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The whole

compendiously Demonstrated :


ARCHIMEDES's Theorems of the

Sphere and Cylinder, Investigated by the
Method of Indivisibles.


and a brief Treatise of REGULAR SOLIDS.

By ISAAC BARROW, D.D. late Master of

Trinity College in Cambridge.

The whole carefully Corrected, and Illustrated

with Copper Plates.

To which is now added an
A P P E N D I X,

The Nature, Construction, and Application of


By J. BARROW, Author of Navigatio Britannica, &c.

LONDON: Printed for W. and J. MOUNT, and T. PAGE

on Tower-Hill; and C. Hitch and L. Hawes in Pater-nefterRow; R. MANBY and S. Cox on Ludgate-Hill; E. COMENS under the Royal-Exchange ; J. and J. RivingTon in St. Paul's Church-rard; and J. WARD in Carnhill, opposite the Royal. Exchange, 1751.

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F you are defirous, Courteous Reader, to know what I have performed in this Edition of the ELEMENTS of EUCLIDE, I Mall here explain it to

you in sport, according to the Nature of the Work. I have endeavoured to attain two Ends chiefly; the first, to be very perspicuous, and at the same time so very brief, that the Book may not (well to such a Bulk, as may be troublesome to carry about one, in both which I think I have succeeded. Some of a brighter Genius, and endued with greater Skill, might have demonstrated most of these Propofitions with more nicety, but per. haps none with more succinɛtness than I have; especially since I alter'd nothing in the Number and Order

of the Author's Propositions ; nor presum'd either to, take the Liberty of rejecting, as lefs necessary, any of

them, or of reducing some of the easier fort into the Rank of Axioms, as several have done ; and among others, that most expert Geométrician A. Tacquetus C.

(whom I the more willingly name, because I think it is !

but civil to acknowledge that I bave imitated him in fome Points) after whose most accurate Edition I had no Thoughts of attempting any thing of this Nature, 'till I considered that this most learned Man thought fit to publish only Eight of Euclide's Books, which be took the pains to explain and embellish, having in a manner rejected and undervalued the other Seven, as less appertaining to the Elements of Geometry. But my Province was originally quite different, not that of writing the Elements of Geometry after what method foever I pleas'd, but of demonstrating, in as few Words as possible I could, the whole Works of EUCLIDE, As

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