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Ε L Ε Μ Ε Ν Τ S

OF

EUCLID;

VIZ.

THE FIRST SIX BOOKS,

TOGETHER WITH THE

ELEVENTH AND TWELFTH.

The ERRORS by which Theon, or others, have long ago

vitiated these Books, are CORRECTED,

And some of EUCLID'S DÉMONSTRATIONS are Restored.

ALSO

THE BOOK OF

EUCLID'S DA TA,

In like Manner CORRECTED.

By ROBERT SIMSON, M. D. .
Emeritus Professor of Mathematics in the University of Glasgow.

To this TWELFTH EDITION are also annexed

ELEMENTS OF PLAIN AND SPHERICAL TRIGONOMETRY.

LONDON:

Printed for F. WINGRAVE, in the Strand, Succeffor to Mr. NOURSE.

1 804.

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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

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