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and eafy Order, and given the Reader full and ample Directions how he is to manage this Part of Arithmetic. Then follow Decimal Fractions, of more general Use, and a much more neat and elegant Method of Computation. The Doctrine of Decimal Fractions differs little from that of whole Numbers, except in the Article of Divifion, the Rule for which I have copiously explained in feveral Operations. Both Vulgar and Decimal Fractions have their particular Advantages.

The Reader having acquired the Knowledge of Vulgar and Decimal Fractions, the Extraction of the Square Root follows, an Operation but little harder than common Divifion. Then follows the Extraction of the Cube Root, by a Method which, I think, is the best I have yet feen published. The Extraction of thefe Roots are illuftrated by a great Variety of Examples, connected, for the Eafe of the Learner, in a natural and eafy Manner. I am obliged to Mr. Triplett, Teacher of the Mathematics at Kingston, for his communicating to me the Rule for the Cube Root.

Artificers, in computing their Work, may use either Decimal Fractions, or the Multiplication of Feet, Inches and Parts, by Feet, Inches and Parts; the laft is mostly used, and commonly called CrossMultiplication; for which Mr. Triplett has likewife been fo kind as to favour me with a new and

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eafy Rule, and which the Reader will find fufficiently illuftrated by Examples. To this follows the Menfuration of Superficies and Solids, the Meafuring Boards and Timber, the Explanation of the five regular or Platonic Bodies, the Defcription and Ufe of the Sliding-Rule, with a few Questions to exercife the Learner in the foregoing Rules.

Thefe Things being learnt, it naturally follows to teach the Reader the measuring the Works of Carpenters, Bricklayers, Joyners, Plaifterers, Painters, Glaziers, Mafons, &c. which are particularly explained; and, in the difficult Parts, I have confulted Some of the most eminent Surveyors.

Practical Geometry next follows, the useful Problems of which are here taught. To this fucceeds the Use of Logarithms, that great Discovery in Mathematics, which does its noble Inventor immortal Honour. The Ufe of the Logarithms, with the Table of Sines and Tangents, I have endeavoured to explain in an eafy Manner. The Knowledge of these Tables being acquired, the Reader is shown their excellent Ufe in Plain Trigonometry, both right and obliqueangled; where there are particular Directions how to conftruct the Figures and folve the Problems. After this, the Doctrine of plain Triangles is, in the fame ample Manner, applied to the measuring of acceffible and inaccfible Heights and Distances. Then follows the Method of Surveying: And, to give the Reader a fur

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a further Pleasure, he is now shown the Conftruction of the Line of Chords, Sines, Tangents and Secants.

In the Spherical Geometry I have attentively fiudied the most eafy Order in connecting the several Problems of this Part of Science; and, however new and different it may appear from the preceding Parts of the Book, I have taken fuch particular Care in the Directions, that, I am perfuaded, the Conftruction of thefe Problems will not be difficult to the Reader. In Spherical Trigonometry there are Directions how to confiruct the Problems, and the Solutions fully explained by Lord Nepier's Catholic Propofition. In the oblique Part of Spherical Trigonometry all Care was taken to render it as eafy as may be.

By thefe moft natural and eafy Steps, in which every Thing that is fuperfluous has been induftriously avoided, is the Reader led to Aftronomy, a Science which has its particular Charms. Here he will find a Collection of the most useful and practical Problems; with fome Idea of the Grandeur of the Solar System, in the Magnitude, Diftances, and other Affections of the Planets; and of the furprifing Comet which appeared in 1680, and the intenfe Heat it fuftained in its nearest Approach to the Sun. After this follows. Dialling.

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Then the Explication of the Gregorian or New Style, with the Method of finding the Golden Number, Epact, Age and Change of the Moon, &c. follows. Yet the Reader may begin and learn these first, or when he pleafes, the Rules having no Connexion with any other Parts of the Book.

The Appendix, containing the Cycles of the Planets, is a Difcovery I made many Years fince ; and have here added it together with Mr. Whifton's Cycle for Eclipfes, as I thought it would be acceptable to the Curious.

I have nothing more to add, but that I do not fee any Objection why an induftrious Reader may not, by himself, acquire all the Knowledge of the feveral Parts of this Book; the Directions and Inftructions are defigned for that Purpose, in regard to Individuals; and the whole Collection to be a regular Syftem for the Ufe of School.

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