EUCLIDE's ELEMENTS; The whole FIFTEEN BOOKS, WITH ARCHIMEDES's Theorems of the Sphere and Cylinder, Investigated by the Method of Indivifibles. ALSO, EUCLIDE's DATA, and a brief Treatife of REGULAR SOLIDS. By ISAAC BARROW, D.D. late Master of Trinity College in Cambridge. The whole carefully Corrected, and Illuftrated with Copper Plates. To which is now added an APPENDIX, Containing, The Nature, Conftruction, and Application of Logarithms. 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-n‹fterRow; R. MANBY and S. Cox on Ludgate-Hill; E. COMYNS under the Royal-Exchange; J. and J. RIVINGTON in St. Paul's Church Yard; and J. WARD in Cornhill, oppofite the RoyalExchange, 1751. F you are defirous, Courteous Reader, to know what I have performed in this Edition of the ELEMENTS Of EUCLIDE, I shall here explain it to you in fhort, according to the Nature of the Work. I have endeavoured to attain two Ends chiefly; the first, to be very perfpicuous, and at the fame time fo very brief, that the Book may not fwell to fuch a Bulk, as may be troublefome to carry about one, in both which I think I have fucceeded. Some of a brighter Genius, and endued with greater Skill, might have demonftrated most of these Propofitions with more nicety, but perhaps none with more fuccinctness than I have; efpecially fince I alter'd nothing in the Number and Order of the Author's Propofitions; nor prefum'd either to. take the Liberty of rejecting, as less neceffary, any of them, or of reducing fome of the easier fort into the · Rank of Axioms, as feveral have done; and among others, that most expert Geometrician 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 whofe most accurate Edition I had no Thoughts of attempting any thing of this Nature, 'till I confidered that this most learned Man thought fit to publish only Eight of EUCLIDE's Books, which he took the pains to explain and embellish, having in a manner rejected and undervalued the other Seven, as lefs 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 demonftrating, in as few Words as possible I could, the whole Works of EUCLIDE. As |