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DR. SIMSON'S PREFACE.
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 much embarrass
beginners, and is quite useless, it is now thrown out of
demonstration in the Elements we now have,
accuracy, and which plainly shew that his Elements have been much corrupted by unskilful geometers; and though these are not so gross as the others now mentioned, they ought by no means to remain uncorrected.
Upon these accounts it appeared necessary, and I hope will prove acceptable to all lovers of accurate reasoning and of mathematical learning, to remove such blemishes, and restore the principal Books of the Elements to their original accuracy, as far as I was able; especially since these Elements are the foundation of a science, by which the investigation and discovery of useful truths, at least in mathematical learning, is promoted as far as the limited powers of the mind allow : and which likewise is of the greatest use in the arts both of peace and war, to many of which geometry is absolutely necessary. This I have endeavoured to do, by taking away the inaccurate and false reasonings which unskilfal editors have put into the place of some of the genuine Demonstrations of Euclid, who has ever been justly celebrated as the most accurate of geometers, and by restoring to him those things which Theon or others have suppressed, and which have these many ages been buried in oblivion.
* In this Edition, Ptolemy's Proposition concerning a property of quadrilateral figures in a circle, is added at the end of the sixth Book. Also the Note on the 29th Proposition, Book Ist, is altered, and made more explicit, and a more general Demonstration is given, instead of that which was in the Note on the 10th Definition of Book 11th; besides, the translation is much amended by the friendly assistance of a learned gentleman.
* This Paragraph (it is believed) was added by Dr. Simson to the Preface for the second edition in 1763.
TO THIS EDITION.
In this twenty-second Edition of the ELEMENTS of Euclid by Professor Simson, the first six Books and the Eleventh and Twelfth have been printed, with the additional references and corrections from the small Edition of 1824; and the Notes, and Euclid's DATA, from the last octavo.
The ELEMENTS of Plane and SPHERICAL TRIGONOMETRY ; the TREATISE on the ConsTRUCTION of the TRIGONOMETRICAL CANON, together with Dr. Robertson's concise account of Logarithms (being highly useful additions), are preserved in this impression, and the whole has been carefully revised throughout.
Short Notices of the Lives of Euclid, and of his ablest translator and commentator, Dr. Simson, are now, for the first time, prefixed, and are chiefly drawn from Dr. Hutton's Mathematical Dictionary.
R. N. ADAMS.