THE

Young Mathematician's Guide:

Being a PLAIN and EASY

INTRODUCTION

TO THE

MATHEMATICKS.

In FIVE PARTS.

VIZ.

I. Arithmetick, Vulgar and Decimal, with all the useful Rules;
And a General Method of Extracting the Roots of all Single Powers.
II. Algebra, or Arithmetick in Species; wherein the Method of
Raifing and Refolving Equations is rendered Easy; and illustrated with
Variety of Examples, and Numerical Queftions. Alfo the whole
Bufinefs of Intereft and Annuities, &c. performed by the Pen.

III. The Elements of Geometry contracted, and Analytically
demonftrated; with a New and eafy Method of finding the Circle's
Periphery and Area to any affigned Exactness, by one Equation only:
Alfo a New Way of making Sines and Tangents.

IV. Cortick Sections, wherein the chief Properties, &c. of the
Ellipfis, Parabola, and Hyperbola, are clearly demonstrated.

V. The Arithmetick of Infinites explained, and rendered Eafy;
with it's Application to fuperficial and folid Geometry.

With an APPENDIX of Practical Gauging.

By JOHN WARD.

The EIGHTH EDITION, carefully Corrected.

To which is now firft added,

A SUPPLEMENT, containing the Hiftory of LOGARITHMS,
and an INDEX to the whole Work.

LONDON: Printed for S. BIRT, C. HITCH, E. WICKSTEED,
J. HODGES, and E. COмYNS. 1747.

Holliday

5-19-25 To the HONOURABLE

11788

Sir RICHARD GROSVENOR, of Eaton, in the County Palatine of Chefter, Baronet.

SIR,

W

HEN requested by fome Booksellers in London, to Revife and Prepare this Trea tife for a New Impreffion, and once refolved to answer their Demands; I was not long confidering at whofe Feet to lay it.

My Memory may indeed be impaired by Age, Misfortunes, and Accidents; nay, I am fenfible it is fo: But it must be entirely loft, when I am. forgetful of the great Obligations I lie under to Sir Richard Grofvenor.

Your Hofpitality and Generofity make you stand unenvied in the Abundance of Fortune. Any Upftart may contrive to spend a Great Eftate; but it is a Felicity almoft peculiar to Great Birth to become

One.

Were I now to defcribe Liberality, without Profufenefs; Steadiness in Principles, without any private View; Candour and Affability, Good Nature joined to found Judgment, and a Serenity of Temper, which your Enemies will always find the Companion of true Courage; and then pronouce that you are poffeffed of all thefe good Qualities in as high a Degree as moft Men living; No Gentleman that knows you well, would think I flattered you.

Sir, Give me Leave to fay, I honour you Character, and love your Perfon; My Expreffions are uncourtly, my Stile unpolifhed, and therefore more proper to be prefixed to a Work wherein the Matters related are indeed clad in a plain and homely Drefs; 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 fent into the World under your Protection.

That you may long live, to promote the Good of your Country, and that City in whofe Interest you have fo heartily engaged your Self; 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.

To

To the READER.

I

Think it needlefs (and almost endless) to run over all the Ufefulness, and Advantages of Mathematicks in General; and hall 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 whatfoever, 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 affifting Principles; tho' perhaps the Artift, or Workman, bas 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 Bufinefs 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 fe 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 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 firft Elements or Principles.

That