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G E O M E T RY,

FROM THE
Latin Translation of COMMANDINE.

To which is added,
A TRE A TISE 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.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. CASWEL,
Mr. HEYNES, and other TRIGONOMETRICAL
WRIT E RS, 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 PREFACE,

By S A MUEL CUN N.
The THIRD EDITION, carefully revised and corrected,

By Y OHN HA M,
Teacher of MATHEMATics in Great-Kirby-street, Hatton-Garden.
By whom is subjoined an A P PENDIX, 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. OS BORN at St. Saviour's Deckhead near Rotberbitb.

MDCCXXXIII.

2 //

5214-40

Dr. K E l L's

PREFACE.

A

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.

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

perplexed

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