STUDY OF EUCLID IN THE MIDDLE AGES 369 
lectures on the Sphaera mundi, planetary theory, three Books 
of Euclid, optics and arithmetic. At Leipzig (founded 1409), 
as at Vienna and Prague, there were lectures on Euclid for 
some time at all events, though Hankel says that he found no 
mention of Euclid in a list of lectures given in the consecutive 
years 1437-8, and Regiomontanus, when he went to Leipzig, 
found no fellow-students in geometry. At Oxford, in the 
middle of the fifteenth century, the first two Books of Euclid 
were read, and doubtless the Cambridge course was similar. 
The first English editions. 
After the issue of the first printed editions of Euclid, 
beginning with the translation -of Campano, published by 
Ratdolt, and. of the editio princeps of the Greek text (1533), 
the study of Euclid received a great impetus, as is shown 
by the number of separate editions and commentaries which 
appeared in the sixteenth century. The first complete English 
translation by Sir Henry Billingsley (1570) was a monumental 
work of 928 pages of folio size, with a preface by John Dee, 
and notes extracted from all the most important commentaries 
from Proclus down to Dee himself, a magnificent tribute to 
the immortal Euclid. About the same time Sir Henry Savile 
began to give unpaid lectures on the Greek geometers; those 
on Euclid do not indeed extend beyond I. 8, but they are 
valuable because they deal with the difficulties connected with 
the preliminary matter, the definitions, &c., and the tacit 
assumptions contained in the first propositions. But it was 
in the period from about 1660 to 1730, during which Wallis 
. and Halley were Professors at Oxford, and Barrow and 
Newton at Cambridge, that the study of Greek mathematics 
was at its height in England. As regards Euclid in particular 
Barrow’s influence was doubtless very great. His Latin 
version (Euclidis Elementorum Libri XV hreviter demon- 
strati) came out in 1655, and there were several more editions 
of the same published up to 1732; his first English edition 
appeared in 1660, and was followed by others in 1705, 1722, 
1732,1751. This brings us to Simson’s edition, first published 
both in Latin and English in 1756. It is presumably from 
this time onwards that Euclid acquired the unique status as 
1523 B b 
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