BY WHICH THEON, OR OTHERS, HAVE LONG AGO VITIATED THESE BOOKS, ARE CORRECTED, AND SOME OF EUCLID'S DEMONSTRATIONS ARE RESTORED. ALSO, THE BOOK OF EUCLID'S DATA, IN LIKE MANNER CORRECTED. BY ROBERT SIMSON, M. D. EXERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW. TO THIS EDITION ARE ALSO ANNEXED, ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY, PHILADELPHIA: PUBLISHED BY THOMAS DESILVER JR., No. 247, MARKET STREET, AND ROBERT DESILVER, No. 110, WALNUT STREET. LYDIA R. BAILEY, PRINTER. ALSO, THE BOOK OF EUCLID'S DATA, IN LIKE MANNER CORRECTED. BY ROBERT SIMSON, M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW. TO THIS EDITION ARE ALSO ANNEXED, ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY. PHILADELPHIA : PUBLISHED BY THOMAS DESILVER Jn., No. 247, MARKET STREET, AND ROBERT DESILVER, No. 110, WALNUT STREET. LYDIA R. BAILEY, PRINTER. 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, 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 |