ELEMENTS O F GEOMETRY, FROM THE Latin Translation of COMMANDINE. To which is added, A TREATISE of the Nature of Arithmetic of LOGARITHMS; Likewife Another of the ELEMENTS of Plain and Spherical TRIGONOMETRY; With A PREFACE, fhewing the Usefulness and Excellency of this WORK. By Doctor JOHN KEIL F. R. S. and late Profeffor of ASTRONOMY in Oxford. The Whole revised; where deficient, fupplied; where loft or corrupted, reftored. Alfo Many Faults committed by Dr. HARRIS, Mr. CASWEL, An Ample Account of which may be seen in the PREFACE, The THIRD EDITION, carefully revised and corrected, By JOHN HAM, Teacher of MATHEMATICS in Great-Kirby-ftreet, Hatton-Garden. By whom is fubjoined an APPENDIX, containing the Investigation of thofe Series's omitted by the AUTHOR. And the Difference between Dr. K E IL and Mr. CUNN impartially examined and adjusted. LONDON: Printed for To. WOODWARD at the Half-Moon, between the Two Temple-Gates in Fleet-fltreet; And Sold by J. OSBORN at St. Saviour's Deckhead near Rotherhith. MDCCXXXIII. 1733 5-14-40 Dr. KE I L's PREFACE. A YOUNG Mathematician may be furprised, to fee the old obfolete Elements of Euclid appear afresh in Print; and that too after fo many new Elements of Geometry, as have been lately publish'd; especially fince thofe who gave us the Elements of Geometry, in a new Manner, o would have us believe they have detected a great many Faults in Euclid. Thefe acute Philofophers pretend to have difcovered that Euclid's Definitions are not perfpicuous enough; that his Demonftrations are fcarcely evident; that his whole Elements are ill difpos'd; and that they have found out innumerable Falfities in them, which had lain bid to their times. But by their Leave, I make bold to affirm, that they carp at Euclid undefervedly: For his Definitions are diftinct and clear, as being taken from first Principles, and our most easy and fimple Conceptions; and his Demonftrations elegant, perfpicuous and concife, carrying with them fuch Evidence, and fo much Strength of Reafon, that I am eafily induced to believe the Obfcurity, Sciolifts fo often accufe Euclid with, is rather to be attributed to their own perplexed A 2 |