EUCLIDE's ELEMENTS; The whole FIFTEEN BOOK'S, WITH ARCHIMEDES's Theorems of the ALSO, EUCLIDE's DATA, and a brief Treatife of REGULAR SOLIDS. By ISAAC BARROW, D.D. late Master of The whole carefully Corrected, and Illustrated To which is now added an APPENDIX, Containing, The Nature, Conftruction, and Application of By J. BARROW, Author of Navigatio Britannica, &c. LONDON: Printed for W, and J. MOUNT, and T. PAGE F you are defirous, Courteous Reader, to know what I have performed in this Edition of the ELEMENTS OF EUCLIDE, I fball here explain it to you in fport, 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 thefe 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 have 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 be 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 poffible I could, the whole Works of EUCLIDE. As a 2 to to Four of the Books, viz. the Seventh, Eighth, Ninth, and Tenth, although they do not fo nearly appertain to the Elements of plain and folid Geometry, as the fix precedent and the two fubfequent, yet none of the more Skilful Geometricians can be fo ignorant as not to know that they are very useful for Geometrical Matters, not only by reafon of the very near affinity that is between Arithmetick and Geometry, but also for the Know- . ledge of both commenfurable and incommenfurable Magnitudes, fo exceeding neceffary for the Doctrine of both plain and folid Figures. Now the noble Contemplation of the five regular Bodies that is contained in the three laft Books, cannot, without great Injustice, be pretermitted, fince that for the fake thereof our soyens, being a Philofopher of the Platonic Sect, is faid to have compos'd this univerfal Syftem of Elements; as Proclus lib. 2. witneJetb in thefe Words, Ὅθεν δὴ καὶ τῆς συμπάσης τοιχειώσεως τέλω προεςήσατο τὴν τῶν καλεμένων πλαγωνικών χημάτων σύςασιν. Befides, I eaftly per fuaded my felf to think, that it would not be unacceptable to any Lover of thefe Sciences to have in his Poffeffion the whole Euclidean Work, as it is commonly cited and celebrated by all Men Wherefore I refolved to omit no Book or Propofition of those that are found in P. Herigonius's Edition, whofe Steps I was obliged closely to follow, by reafon I took a Refolution to make use of most of the Schemes of the faid Book, very well forefeeing that Time would not allow me to form new ones, though fometimes I chofe rather to do it. For the fame Reafon I was willing to use for the most part EUCLIDE's own Demonftrations, having only exprefs'd them in a more fuccinct Form, unless perhaps in the Second, Thirteenth, and very few in the Seventh, Eighth, and Ninth Books, in which it feem'd not worth my while to deviate in any Particular from him: Therefore I am not without 1 without great hopes, that as to this Part I have in fome meafure fatisfied both my own Intentions, and the Defire of the Studious. As for fome certain Problems and Theorems that are added in the Scholions (or short. Expofitions) either appertaining (by reason of their frequent Use) to the Nature of these Elements, or con◄ ducing to the ready Demonftration of thofe Things that follow, or which imitate the Reafons of fome prin- cipal Rules of Practical Geometry, reducing them to their original Fountains, thefe I fay, will not, I hope, make the Book fwell to a Size beyond the defign'd The other Butt which I levell'd at, is to content the Defires of those who are delighted more with fym-. |