PREFACE.
T HE Opinions of the Modems concerning the Author of the Elements of Geometry which go under Euclid’s Name, are very different and contrary to one another. Peter Ramus aferibes the Propofitions, as well as their Demonftrations, to Thcon ; others think the Propofitions to be Euclid’s, but that the Demonftrations are Theon’s; and others maintain that all the Propofitions and their Demonftrations are Euclid’s own. John Butco and Sir Henry SavUc arc the Authors of greateft Note who affert this laft, and the greater part of Geome- ters have ever fince been of this Opinion, as they thought it the moft probable. Sir Hmry Aavilc, after the feverai Aigum#>nts he brings to prove it, makes this Conclufion (Pag. I 3 . PracleA.) “ That excepting “ a very few Interpolations, Explications and Additions, Theon altered “ nothing in Euclid.” But, by often confidcring and comparing to- gether the Definitions and Demonftrations as they are in the Greek Editions we now have, I found that Thcon, or whoever was the Edi- tor of the prefect Greek Text, by adding fome things, fupprefling others, and mixing his own with Euclid's Demonftrations, had changed more things to the worfe than is commonly fuppofed, and thofe not of fmall moment, efpecially in the Fifth and Eleventh Books of the Elements, which this Editor has greatly vitiated, for inftance, by fub- ftituting a fliortcr, but infufficient Demonftration of the 18 lh Prop, of the 5 th Book, in place of the legitimate one which Euclid had gi- ven; and by taking out of this Book, befides other things, the good Definition which Eudoxus or Euclid had given of Compound Ratio, and giving an abfurd one in place of it in the Definition of the 6 th Book, which neither Euclid, Archimedes, Apollonius, nor any Geometer before Theon’s Time, ever made ufe of, and of which there is not to be found the leaft appearance in any of their Writings.
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