As to the Work in general, I think there is nothing left undemonftrated, that is capable of it; and, if any small Miftake may have happened, which in a Work of this Nature is not altogether unlikely, I am fure the generous and boneft Part of Mankind will excufe it; and as for thofe Perfons whofe Excel- lency lies in finding Fault with every Thing, and very often when there is no real Occafion, and of difcovering Errors where there are none; all I can fay to them is, that they would F. Holliday. TABLE of CONTENT S. Of Transforming and Exterminating one, or more, unknown Quantities out of Equations P. 162 170 178 189 203 208 225 229 231 242 248 261 284 285 Conftruction of Equations Some Properties of Conic Sections Of the Meafure of Ratios Of Ares, Sines, and Cofines, &c. Converging A new Method of Computing Logarithms Sir Ifaac Newton's Differentials, or Method of Fluxions, How to find the Values of Arithmetical Series, how flow fo A Solution of the inverfe Problem of Centripetal Forces Investigation of feveral curious Problems &c. p. 146. laft 1. but one, for for x2, read 2. p. 148. 1. 5. read 25. p. 148. 8 lines from x the bottom, ga, p. 156. 1. 3. xv4 p. ditto, 1. 8. P. 157. 1. 9. 2x. p. ditto, ftep 1. x -- xx · 2x p. 171. 1. 17. CR. p. 174. 1.4. after Velocity read in. p. ditto, 1. 19. for F, f, read S, f, and for SP read Sp. p. ditto, 1. 27. for leaft Velocity, read laft Velocity. 1. laft, for Sp, read S P. p. 191. read in the Margin the Fig. o. p. 198. 1. 1. read Sums. p.211. 1.7. read B4 for B6. p. 226. 1. 8. ,004. p. 228. 1. 2. 4x-4. p. 240. 1. 7. and 11. read Perpendiculars. p. 245. laft 1. dele to. p. 246. 6 lines from bottom, √2.p.250. 1. 1. read partis for partae. p. ditto, 1. 16. read in for its. p. 251: 5 lines from bottom, read Perpendiculars. [Place this before the Effay. ] I Would have the Reader understand, that the following are Translations from the Latin of the Philofophical Tranfactions, Motte's Abridgment, Vol 1. 1. An Univerfal Solution of Cubic and Biquadratic Equations analytically 2. A Method of Approximating in extracting the Root of Equations 3. Conftruction of Equations 4. Some Properties of Conic Sections, from Mr. De Moivre Page 140 154 162 170 5. Of the Meafure of Ratios, from Mr. Cotes 189 6. A new Method of Computing Logarithms 203 7. Sir Ifaac Newton's Differentials, illuftrated by Mr. Stirling 208 8. To find the Center of Ofcillation 231 9. Of the Motion of a Mufical String 242 10. Of the Laws of Centripetal Force 248 11. Of the Length of Curve Lines, by Craig 284 And alfo, I would have the Reader underftand, that Part of the Essay on the Usefulness of Mathematical Learning was printed in 1701, being a Letter from a Gentleman in Town to his Friend at Oxford: But, as it has been long out of Print, I thought it would not be amifs to revive it; which I have done, by carrying it on much further. An A N ESSAY ΟΝ ΤΗΕ USEFULNESS O F Mathematical Learning. N all Ages and Countries, where Learning hath prevailed, the Mathematical Sciences have been look'd upon as the moft confiderable Branch of it. The very Name Mános implies no lefs, by which they were called either for their Excellency, or because, of all the Sciences, they were firft taught, or becaufe they were judged to comprehend πάντα τὰ Μαθήματα. And amongst those that are commonly reckoned to be the Seven Liberal Arts, four are Mathematical, to wit, Arithmetic, Mufic, Geometry and Aftronomy. But notwithstanding their Excellency and Reputation, they have not been taught nor study'd fo univerfally, as fome of the reft, which I take to have proceeded from the following Causes: B The |