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Containing the whole Subftance of Euclid's first fix, the
eleventh and twelfth Books; with feveral other, useful and
valuable, Theorems; treated in the most brief, easy, and in
telligent manner; for the ufe of Schools, &c.

Being an Attempt to render that most useful and necessary Science
more univerfal, and practically applicable.

With Notes interfperfed, critical, explanatory, and instructive.

To which is annexed, an Appendix, on the Theory of Menfuration OXON
of Superficies and Solids, as deduced from the Elements.





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Knight of the most honourable Order of the Bath, F. R. S. &c.

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S there is an undifputable Propriety in dedicating to a competent Judge of a Science, an Attempt to familiarize the Elements of it, I hope that propriety will plead an excufe for this Prefumption; efpecially, as the Subject is fo nearly connected with the bufinefs of Your Perfonal Station, and too highly important to the Publick, in general, to conceive, that any attempt at a clearer Investigation can be beneath the notice of the SurveyorGeneral of his Majesty's Ordnance, and one of the Representatives of the People.

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How far my Method of treating the Elements of Geometry may merit your Approbation, I prefume not to imagine; farther than, as I flatter myfelf, the fimplicity with which I have endeavoured to elucidate

the first Principles, to render the knowledge and the use of Geometry more general, and practically useful in common Life, where it is most wanted, may prove an additional inducement to your excufing the liberty I have taken, in thus foliciting Your Patronage and Protection; for a Work, whofe Subject, alone, is fufficient to justify the attention You may please to honour it with; whatever may be thought of the manner in which I have treated it; having been, frequently (in order to comprife the whole Elements in lefs compass) under the neceffity of deviating, confiderably, from the Path of Euclid.

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T may appear fomewhat ftrange to call fo copious a Work as

with those who have tranfcribed-Euclid, will be found to be a great abridgment of the Elements, both in the number of Theorems and length of the Demonstrations. !

But, they will find, in this Work, particularly in the 2nd, the 3rd, the 6th, 7th and 8th Books, feveral valuable Theorems which are not Euclid's ;-fome of which are elementary, and really neceflary to be known. Upon the whole, there are upwards of eighty other Theorems and Problems, exclufive of the Ellipfis.

In refpect of the practical Part, with the Introduction, it may be deemed a compleat Work of itfelf; which, with the Appendix, is more than one third part of the whole.

The Applications, Notes, and Remarks, neceffary to a young Student, and the length of fome (in the Fifth Book particularly) have fwelled the Work confiderably. The much greater number of Terms defined; various ways of performing the fame Problem, and also of demonftrating fome Theorems; the number of Fi gures, and the Preamble to each Book, &c. alfo the manner of printing, in order to have the Figure always in View, so that, many Pages are not near-full all which have concurred to extend the Work, greatly beyond my first Defign; yet, when compared with the clofe printing of others, the Elements will be found abridged, almost half; nevertheless, it contains the whole, in Subftance. The full and perfect knowledge of all, and more than is contained in Euclid, may be acquired in a third part of the Time, and with infinitely more Eafe, Pleasure, and Satisfaction to the Learner (having no Affes Bridge to get over, but the Road fmooth and even) confequently, it may, with great Propriety, be called an Abridgment.


The 7tb (fome fay the 5th) of the first Book, bas, in the Seminaries of Eru dition, been long known by the Appellation of the Affes Bridge; on rubich, many baut foundered and never got over ; nor been able to advance one step further.


I N D E X.

Shewing where to find the Propofitions of Euclid, in the First, the Third, the Fifth and Sixth, the Eleventh and Twelfth Books; in cafes of Reference, to Euclid, by Authors in the Mathematics.

In the fecond and fourth Books, the Propofitions follow in the Order of Euclid.

N. B. The Problems, of Euclid, are collected together, in the first Part; amongst other, felect Problems, in Practical Geometry. Note. The Numbers in the First Column are Euclid's; and, oppofire to them is fhewn where each Propofition may be found in this Work, whether Problem or Theorem.

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