to Four of the Books, viz. the Seventh, Eighth, Ninth, and Tenth, although they do not so nearly appertain to the Elements of plain and Solid Geometry, as the fix precedent and the two subsequent, yet none of the more Skilful Geometricians can be so 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 commensurable and incommensurable Magnitudes, so 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 last Books, cannot, without great Injustice, be pretermitted, fince that for the fake thereof our ςοιχειωθής, being a Philofopher of the Platonic Sect, is faid to bave compos'd this universal System of Elements; as Proclus lib. 2. witnesseth in these Words, "Ὅθεν δὴ κὶ τῆς συμπάσης σοιχειώσεως τέλα προεςήσαλο τὴν τῶν καλεμενων πλαζωνικῶν χημάτων σύςασιν. Besides, I eafily perfuaded my self to think, that it would not be unacceptable to any Lover of these Sciences to have in his Possession the whole Euclidean Work, as it is commonly cited and celebrated by all Men: Wherefore I resolved to omit no Book or Propofition of those that are found in P. Herigonius's Edition, whose Steps I was obliged closely to follow, by reason I took a Resolution to make use of most of the Schemes of the said Book, very well foresfeeing that Time would not allow me to form new ones, though Sometimes I chose rather to do it. For the fame Reason I was willing to use for the most part EUCLIDE's own Demonstrations, having only express'd them in a more Succinct 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 Some measure satisfied both my own Intentions, and the Defire of the Studious. As for some certain Problems and Theorems that are added in the Scholions (or short Expositions) either appertaining (by reason of their frequent Use) to the Nature of these Elements, or conducing to the ready Demonstration of those Things that follow, or which imitate the Reasons of some principal Rules of Practical Geometry, reducing them to their original Fountains, these I say, will not, I hope, make the Book fwell to a Size beyond the design'd Proportion.

The other Butt which I levell'd at, is to content the Desires of those who are delighted more with fymbolical than verbal Demonstrations. In which Kind, whereas most among us are accustom'd to the Symbols of Gulielmus Oughtredus, I therefore thought best to make use, 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; whose 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 Propositions produced 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. Besides it frequently happens, that the said Method cannot avoid fuperfluous Repititions, by which the Demonstrations are often

times

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times render'd tedious, and sometimes also more intricate; which Faults my Method easily removes by the arbritary mixture of both Words and Signs: Therefore let what has been said, touching the Intention and Method of this little Work, suffice. As to the rest, 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 these Sciences, and confequently of EUCLIDE bimself, (who digested those Elements) and others ἐξωτερικοί of that kind, may confult other Interpreters. Neither will I (as if I were afraid left these my Endeavours may fall short of being fatisfactory to all Perfons) alledge as an Excuse (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 requisite help for these Studies, nor several other things of the like Nature. But what I have bere employ'd my Labour and Study in for the Use of the ingenious Reader, I wholly Submit to his Censure and Judgment, to approve if useful, or reject if otherwise,

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I, B.

Thus

Thus far the Learned Author. But as the work bas been often printed fince his death, and by that means Several errors committed, I have, at the request of the Booksellers concerned in this treatise, and from a fincere respect and veneration for the memory of the deceased 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, almost obliterated, their place is now Supplied 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 easy as possible. And that nothing might be wanting for understanding the nature of those tables used in trigonometrical calculations, I have added an investigation of the several series invented by the illustrious Sir Ifaac Newton, for finding the length of the circumference of the circle, în equal parts of the radius, also of the fine, tangent and fecant of any arch, in the same parts, with the application of these Series to the constructing the triangular canon, and the quadrature of the Circle. I have also shewn 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.

J. BARROW.

The Explication of the Signs or

Signifies

Equal.

Greater.

Leffer.

Characters.

More, or to be added.

Less, or to be fubtracted.

The Differences, or Excess; Also, that all
the Quantities which follow, are to be
fubtracted, the Signs not being changed.

Multiplication, or the Drawing one fide of
a Rectangle into another.
The fame is denoted by the Conjunction
of Letters; as AB=AX B.

Continued Proportion.

The Side or Root of a Square, or Cube, &c.

A Square.

A Cube.

The Ratio of a square Number to a square
Number.

Other Abbreviations of Words, where-ever they occur, the Reader will without trouble understand of himself; saving some few, which, being of less general use, we refer to be explained in their Places, most commonly at the beginning of each Book in which they are ufed.

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