TH

"HE 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

ascribes the Propositions, as well as their Demonstrations, to

Theon; others think the Propofitions 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 affert this last, and the greater part of geometers

have ever since been of this opinion, as they thought it the

most probable. Sir Henry Savile, after the several arguments

he brings to prove it, makes this conclusion (Page 13. Prælect.)

“ That, excepting a very few interpolations, explications, and

$ additions, Theon altered nothing in Euclid." But, by often

considering and comparing together the Definitions and De-

monftrations 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 fubftituting a shorter, but insufficient Demon-

ftration 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, which neither Euclid, Archimedes, Apollonius, nor

any geometer before Theon's time, ever made use of, and of

which there is not to be found the least

appearance in any

of their writings; and, as this Definition did much embarrass beginners, and is quite useless, it is now thrown out of the Elements, and another, which, without doubt, Euclid had given, is put in its proper place among the Definitions of the

5th