As this, if well executed, is evidently a Work of public Utility, it is hoped all mathematical Matters and Lovers of thofe Sciences will promote it in fuch a Degree as its Usefulness deferves. In Profecution of which Defign, this Volume is offered for public Acceptance, containing Effays on Logarithms, Plane Geometry and Trigonometry. But I It may, perhaps, be objected, by fome, that, fince the first Edition of this Volume was printed, several Volumes of a Courfe have been publifhed, by an ingenious Gentleman, and that therefore a new Courle of the Mathematics is not now neceffary. beg Leave to observe, that the Masters of Academies, and other Teachers, must be sensible that that Courfe is not drawn up in a Manner proper to introduce Learners to thofe difficult Sciences, as, in feveral of the Volumes, the difficult Parts of the Subjects are treated of before the more eafy, &c. Of this the learned Author was fo fenfible, 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 Treatife, without the Affiftance of a Mafter, when I was about 18 Years of Age; he answered, with a Kind of Surprize, "From my Fluxions! My Trea"tife was intended for Mafters, 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 fhall therefore only obferve farther, that, though it would perhaps be thought Prefumption in me to promife to treat of the fame 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. Notwithstanding Notwithstanding it is intended to treat of the feveral Sciences in fucceffive Order, as they ought to be tudied, to form a regular Courfe, for the Sake of fuch Readers as are defirous of acquiring a general Knowledge therein; yet, at the fame Time, on Account of Others, who may only be inclined to study fach Parts as may be more particularly useful to them, we shall endeavour to make each Subject distinct and entire by itself, fo that every Perfon 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 fuppofed to know no more of the Mathematics than is contained in the preceding Ef fays, and therefore must not expect any Theorems, &c. which cannot be, demonftrated by the foregoing; fo that if he happens to find any valuable Things omitted, in any Effay of ours, which he has feen 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 Inftance, in Logarithms, we have omitted the Investigation of Series, because it depends on the higher Parts of the Mathematics, and must therefore be omitted until those Parts are explained. t Effays 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 beft to omit them in this Edition: And, as the Effays on Book-Keeping have been enlarged in Number, by the Addition of The Shopkeeper's, Steward's, and Factor's, Companion, it was thought beft to publish them in a Volume by themfelves, entitled, The Accountant; and, inftead of them, in this Volume, to give the Elements ‡ of Plane Trigonometry, To oblige the Purchasers of the firft Edition of our Geometry, we have printed a larger Number of the Trigonometry, that they may not be put to the Expence of purchafing the whole Volume a fecond Time; but it will only be fold feparate to those who have already the first Edition. Trigonometry, with their Application to Altimetry and Longimetry. For a more circumftantial Account of the Contents of this Volume, we beg Leave to refer By the late pious and ingenious JAMES HERVEY, M. A. Rector of Wefton-Favel, in Northamptonshire, and Author of the Printed for B. LAW, in AVE-MARIA-LANE. AN ESSAY ΟΝ ΤΗΕ NATURE, INVESTIGATION, and APPLICATION, OF LOGARITHM S. By BENJAMIN DONN. Si numeris in ratione geometrica progredientibus fubfcribantur totidem alii æquidifferentes; dicuntur bi illorum Logarithmi. WOLFIUS, Elem. Arith. |