T To the READER. Think it needlefs (and almost endless) to run over all the 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 on, 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 affifling Principles; tho' perhaps the Artift, or Workman, has but little (nay fcarce 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 vast Advantages that accrue to Mankind from the Bufinefs of Navigation only. As alfe from that of Surveying and Dividing of Lands betwixt Party and Party. Befides the great Pleasure 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 aforesaid Sciences. And therefore it is no Wonder, That in all Ages fo many Ingenious and Learned Perfons bave employed themfelves 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 peruse 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 Plainness I could, &c. And for that Reafon I published this Treatife (Anno 1707) by the Title of the Young Mathematician's Guide; which has answered the Title fo well, that I believe I may truly fay (without Vanity) this Treatife hath proved a very helpful Guide to near five thousand Perfons's 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) fo 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 fhart. Account of the feveral Parts treated of, with the Corrections and Additions that are made to this Fifth Edition, which I shall not enlarge upon, but leave the Book to speak for itself; and if it be not able to give Satisfaction to the Reader, I am fure all I can fay here in it's Behalf will never recommend it: But this may be truly faid, Thut whoever reads it over, will find more in it than the Title doth promife, or perhaps he expects: it is true indeed, the Dress is but Plain and Homely, it being wholly intended to instruct, and not to amufe or puzzle the young Learner with hard Words, and obfcure Terms: However, in this I fhall always have the Satisfaction; That I have fincerely aimed at what is ufeful, 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; by his real Well-wisher, London, October 10th, 1706. Corrected, &c. at Chester, January 20th, 1722. J. WAR D. THE Chap. II. Concerning the Principal Rules in Arithmetick, and how they are performed in whole Numbers. I. Concerning the feveral Parts of Arithmetick, and of fuch Characters as are used in this Treatife. Chap. III. Concerning Addition, Subtraction, and Reduction of Numbers that are of different Denominations. 31 Chap. IV. Of Vulgar Fractions, with all their various Rules. 48 Chap. V. Of Decimal Fractions or Parts, with all the useful 57 Chap. VI. Of continued Proportion, both Arithmetical and Geo- metrical; and how to vary the Order of Things. Chap. X. Concerning the Specifick Gravities of Metals, &c. 117 Chap. XI. Evolution or Extracting the Roots of all Single Powers, Algebza. Part II. I. The Method of noting down Quantities, and tracing of the Steps ufed in bringing them to an Equation. 143 Chap. II. The Six Principal Rules of Algebraick Arithmetick, in Chap. III. Of Algebraick Fractions, or Broken Quantities. 163 Chap. IV. Of Surds, or Irrational Quantities, Chap. V. Concerning the Nature of Equations, and how to pre- Chap. VII. Of Proportional Quantities Disjunct, both Simple, Duplicate, and Triplicate; and how turn Equations. Chap. VIII. Of Subftitution; and refolving Quadratick Equations. Chap. XII. Of Compound Intereft, and Annuities both for Years and 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 Solution of one Equation only. Also a New Way of making Natural Sines and Tangents à priore. Chap. I. Definition of a Cone, and all it's Sections, &c. 347 36л Chap. II. Concerning the chief Properties of the Ellipfis, &c. Chap. III. Concerning the chief Properties of the Parabola. The Arithmetick of Infinites explained, and rendered eafy with it's AN ΑΝ INTRODUCTION TO THE Mathematicks, PART I. PRÆCOGNITA. T HE Business of Mathematicks, in all it's Parts, both By Quantity of Matter is here meant the Magnitude, or Big nefs of any vifible thing, whofe Length, Breadth, and Thickness, may either be measured, or estimated. By Quantity of Space is meant the Distance of one thing from another. And by Quantity of Motion is meant the Swiftness of any thing moving from one Place to another. The Confideration of thefe, according as they may be proposed, are the Subjects of the Mathematicks, but chiefly that of Matter. Now the Confideration of Matter, with respect to it's Quantity, Form, and Pofition, which may either be Natural, Accidental, or Defigned, will admit of infinite Varieties: But all the Varieties that are yet known, or indeed poffible to be conceived, are wholly comprized under the due Confideration of thefe Two, Magnitude and Number, which are the proper Subjects of Geometry, Arithmetick, and Algebra. All other Parts of the Mathematicks being only the Branches of these three Sciences, or rather their Application to particular Cafes. B cometr |