ELEMENTS

OF

GEOMETRY,

FROM THE

Latin Tranflation of COMMANDINE.

1

To which is added,

A TREATISE of the Nature and Arithmetic of LOGARITHMS; Likewise

Another of the ELEMENTS of Plane and Spherical TRIGONOMETRY; With

A PREFACE, fhewing the Ufefulness and Excellency of this WORK.

By Doctor JOHN KEILL, F. R. S. and late Profeffor of ASTRONOMY in Oxford.

The Whole Revifed; where deficient, Supplied; where loft, or corrupted, Reftored. Alfo,

Many Faults committed by Dr.HARRIS, Mr. CASWELL, Mr. HEYNES, and other TRIGONOMETRICAL WRITERS, are fhewn; and in thofe Cafes where They are mistaken, here are given Solutions Geometrically True.

An Ample Account of which may be feen in the PREFACE.
By SAMUEL CUN N.

The ELEVENTH EDITION,
Carefully Revised and Corrected.

To which is fubjoined an APPENDIX, containing the
Investigation of those Series omitted by the AUTHOR.
And the Difference between Dr. KEILL and Mr. CUNN
impartially examined and adjusted.

LONDON:

Printed for W. STRAHAN, J. and F. RIVINGTON, HAWES, CLARKE and COLLINS, W. JOHNSTON, T. LONGMAN, T. CADELL, T. DAVIES, T. BECKET, G. ROBINSON, and R. BALDWIN. MDCCLXXII,

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10-15-32 26815

Dr.

KEIL L's

PREFACE.

A YOUNG Mathematician may be Surprized 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 published; efpecially 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. Thefe acute Philofophers pretend to have difcovered, that Euclid's Definitions are not perfpicuous enough; that his Demonftrations are scarcely evident; that his whole Elements are illdifpofed; 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 his Definitions are diftinct and clear, as being taken from first Principles, and our most eafy and fimple Conceptions; and bis Demonftrations elegant, perfpicuous, and concife, carrying with them fuch Evi-. dence, and fo much Strength of Reason, that I am eafily induced to believe, that the Obfcurity Sciolifts fo often accufe Euclid with, is rather to be attributed to their own per

A 2

plexed