Sir, Give me Leave to say, I honour your Character, and love your Perfon: My Expreffions are uncourtly, my Stile unpolished, and therefore more proper to be prefixed to a Work wherein the Matters related are indeed clad in a plain and homely Dress; but they are true, and defigned to propagate Mathematical Learning among fuch as defire to be introduced into that Sort of Knowledge; and I am extreamly pleased they are permitted to be sent into the World under your Protection. That you may long live, to promote the Good of your Country, and that City in whose Interest you have fo heartily engaged yourfelf; and that you may ever fucceed in your own private Affairs, and live to enjoy all the Bleffings that attend a quiet prudent Life, is the earnest Prayer of, Honoured SIR, Your moft Obliged, Humble, and Obedient Servant, J. WARD. I To the REA DE R. Think it needlefs (and almost endless) to run over all the fball therefore only touch upon those two admirable Sciences, Arithmetick and Geometry; which are indeed the two grand Pillars (or rather the Foundations) upon which all other Parts of Mathematical Learning depend. As to the Ufefulness of Arithmetick, it is well known that no Bufinefs, Commerce, Trade, or Employment whatsoever, even from the Merchant to the Shop-keeper, &c. can be managed and carried en, without the Affiftance of Numbers. And as to the Ufefulness of Geometry, it is as certain, that no curious Art, or Mechanick-Work, can either be invented, improved, or performed, without it's affifting Principles; tho' perhaps the Artist, or Workman, has but little (nay scarce any) Knowledge in Geometry. Then, as to the Advantages that arife from both thefe Noble Sciences, when duly joined together, to affift each other, and then apply'd to Practice, (according as Occafion requires) they will readily be granted by all who confider the vaft Advantages that accrue to Mankind from the Business of Navigation only. As alfo from that of Surveying and Dividing of Lands betwixt Party and Party. Befides the great Pleafure and Ufe there is from Timekeepers, as Dials, Clocks, Watches, &c. All these, and a great many more very useful Arts, (too many to be enumerated here) wholly depend upon the aforefaid Sciences. And therefore it is no Wonder, That in all Ages fo many Ingenious and Learned Perfons have employed themselves in writing upon the Subject of Mathematicks; but then most of thofe Authors feem to prefuppofe that their Readers had made fome Progrefs in that Sort of Learning before they attempted to perufe thofe Books, which are generally large Volumes, written in fuch abftrufe Terms, that young Learners were really afraid of looking into thofe Studies. Thefe Confiderations first put me (many Years ago) upon the Thoughts of endeavouring to compofe fuch a plain and familiar Introduction to the Mathematicks, as might encourage thofe that were willing (to fpend fome Time that Way) to venture and proceed on with Chearfulness; tho' perhaps they were wholly ignorant of it's firft Rudiments. Therefore I began with their first Elements or Principles. That That is, I began with an Unit in Arithmetick, and a Point in Geometry; and from these Foundations proceeded gradually.on, leading the young Learner Step by Step with all the Plainnefs I could, &c. And for that Reafon I published this Treatife (Anno 1707) by the Title of the Young Mathematician's Guide; which has anfwered the Title fo well, that I believe I may truly fay (without Vanity) this Treatife bath proved a very helpful Guide to near five thousand Perfons; and perhaps most of them fuch as would never have looked into the Mathematicks at all but for it. And not only fo, but it hath been very well received amongst the Learned, and (I have been often told) so well approved on at the Univerfities, in England, Scotland, and Ireland, that it is ordered to be publickly read to their Pupils, &c, The Title Page gives a fhort Account of the feveral Parts treated of, with the Corrections and Additions that are made to this Twelfth Edition, which I shall not enlarge upon, but leave the Book to fpeak for itself; and if it be not able to give Satisfaction to the Reeder, I am fure all I can fay here in it's Behalf will never recommend it: But this may be truly faid, That whoever reads it over, will find more in it than the Title doth promife, or perhaps he expects it is true indeed, the Drefs is but Plain and Homely, it being wholly intended to inflruct, and not to amufe or puzzle the young Learner with hard Words, and obfcure Terms: However, in this I shall always have the Satisfaction; That I have fincerely aimed at what is useful, tho' in one of the meanest Ways; it is Honour enough for me to be accounted as one of the Under-Labourers in clearing the Ground a little, and removing fome of the Rubbish that lay in the Way to this Sort of Knowledge. How well I have performed That, must be left to proper Judges. To be brief; as I am not fenfible of any Fundamental Error in this Treatife, fo I will not pretend to fay it is without Imperfections, (Humanum eft errare) which I hope the Reader will excufe, and pafs over with the like Candour and Good-Will that it was compofed for his Ufe. THE THE CONTENTS. Arithmetick. Part I. PRecognita, Concerning the proper Subjects, or Business of Ma- Chap. I. Concerning the feveral Parts of Arithmetick, and of Chap. II. Concerning the Principal Rules in Arithmetick, and how they are performed in whole Numbers. Chap. III. Concerning Addition, Subtraction, and Reduction of Numbers that are of different Denominations. Chap. IV. Of Vulgar Fractions, with all their various Rules. 48 Chap. V. Of Decimal Fractions or Parts, with all the useful Chap. VI. Of continued Proportion, both Arithmetical and Geo- metrical; and how to vary the Order of Things. Chap. VII. Of Disjunct Proportion, or the Golden Rule, both Direct, Reciprocal or Inverfe, and Compound. Chap. VIII. The Rules of Fellowship, Bartering, and Exchanging 57 Chap. IX. Of Alligation or Mixing of Things, with all it's Chap. X. Concerning the Specifick Gravities of Metals, &c. 117 Chap. XI. Evolution or Extracting the Roots of all Single Powers, Chap. of the Steps ufed in bringing them to an Equation. 143 Chap. II. The Six Principal Rules of Algebraick Arithmetick, in Chap. VII. Of Proportional Quantities Disjunct, both Simple, Duplicate, and Triplicate; and how to turn Equations Chap. VIII. Of Subftitution; and refolving Quadratick Equations. Chap. IX. Of Analysis, or the Method of Refolving Problems, Chap. XI. Of Simple Intereft, and Annuities in all their various Chap. XII. Of Compound Intereft, and Annuities both for Years and Chap. III. A Collection of the most useful Theorems in Plane Geometry, Analytically demonftrated. Chap. IV. The Algebraical Solution of Twenty eafy Problems in Chap. VI. A New and Eafy Method of finding the Circle's Pe- riphery, and Area, to any affigned Exactness; by the Chap. I. Definition of a Cine, and all it's Sections, &c. 361 Chap. II. Concerning the chief Properties of the Ellipfis, Chap. III. Concerning the chief Properties of the Parabola. &c. The Arithmetick of Infinites explained, and rendered eafy; with it's An Appendix of Practical Gauging. |