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To which is added, A TREATISE of the Nature of Arithmetic of

LOGARITHMS; Likewise Another of the ELEMENTS of Plain and Spherical TRIGONOMETRY;

With A PREFACE, Thewing the Usefulness and Excellency of

this WORK. By Doctor JOHN KEIL, F. R. $. and late Professor

of ASTRONOMY in Oxford. The Whole revised; where deficient, supplied; where lost

or corrupted, restored. Also Many Faults committed by Dr. HARRIS, Mr. CASWEL, Mr. Heynes, and other TRIGONOMETRICAL WRITERS, are shewn; and in those Cases where They are mistaken, here are

given Solutions Geometrically true. An Ample Account of which may be seen in the PREFAC E,

By S A MU EL CU N N. The THIRD EDITION, carefully revised and corrected,

By JOHN HA M, Teacher of MATHEMATics in Great-Kirby-street, Hatton-Garden.

whom is subjoined an APPENDIX, containing the Investigation of those Series's omitted by the AUTHOR. And the Difference between Dr. KE IL and Mr.

CUNN impartially examined and adjusted.

LONDON: Printed for Tho. WOODWARD at the Half-Moon, between the Two

Temple-Gates in Fleet-street; And Sold by J. OSBORN at St. Saviour's Dockbead near Rotberbitb.


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Dr. K E I L's



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YOUNG Mathematician may be surprised, to see the old obsolete Elements of Euclid appear afresh in

Print ; and that too after so many new Elements of Geometry, as have been lately publishd; especially since those who gave us the Elements of Geometry, in a new Manner, would have us believe they have detected a great many Faults in Euclid. These acute Philosophers pretend to bave discovered that Euclid's Definitions are not perspicuous enough; that his Demonstrations are scarcely evident'; that his whole Elements are ill dispos’d; and that they have found out innumerable Falsities in them, which had lain bid to their times.

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But by their Leave, I make bold to affirm, that they carp at Euclid undeservedly: For his Definitions are diftinet and clear, as being taken from first Principles, and our most easy and simple Conceptions ; and his Demonstrations elegant, perspicuous and concisë, carrying with them such Evidence, and so much Strength of Reason, that I am eafily induced to believe the Obscurity, Sciolifts so often accuje Euclid with, is rather to be attributed to their own


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