the collection of two lines is signified by letters placed next to each other, e.g., the line ag = the line a + the line g.

It remains that I speak about the division by which the commentaries of Proclus are divided into four books, and each book into chapters and commentaries. Proclus himself, in only one place on line 24 of page 352, uses the word tmēma section/segment to note a part of one of Euclid’s propositions. He calls the propositions that precede, on page 354, line 8, hypothéseis hypotheses, and on page 364, line 19, he calls them tà prò tôn theōrēmátōn those things before the theorems. He never transitions to other questions in such a way that you could say he concludes one book and begins another. He only closes individual questions and adds what he is about to say, as on lines 23–26 of page 81. If you inspect the codex, you might conjecture that the prologue and the four books are distinguished by a title written in red ink, and you would think you have judged correctly, since on the folio of the codex marked with the number 44 (below on line 20 of page 85) you find the red inscription: archē toû keiménou beginning of the text. But already on folio 23 (below 48, 19), according to the inscription, the first book begins; according to a margin note, the second book begins; on folio 97 (below 178, 17) book II (III) begins; on folio 192