VII

PREFACE.

Another peculiar usage must also be mentioned, whether it is Proclus’s alone or that of his age, namely that the same letter signifies two things. For in the figure described on page 290, ε denotes both the circle described with center γ and radius γδ, and also a point somewhat beyond its circumference; in a similar way, in the figure described on page 346, ε denotes both the triangle and the point of the circle drawn with center δ and radius δζ. Finally, it is worthy of memory that the collection of two straight lines is signified by letters placed next to each other, e.g., line segment αγ = line segment α + line segment γ.

It remains for me to speak of the partition by which Proclus’s commentaries are divided into four books, and the individual books into chapters and commentaries. Proclus himself in only one place, on line 24 of page 352, uses the word tmēma section/segment to denote one part of Euclid’s propositions. Those propositions which precede, he calls hypotheseis hypotheses/premises on page 354, line 8, and ta pro tōn theōrēmatōn those things before the theorems on page 364, line 19. Never does he cross over to other questions in such a way that you could say he is concluding one book and beginning another. He only concludes individual questions and adds what he is about to say, such as in lines 23—26 of page 81. If you inspect the codex, you might guess that the prologue and the four books are distinguished by a title written in red ink, and you might judge that you have rightly understood, since on the folio of the codex marked number 44 (below on page 85, line 20) you find the red inscription: archē tou keimenou beginning of the text. But already on folio 23 (below 48, 19), according to one inscription, the first book begins; according to a marginal note, the second book begins; on folio 97 (below 178, 17), the second (third) book; on folio 192...