356 EUCLID 
Maximus (in the time ot‘ Tiberius) who says 1 that Plato, 
on being appealed to for a solution of the problem of doubling 
the cube, sent the inquirers to ‘ Euclid the geometer The 
mistake was seen by one Constantinus Lascaris (d. about 
1493), and the first translator to point it out clearly was 
Commandinus (in his translation of Euclid published in 1572). 
Euclid may have been a Platonist, as Proclus says, though 
this is not certain. In any case, he probably received his 
mathematical training in Athens from the pupils of Plato; 
most of the geometers who could have taught him were of 
that school. But he himself taught and founded a school 
at Alexandria, as we learn from Pappus’s statement that 
Apollonius ‘ spent a very long time with the pupils of Euclid 
at Alexandria ’. 2 Here again come in our picturesque 
Arabians, 3 who made out that the Elements were originally 
written by a man whose name was Apollonius, a carpenter, 
who wrote the work in fifteen books or sections (this idea 
seems to be based on some misunderstanding of Hypsicl.es’s 
preface to the so-called Book XIV of Euclid), and that, as 
some of the work was lost in course of time and the rest 
disarranged, one of the kings at Alexandria who desired to 
study geometry and to master this treatise in particular first 
questioned about it certain learned men who visited him, and 
then sent for Euclid, who was at that time famous as a 
geometer, and asked him to revise and complete the work 
and reduce it to order, upon which Euclid rewrote the work 
in thirteen books, thereafter known by his name. 
On the character of Euclid Pappus has a remark which, 
however, was probably influenced by his obvious animus 
against Apollonius, whose preface to the Conics seemed to him 
to give too little credit to Euclid for his earlier work in the same 
subject. Pappus contrasts Euclid’s attitude to his predecessors. 
Euclid, he says, was no such boaster or controversialist: thus 
he regarded Aristaeus as deserving credit for the discoveries 
he had made in conics, and made no attempt to anticipate 
him or to construct afresh the same system, such was his 
scrupulous fairness and his exemplary kindliness to all who 
1 viii. 12, ext. 1. 2 Pappus, vii, p. 678. 10-12. 
3 The authorities are al-Kindl, Ue institute libri Euclidis and a commen 
tary by Qadlzade on the Ashkal at-ta'sis of Ashraf Shamsaddln as-Samar- 
qandi (quoted by Casiri and Haji Khalfa).