THE opinions of the moderns concerning the author of the
Elements of Geometry, which go under Euclid's name, are
very different and contrary to one another. Peter Ramus
ascr bes the propositions, as well as their demonstrations, to
Theon; others think the propositions to be Euclid's, but that
the demonstrations are Theon's; and others maintain that all
the propositions and their demonstrations are Euclid's own.
John Buteo and Sir Henry Savile are the authors of greatest)
note who assert this last, and the greater part of geometers
have ever since been of this opinion, as they thought it the
most pbable. Sir Henry Savile, after the several arguments
he brings to prove it, makes this conclusion (page 13 Prae-
lect.), "That, excepting a very few interpolations, explications,
" and additions, Theon altered nothing in Euclid." But, by
often considering and comparing together the definitions and
demonstrations as they are in the Greek editions we now have,
I found that Theon, or whoever was the editor of the present
Greek text, by adding some things, suppressing others, and
mixing his own with Euclid's demonstrations, had changed
more things to the worse than is commonly supposed, and
those not of small moment, especially in the fifth and eleventh
books of the Elements, which this editor has greatly vitiated;
for instance, by substituting a shorter, but insufficient demon-
stration of the 18th prop. of the 5th book, in place of the le-
gitimate one which Euclid had given; and by taking out of
this book, besides other things, the good definition which Eu-
doxus or Euclid had given of compound ratio, and giving an
absurd one in place of it in the 5th definition of the 6th book,