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To the READER.
Think it needlefs (and almof endless) to run over all the
ball therefore only touch upon those two admirable Sciences,
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 en, without the Afiftance of Numbers.
And as to the Usefulness of Geometry, it is as certain, that no curicus Art, or Mechanick-Work, can either be invented, improved, er performed, without it's alifting Principles; tho' perhaps the Arif, or Workman, bas but little (nay scarce aoy) Knowledge in Geometry.
Ther, as to the Advantages that arise from both these Noble Sciences, wben duly joined together, to all each other, and then apply'd to Practice, (according as Occafion requires) they will Teadily be granted by all who conßder 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 thefe, and a great many more very useful Arts, (too many to be enumerated here) wbelly 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 Subject 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 porufe those Books, which are generally large Volumes, written in such abftrufe Terms, that young Learners were really afraid of looking into abole Studies.
These Confideration's 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; tho' perhaps they were wholly ignorant of it's forft Rudiments. Therefore I began with their first Elemenes or Principles.
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 Reason 1 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 fay (without Vanity) this Treatise hath proved a very helpful Guide to near five thousand Persons"; and perhaps most of them such as would never bave looked into the Mathematicks at all but for it.
And not only fo, but it bath been very well received among At 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 read to their Pupils, &c.
The Title Page gives a fort. Account of the several Parts treated of, with the Corrections and Additions that are made to ibis Fifth Edition, which I fall nat enlarge upon, but leave the Book to speak for itself; and if it be not able to give Satisfaction to the Reader, I am sure all I can say 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 promise, or perhaps he expects: it is irue indeed, the Dress is but Plain and Homely, is 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 fome of the Rubbishi that lay in the Way to this Sort of Knowledge. How well libave pero formed That, must be left to proper Judges.
To be brief; as I am noi sensible of any Fundamental: Error in this Treatife, so I will not pretend to say it is without Imperfections, (Humanum eft errare) which I hope the Reader will excufe, and pass over with the like Candour and Good-Will thar it was composed for his Use; by his real Well-wisher,
Arithmetick. Part I.
Chap. V. Of Decimal Fractions or Parts, with all the useful
Chap. IX. Of Alligation or Mixing of Things, with all it's
Varieties or Cafes.
Chap. VI. A New and caly Method of finding the Circle's Deo
riphery, and Area, to any assigned Exaltness; by the
. Alfe a Neiu Way of
Tonick Setions. Part IV.
The Arithmetick of Infinites explained, and rendered'easy; with it's
Application to Geometry; in demonstrating the Super:
HE Business of Mathematicks, in all it's Parts, both
according as Occasion requires.
By Quantity of Space is meant the Distance of one thing from another.
And by Quantity of Motion is meant the Swiftnefs of any thing moving from one place to another.
The Confideration of these, 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 Position, which may either be Natural, Accidental, or Designed, will admit of infinite Varieties : But all the Varieties that are yet known, or indeed possible to be conceived, are wholly comprized under the due Confideration of these 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,
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