(7) q = Paris MS. 2344, folio; 12th c.
It is written by one hand but includes scholia by many hands. On leaves 1 to 16 (recto) are scholia with the same title as that found by Wachsmuth in a Vatican MS. and relied upon by him to prove that Proclus continued his commentaries beyond Book I.1 Leaves 17 to 357 contain the Elements I.—XIII. (except that there is a lacuna from the middle of VIII. 25 to the ἔκθεσις of IX. 14); before Books VII. and X. there are some leaves filled with scholia only, and leaves 358 to 366 contain nothing but scholia.
(8) Heiberg also used a palimpsest in the British Museum (Add. 17211). Five pages are of the 7th—8th c. and are contained (leaves 49-53) in the second volume of the Syrian MS. Brit. Mus. 687 of the 9th c.; half of leaf 50 has perished. The leaves contain various fragments from Book X. enumerated by Heiberg, Vol. III., p. v, and nearly the whole of XIII. 14.
Since his edition of the Elements was published, Heiberg has collected further material bearing on the history of the text2. Besides giving the results of further or new examination of MSS., he has collected the fresh evidence contained in an-Nairīzī's commentary, and particularly in the quotations from Heron's commentary given in it (often word for word), which enable us in several cases to trace differences between our text and the text as Heron had it, and to identify some interpolations which actually found their way into the text from Heron's commentary itself; and lastly he has dealt with some valuable fragments of ancient papyri which have recently come to light, and which are especially important in that the evidence drawn from them necessitates some modification in the views expressed in the preface to Vol. V. as to the nature of the changes made in Theon's recension, and in the principles laid down for differentiating between Theon's recension and the original text, on the basis of a comparison between P and the Theonine MSS. alone.
The fragments of ancient papyri referred to are the following.
1.
Papyrus Herculanensis No. 1061.3
This fragment quotes Def. 15 of Book I. in Greek, and omits the words ἣ καλεῖται περιφέρεια, “which is called the circumference,”
found in all our MSS., and the further addition πρὸς τὴν τοῦ κύκλου περιφέρειαν also found in practically all the MSS. Thus Heiberg's assumption that both expressions are interpolations is now confirmed by this oldest of all sources.
2.
The Oxyrhynchus Papyri I. p. 58, No. XXIX. of the 3rd or 4th c. This fragment contains the enunciation of Eucl. II. 5 (with figure, apparently without letters, immediately following, and not, as usual in our MSS., at the end of the proof) and before it the part of a word περιεχομε belonging to II. 4 (with room for -νῳ ὀρθογωνίῳ: ὅπερ ἔδει
1 [εἰς τ]ὰ τοῦ Εὐκλείδου στοιχεῖα προλαμβανόμενα ἐκ τῶν Πρόκλου σποράδην καὶ κατ̓ ἐπιτομήν. Cf. p. 32, note 8, above.
2 Heiberg, Paralipomena zu Euklid in Hermes, XXXVIII., 1903, pp. 46-74, 161-201, 321-356.
3 Described by Heiberg in Oversigt over det kngl. danske Videnskabernes Selskabs Forhandlinger, 1900, p. 161.
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
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