CHAPTER VI.
THE SCHOLIA.
Heiberg has collected scholia, to the number of about 1500, in Vol. v. of his edition of Euclid, and has also discussed and classified them in a separate short treatise, in which he added a few others.
1
These scholia cannot be regarded as doing much to facilitate the reading of the
Elements. As a rule, they contain only such observations as any intelligent reader could make for himself. Among the few exceptions are XI. Nos. 33, 35 (where XI. 22, 23 are extended to solid angles formed by any number of plane angles), XII. No. 85 (where an assumption tacitly made by Euclid in XII. 17 is proved), IX. Nos. 28, 29 (where the scholiast has pointed out the error in the text of IX. 19).
Nor are they very rich in historical information; they cannot be compared in this respect with Proclus' commentary on Book I. or with those of Eutocius on Archimedes and Apollonius. But even under this head they contain some things of interest, e.g. II. No. 11 explaining that the gnomon was invented by geometers for the sake of brevity, and that its name was suggested by an incidental characteristic, namely that “from it the whole is known (
γνωρίζεται), either of the whole area or of the remainder, when it (the
γνώμων) is either placed round or taken away”
; II. No. 13, also on the gnomon; IV. No. 2 stating that Book IV. was the discovery of the Pythagoreans; V. No. 1 attributing the content of Book V. to Eudoxus; X. No. 1 with its allusion to the discovery of incommensurability by the Pythagoreans and to Apollonius' work on irrationals; X. No. 62 definitely attributing X. 9 to Theaetetus; XIII. No. 1 about the “Platonic”
figures, which attributes the cube, the pyramid, and the dodecahedron to the Pythagoreans, and the octahedron and icosahedron to Theaetetus.
Sometimes the scholia are useful in connexion with the settlement of the text, (1) directly, e.g. III. No. 16 on the interpolation of the word “within”
(
ἐντός) in the enunciation of III. 6, and X. No. 1 alluding to the discussion by “Theon and some others”
of irrational “surfaces”
and “solids,”
as well as “lines,”
from which we may
