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 fixe 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 reason of the very near affinity that is between Arithmetick and Geometry, but also for the Knowledge of both commenfurable and incommenfurable Magnitudes, fo exceeding necessary 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 soixeins, τοιχειωτής, being a Philofopher of the Platonic Sect, is faid to bave compos'd this universal System of Elements; as Proclus lib. 2. witnesseth in thefe Words, "Olev dny tãs ovjerάons τοιχειώσεως τέλα προεςήσατο τὴν τῶν καλεμένων πλαγωνικών χημάτων σύςασιν. Befides, I eafily per fuaded y 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 thofe that are found in P. Herigonius's Edition, whofe Steps I was obliged clofely to follow, by reafon I took a Resolution 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 fuccinit Form, unless perhaps in the Second, Thirteenth, and very few in the Seventh, Eighth, and Ninth Books, in which it seem'd not worth my while to deviate in any Particular from him: Therefore I am not without without great hopes, that as to this Part I have in fome measure 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 Ufe) to the Nature of thefe Elements, or con- ducing to the ready Demonftration of thofe Things that follow, or which imitate the Reasons 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- bolical than verbal Demonftrations. In which Kind, whereas most among us are accuftom'd to the Symbols of Gulielmus Oughtredus, I therefore thought beft to make ufe, for the most part, of his. None hitherto (as I know of) has attempted to interpret and publish EUCLIDE after this manner, except P. Herigonius; whofe Method (tho' indeed most excellent in many things, and very well accommodated for the particular purpose of that most ingenious Man) yet it seems in my Opinion to labour under a double Defect. First, in regard, that, altho' of two or more Propofitions produ- ced for the Proof of any one Problem or Theorem, the former do not always depend on the latter, yet it do not readily enough appear, either from the order of each, or by any other manner, when they agree together, and when not; wherefore, for want of the Conjunctions and Adjectives, ergo, rurfus, &c. many difficulties and occafions of doubt often arise in reading, especially to those that are Novices. Befides it frequently hap- times render'd tedious, and fometimes also more intricate; which Faults my Method easily removes by the arbritary mixture of both Words and Signs: Therefore let what has been faid, touching the Intention and Method of this little Work, fuffice. As to the reft, whoever covets to please himself with what may be said, either in Praise of the Mathematicks in general, or of Geometry in particular, or touching the HiStory of thefe Sciences, and confequently of EUCLIDE bimfelf, (who digefted thofe Elements) and others 3alremoì of that kind, may confult other Interpreters. Neither will I (as if I were afraid left thefe my Endeavours may fall fhort of being fatisfactory to all Perfons) alledge as an Excufe (though I may very lawfully do it) the want of due time which ought to be employ'd in this Work, nor the Interruption occafioned by other Affairs, nor yet the want of requifite help for these Studies, nor feveral other things of the like Nature. But what I have bere employ'd my Labour and Study in for the Ufe of the ingenious Reader, I wholly Submit to his Cenfure and Judgment, to approve if useful, or reject if otherwise, Thus far the Learned Author. But as the work bas been often printed fince his death, and by that means feveral errors committed, I have, at the request of the Bookfellers concerned in this treatise, and from a fincere respect and veneration for the memory of the deceafed Author, carefully revised the whole performance; and flatter myself, from the great pains and care I have taken, that very few errors will be found in this Edition. And as the wooden cuts in the former editions, were, by often printing, almoft obliterated, their place is now fupplied by figures engraven on Copper Plates, and proper care taken to correct the inaccuracies and errors committed by cutting them on Wood; which has given this edition great advantages over the former, both with regard to beauty and correctness. In the Appendix which I have added to this work, I have endeavoured to render the construction and use of Logarithms as plain and eafy as poffible. And that nothing might be wanting for understanding the nature of those tables used in trigonometrical calculations, I have added an investigation of the feveral feries invented by the illuftrious Sir Ifaac Newton, for finding the length of the circumference of the circle, in equal parts of the radius, alfo of the fine, tangent and fecant of any arch, in the fame parts; with the application of thefe feries to the conftructing the triangular canon, and the quadrature of the Circle. I have also fhewn the manner of computing the artificial or logarithmic fines, tangents, and fecants, from the length of the arch of the circle first given in equal parts of the radius, independant of the tables of logarithms, fines, tangents, and fecants. |
