ELEMENTS

OF

GEOMETRY,

FROM THE

Latin Translation of COMMANDINE.

To which is added,

A TREATISE of the Nature of Arithmetic of LOGARITHMѕ; Likewise

Another of the ELEMENTS of Plain and Spherical TRIGONOMETRY; With

A PREFACE, shewing the Usefulness and Excellency of this WORK.

By Doctor JOHN KEIL, F. R. S. and late Professor of ASTRONOMY in Oxford.

The Whole revised; where deficient, supplied; where loft or corrupted, restored. Alfo

Many Faults committed by Dr. HARRIS, Mr. CASWEL,
Mr. HEYNES, and other TRIGONOMETRICAL
WRITERS, are shewn; and in those
Cafes where They are mistaken, here are
given Solutions Geometrically true.

An Ample Account of which may be seen in the PREFACE,
By SAMUEL CUΝ Ν.

The THIRD EDITION, carefully revised and corrected,
By JOHN HAM,
Teacher of MATHEMATICS in Great-Kirby-ftreet, Hatton-Garden.
By whom is subjoined an APPENDIX, containing the
Investigation of those Series's omitted by the AUTHOR.
And the Difference between Dr. KEIL and Mr.
CUNN impartially examined and adjusted.

Printed for TAO.

And Sold by J.

LONDON:

WOODWARD at the Half-Moon, between the Two
Temple-Gates in Fleet-fitreet;

OSBORN at St. Saviour's Dockhead near Rotberbith.

MDCCXXXIII.

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Dr. KE I L's

PREFAСЕ.

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YOUNG Mathematician may be Surprised, to fee the old obfolete Elements of Euclid appear afresh in Print ; and that too after so many new Elements of Geometry, as have been lately publish'd; especially fince 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 have discovered that Euclid's Definitions are not perfpicuous enough; that his Demonstrations are scarcely evident; that his whole Elements are ill dispos'd; and that they have found out innumerable Falfities in them, which had lain hid to their times.

But by their Leave, I make bold to affirm, that they carp at Euclid undefervedly: For bis Definitions are distinct and clear, as being taken from first Principles, and our most eafy and fimple Conceptions; and his Demonstrations elegant, perspicuous and concise, carrying with them fuch Evidence, and fo much Strength of Reason, that I am eafily induced to believe the Obscurity, Sciolists so often accufe Euclid with, is rather to be attributed to their own perplexed

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