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THE ERRORS BY WHICH THEON, OR OTHERS, HAVE LONG

AGO VITIATED THESE BOOKS, ARE CORRECTED,

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BY ROBERT SIMSON, M. D.
E MERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY

GLASGOW.

BIBLIJUCA

THE SEVENTEENTH EDITION,

CAREFULLY REVISED AND IMPROVED.

TO WHICH IS ADDED,
A TREATISE ON THE CONSTRUCTION OF THE TRIGONO-
METRICAL CANON; AND A CONCISE ACCOUNT

OF LOGARITHMS.

LONDON:
PRINTED FOR WINGRAVE AND COLLINGWOOD; F. C. AND J.

RIVINGTON; SCATCHERD AND LETTERMAN; G.WILKIE; LONG-
MAN, HURST, REES, ORME, AND BROWN; CADELL AND DAVIES;
LAW AND WHITTA KER; J. RICHARDSON; J. M, RICHARDSON;
J. MAWMAN; AND WALKER AND EDWARDS,

Printed by S. Hamilton, Weybridge, Surrey.

TO

THE KING,

THIS EDITION

OF THE

PRINCIPAL BOOKS

OF THE

ELEMENTS OF EUCLID,

AND OR THE

BOOK OF HIS DATA,

IS MOST HUMBLY DEDICATED,

BY

HIS MAJESTY'S

MOST DUTIFUL,

AND MOST DEVOTED SUBJECT AND SERVANT,

ROBERT SIMSON.

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PRE FACE.

1

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 ascribes 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 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 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, has 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 Demonstration of the 18th Prop. of the 5th Book, in place of the legitimate one which Euclid had given; and by taking out of this Book, besides other things, the good definition which Eudoxus 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 mych 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

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