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ELEMENTS

OF

GEOMETRY,

FROM THE Latin Translation of COMMANDINE.

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

LOGARITHMS; Likewise Another of the ÉLEMENTS of Plane and Spherical

TRIGONOMETRY; With A PREFACE, shewing the Usefulness and Excel

lency of this WORK. By Doctor JOHN KEILL, F.R. S. and late

Professor of ASTRONOMY in Oxford. The Whole Revised; where deficient, Supplied; where

loft, or corrupted, Restored. Also, Many Faults committed by Dr.HARRIS,Mr.CASWELL,

Mr. Heynes, and other TRIGONOMETRICAL
WRITERS, are shewn ; and in those Cases where
They are mistaken, here are given Solutions Geome-

trically True. An Ample Account of which may be seen in the Preface.

By S A MU EL CUN N.

The ELEVENTH EDITION,

Carefully Revised and Corrected. To which is subjoined 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. JOHN-
STON, T. LONGMAN, T. CADELL,

T. DAVIES,
T. Becke T, G. ROBINSON, and R. BALDWIN.

MDCCLXXII.

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Dr.

K E IL L's

PRE FACE.

03

YOUNG Mathematician may be

surprized 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 published; especially 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 perspicuous enough; that bis Demonstrations are scarcely evident ; that his whole Elements are illdisposed; and that they have found out innumerable Falsties in them, which bad lain bid to their Times.

But, by their Leave, I make bold to offirm, that they carp at Euclid undeservedly: For his Definitions are distinct and clear, as being taken from firs Principles, and our most easy and fimple Conceptions ; and bis Demonstrations elegant, perspicuous, and concise, carrying with them such Evidence, and so much Strength of Reason, that I am easily induced to believe, that the Obscurity Sciolists fo often accuse Euclid with, is raiber to be attributed to their own per

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