THE DATA 
425 
Again, since the triangles ADC, BDE are similar, 
BE: ED = AG: CD = (BA + AG): BC. 
Therefore (BA +AG).ED = BO, BE, which is given. 
On divisions (of figures). 
The only other work of Euclid in pure geometry which has 
survived (but not in Greek) is the book On divisions (of 
figures), irepl ^laipéaeonv (3l(3\îov. It is mentioned by Proclus, 
who gives some hints as to its content 1 ; he speaks of the 
business of the author being divisions of figures, circles or 
rectilineal figures, and remarks that the parts may be like 
in definition or notion, or unlike ; thus to divide a triangle 
into triangles is to divide it into like figures, whereas to 
divide it into a triangle and a quadrilateral is to divide it into 
unlike figures. These hints enable’ us to check to some extent 
the genuineness of the books dealing with divisions of figures 
which have come down through the Arabic. It was John Dee 
who first brought to light a treatise De divisionifms by one 
Muhammad Bagdadinus (died 1141) and handed over a copy 
of it (in Latin) to Commandinus in 1563 ; it was published by 
the latter in Dee’s, name and his own in 1570. Dee appears 
not to have translated the book from the Arabic himself, but 
to have made a copy for Commandinus from a manuscript of 
a Latin translation which he himself possessed at one time but 
which was apparently stolen and probably destroyed some 
twenty years after the copy was made. The copy does not 
seem to have been made from the Cotton MS, which passed to 
the British Museum after it had been almost destroyed by 
a fire in 1731. 2 The Latin translation may have been that 
made by Gherard of Cremona (1114-87), since in the list of 
his numerous translations a ‘ liber divisionum ’ occurs. But 
the Arabic original cannot have been a direct translation from 
Euclid, and probably was not even a direct adaptation of it, 
since it contains mistakes and unmathematical expressions; 
moreover, as it does not contain the propositions about the 
3 Pi’oclus on End. I, p. 144. 22-6. 
2 The question is fully discussed by R. C. Archibald, Euclid's Book on 
Divisions of Figures with a restoration based on Woepche's text and on the 
Practica Geometriae of Leonardo Pisano (Cambridge 1915),