[168] πρὸς ὃ, or, to which, is wanting in the original, and in all the published collections of the Zoroastrian oracles.
[169] That is Jupiter, who is called triadic, because he proceeds from Saturn and Rhea; and because his government is participated by Neptune and Pluto, for each of these is called Jupiter by Orpheus.
[170] This sentence, within the brackets, is omitted in the printed Greek.
Fig. I. Fig. II.
Thus let a part A E B cut off by the diameter A B (fig. I.) of the circle A E B D be placed on the other part A D B, as in fig. II. Then, if it is not equal to the other part, either A E B will fall within A D B, or A D B within A E B: but in either case, C E will be equal to C D, which is absurd.
[172] This objection is urged by Philoponus, in his book against Proclus on the eternity of the world; but not, in my opinion, with any success. See also Simplicius, in his third digression against Philoponus, in his commentary on the 8th book of Aristotle’s Physics.
[173] This definition is no where extant but in the commentaries of Proclus. Instead of it, in almost all the printed editions of Euclid, the following is substituted. A segment of a circle is the figure contained by a diameter, and the part of the circumference cut off by the diameter. This Mr. Simson has marked with commas, as a symbol of its being interpolated: but he has taken no notice of the different reading in the commentaries of Proclus. And what is still more remarkable, this variation is not noticed by any editor of Euclid’s Elements, either ancient or modern.
[174] As in every hyperbola.