Complete Works of Euclid, Vol. 6 (Optics, Catoptrics, etc.)

very often (sometimes even with an almost ridiculous consistency, as in II p. 434) have perished, this has not happened through my fault.

In the testimonies, it must be added that most of the definitions of book I, with the five postulates and the common notions 2, 3, 1, translated into Latin, are read in a fragment edited by Hultsch after Censorinus, pp. 60—63 (it has "ἴσων" on I p. 4, 2; def. 13 is omitted; in def. 15, which is altogether shorter and corrupt — see Hultsch Neue Jahrb. 1880 p. 288 — both "ἢ καλεῖται περιφέρεια" and "πρὸς τὴν τοῦ κύκλου περιφέρειαν" are omitted; def. 18 is "hemicyclium circuli dimidium", then follows def. 19; in def. 21 before "ἔχον" on p. 6, 13, I added unum by conjecture, the codices have ide; at the beginning of the postulates: "postulata geometrarum sunt quinque"; then follows without a title "κοιν. ἔνν. 2, 3, 1").

With IV p. 336, 15 sq., compare Pappus V, 37 p. 358: "ὅτι δὲ πλείω τῶν ε̅ τούτων ἀδύνατόν ἐστιν εὑρεῖν ἄλλα σχήματα ἴσοις καὶ ὁμοίοις ἰσοπλεύροις πολυγώνοις περιλαμβανόμενα, καὶ ὑπὸ τοῦ Εὐκλείδου καὶ ὑπό τινων ἄλλων ἀποδέδεικται."

Concerning the Arabic numeral marks, which occur in the Viennese scholia mostly in book X, I will only mention this, that those scholia were written by hand V^b, i.e., without a doubt in the 12th century. For the number 5, 𐍁 is used, but our 0 is a point or ᵒ; the series of numbers are exactly similar in B fol. 32^u (at the beginning of book II) by a more recent hand: 𐍀𐍁𐍂𐍃𐍄𐍅𐍆𐍇𐍈 and in b at II, 1 by a more recent hand: "ψῆφος ἰνδική" α β γ δ ε ϛ ζ η θ ι — 𐍀𐍁𐍂𐍃𐍄𐍅𐍆𐍇𐍈

Written in Copenhagen in the month of March, MDCCCLXXXVII.