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Young Mathematician's Guide :

Being a PLAIN and EASY




In Five PAR T S.

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V I Z.
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

Railing and Resolving Equations is rendered Easy; and illustrated with
Variety of Examples, and Numerical Questions. Also the whole

Business of Interest and Annuities, Etc. performed by the Pen.
III. The Elements of Gcometry contracted, and Analytically.

demonstrated; with a New and easy Method of finding the Circle's
Periphery and Area to any assigned Éxactness, by one Equation only:

Also a New Way of making Sines and Tangents.
IV. Cortick Sections, wherein the chief Properties, &c. of the

Ellipsis, Parabola, and Hyperbola, are clearly demonstrated.
V. The Arithmetick of Infinites explained, and rendered Easy;
with it's Application to fuperficial and solid Geometry.
With an APPENDIX of Practical Sauging.

The EIGHTH EDITION, carefully Corrected.

To which is now first added,
A SUPPLEMENT, containing the History of LOGARITHMS,

and an INDEX to the whole Work.

LONDON: Printed for S. Birt, C. HITCH, E. WICKSTEBD,

J. HODGES, and E. COMYNs. 1747.


5-19-23 To the HONOUR ABLE


Eaton, in the County Palatine of Chester, Baronet.



HEN requested by some Booksellers in
London, to Revise and Prepare this Tream

tise for a New Impression, and once resolved to answer their Demands; I was not long considering at whosc Feet to lay it.

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

Your Hospitality and Generofity make you stand unenvied in the Abundance of Fortune. Any Upstart may contrive to spend a Great Estate ; but it is a Felicity almost peculiar to Great Birth to become One.

Were I now to describe Liberality, without Pro fuseness ; 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 possessed of all these good Qualities in as high a Degree as moft Men living ; No Gentleman that knows you well, would think I flattered you.

A 2



Sir, Give me Leave to say, I honour

you racter, and love your Person; My Expressions are uncourtly, my Stile unpolished, and therefore more proper to be prefixed to a Work wherein the Matters telated are indeed clad in a plain and homely Dress; but they are true, and designed to propagate Mathematical Learning among such as desire to be introduced into that sort of Knowledge; and I am extreamly pleased they are permitted to be sent into the World under


Protection. That you may long live, to promote the Good of your Country, and that City in whose Interest you have so heartily engaged your Self; and that you may ever succeed in your own private Affairs, and dive to enjoy all the Blessings that attend a quiet prudent Life, is the earnest Prayer of,

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To the REA DE R.


Think it needless (and almost endless) to run over all the
Usefulness, and Advantages of Mathematicks in General; and

hall therefore only touch upon those two admirable Sciences, Arichmetick 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 Usefulness of Arithmetick, it is well known that no Business, Commerce, Trade, or Employment whatsoever, even from the Merchant to the Shop-keeper, &c. can be managed and carried on, without the Alifance of Numbers.

And as to the Usefulness of Geometry, it is as certain, that no curious Art, or Mechanick-Work, can either be invented, improved, or performed, without it's afifling Principles; tho' perhaps the Artif, or Workman, bas but little (nay scarce any) Knowledge in Geometry.

Then, as to the Advantages that arise from both these Noble Sciences, when duly joined togetber, to alij each other, and then apply'd to Pratice, (according as Occasion requires) they will readily be granted by all who consider the vast Advantages that accrue to Mankind from the Business of Navigation only. As also from that of Surveying and Dividing of Lands betwixt Party and Party. Besides the great pleasure and Use 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 so many Ingenious and Learned Persons bave employed themselves in writing upon the Subjęlt of Mathematicks; but then most of those Authors seem to presuppose that their Readers had made fome Progress in that sort of Learning before they attempted to peruse those Books, which are generally large Volumes, written in such abftrufe Terms, that young Learners were really afraid of looking into sbose Studies.

These Confiderations first put me (many Years ago) upon the Thoughts of endeavouring to compose such a plain and familiar Ina troduction to the Mathematicks, as might encourage those that were willing (to spend some Time that Way) to venture and proceed on with Chearfulness; ibo' perhaps they were wholly ignorant of it's for ft Rudiments. Therefore I began with their first Elements or Principles.


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