As this, if well executed, is evidently a Work of public Utility, it is hoped all mathematical Masters and Lovers of those Sciences will promote it in such * Degree as its Usefulness deserves. In Prosecution of which Design, this Volume is offered for public Acceptance, containing Esays on Logarithms, Plane Geometry and Trigonometry. It may, perhaps, be objected, by some, that, since the first Edition of this Volume was printed, several Volumes of a Course have been published, by an ingenious Gentleman, and that therefore a new Course of the Mathematics is not now necessary. But I beg Leave to observe, that the Masters of Academies, and other Teachers, must be sensible that that Course is not drawn up in a Manner proper to introduce Learners to those difficult Sciences, as, in several of the Volumes, the difficult Parts of the Subjects are treated of before the more easy, &c. Of this the learned Author was so sensible, that, on my acquainting him (when I had the Pleafure of feeing him in London) that I obtained my firft Knowledge of Fluxions from his excellent Treatise, without the Alistance of a Master, when I was about 18 Years of Age; he answered, with a Kind of Surprize, “ From my Fluxions! My Trea6 tise was intended for Masters, not for Learners." I have not made this Remark either out of any high Opinion I entertain of my own Abilities or to depreciate his Works, but only to give his own Idea of his Publications. I efteem him as an excellent Mathematician, and shall therefore only observe farther, that, though it would perhaps be thought Presumption in me to promise to treat of the same Subjects in a more masterly Manner, yet, I may venture to say, I hope to give them on a much more enlarged Plan, with respect to practical Mathematics, and more easy to be understood by young Mathematicians. Notwithftanding Notwithstanding it is intended to treat of the fevefal Sciences in successive Order, as they ought to be tudied, to form a regular Course, for the Sake of fuch Readers as are desirous of acquiring a general Knowledge therein; yet, at the fame Time, on Ac: count of Others, who may only be inclined to study sach Parts as may be more particularly useful to them, we shall endeavour to make each Subject distinct and entire by itself, so that every Person may have it at his own Choice to read what Subjects he pleases. As this work is written as a Course, the Reader of any Effay is supposed to know no more of the Mathematics than is contained in the preceding Elsays, and therefore must not expect any Theorems, &c. which cannot be demonstrated by the foregoing; so that if he happens to find any valuable Things omitted, in any Effay of ours, which he has seen in any other Work, we would not have him think we have forgot to infert it, but that we refer it to a more proper Place, in a future Effay. For Instance, in Logarithms, we have omitted the Investigation of Series, because it depends on the higher Parts of the Mathematics, and must cherefore be omitted until those Parts are explained. Essays on Circulating-Decimals and Book-Keeping were prefixed to the first Edition of our Geometrician, and published under the Title of The Accountant and Geometrician; but, as they have no Connection with Geometry, it was thought best to omit them in this Edition : And, as the Essays on Book-keeping have been enlarged in Nurnber, by the Addition of The Shopkeeper's, Steward's, and Faetor's, Companion, it was thought best to publish them in a Volume by themselves, entitled, The Accountant; and," inftead of them, in this Volume, to give the Elements I of Plane Trigonometry, 1 To oblige the Purchasers of the first Edition of our Geometry, we have printed a larger Number of the Trigonometry, that they may not be put to the Expence of purchasing the whole Volume a second Time ; but it will only be sold separate to those who have already the firft Edition. Trigonometry, with their Application to Altimetry and Longimetry. For a more circumstantial Account of the Contents of this Volume, we beg Leave to refer Just published, Preached at the Funeral of Mr. ABRAHAM Donn, By the late pious and ingenious JAMES HERVEY, M. A. MEDITATIONS and CONTEMPLATIONS. Printed for B. LAW, in Ave-MARIA-LANE, |