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To the READER.


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 Bufiness, Commerce, Trade, or Employment whatsoever, even from the Merchant to the Shop-keeper, &c. can be managed and carried an, 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 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 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 aforefaid 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 those 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 firft put me (many Years ago) upon the Thoughts of endeavouring to compofe fuch a plain and familiar Introduction to the Mathematicks, as might encourage those that were willing (to spend 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 is, I began with an Unit in Arithmetick, and a Point in Geometry; and from thefe Foundations proceeded gradually on, leading the young Learner Step by Step with all the Plainnefs 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 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 Universities, in England, Scotland, and Ireland, that it is ordered to be publickly read to their Pupils, &c.

The Title Page gives a fhort. 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 inftruct, and not to amuse 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 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 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 Chefter,
January 20th, 1722.




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Chap. I. Definition of a Cone, and all it's Sections, &c. 361

Chap. II. Concerning the chief Properties of the Ellipfis, &c.

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HE Bufinefs of Mathematicks, in all it's Parts, both
Theory and Practice, is only to fearch out and determine
the true Quantity; either of Matter, Space, or Motion,
according as Occafion requires.


By Quantity of Matter is here meant the Magnitude, or Big nefs of any visible thing, whofe Length, Breadth, and Thickness, may either be measured, or estimated.


By Quantity of Space is meant the Distance of one thing from
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 propofed, 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, Arith-
metick, 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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