Full Title: 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 Raising and Resolving Equations is Rendered Easy; and Illustrated with a Variety of Examples, and Numerical Questions. Also the Whole Business of Interest and Annuities, &c, Performed by the Pen. III. The Elements of Geometry Contracted, and Analytically Demonstrated; with a New and Easy Method of Finding the Circle’s Periphery and Area to Any Assigned Exactness, by One Equation Only: Also a New Way of Making Sines and Tangents. IV. Conick Sections, wherein the Chief Properties, &c. of the Ellipsis, Parabola, and Hyperbola, are Clearly Demonstrated. V. The Arithmetick of Infinities Explained, and Rendered Easy; with it’s [sic] Application to Superficial and Solid Geometry. With an Appendix of Practical Gauging. By John Ward. The Seventh 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. Wicksteed, J. Hodges, and E. Comyns, 1740.
To the READER.
I Think it is needless (and almost endless) to run over all the Usefulness, and Advantages of Mathematicks in General; and shall 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 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 Assistance 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 assisting Principles; tho’ perhaps the Artist, or Workman, has but little (nay, scarce any) Knowledge in Geometry.
Then, as to the Advantages that arise from both these Noble Sciences, when duly joined together, to assist each other, and then apply’d to Practice, (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 have employed themselves in writing upon the Subject of Mathematicks; but then most of those Authors seem to presuppose that their Readers had made some Progress in that Sort of Learning before they attempted to peruse those Books, which are generally large Volumes, written in such abstruse Terms, that young Learners were really afraid of looking into those Studies.
These Considerations first put me (many years ago) upon the Thoughts of endeavouring to compose such a plain and familiar Introduction to the Mathematicks, as might encourage those that were willing (to spend some Time that Way) to venture and proceed on with Chearfulness [sic]; tho’ perhaps they were wholly ignorant of it’s [sic] first Rudiments. Therefore I began with their first Elements or Principles.
That is, I began with an Unit in Arithmetick and a Pint 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 Reason I published this Treatise (Anno 1707) by the Title of the Young Mathematician’s Guide; which has answered the Title so well, that I believe I may truly say (without Vanity) this Treatise hath proved a very helpful Guide to near five thousand Persons; and perhaps most of them such as would never have looked into the Mathematicks at all but for it.
And not only so, but it hath been very well received amongst the Learned, and (I have been often told) so well approved on at the Universities, in England, Scotland, and Ireland, that it is ordered to be publickly[sic] read to their Pupils, &c.
The Title Page give a short Account of the several 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 it self; and if it be not able to give Satisfaction to the Reader, I am sure all I can say here in it’s [sic] Behalf will never recommend it; But this may be truly said, That whoever reads it over, will find more in it than the Title doth promise, or perhaps he expects: it is true indeed, the Dress is but Plain and Homely it being wholly intended to instruct, and not to amuse or puzzle the young Learner with hard Words, and obscure Terms: However, in this I shall always have the Satisfaction; That I have sincerely 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 some of the Rubbish that lay in the Way to this Sort of Knowledge. How well I have performed That, must be left to the proper Judges.
To be brief; as I am not sensible of any Fundamental Error in this Treatise, so I will not pretend to say it is without Imperfections, (Humanum est errare) which I hope the Reader will excuse, and pass over with the like Candour and Good-Will that it was composed for his Use; by his real Well-wisher,
London October 10th, 1706.
Corrected, &c. at Chester, January 20th, 1722.