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ing the mind, and establishing a habit of close thinking and just reafoning, in every enquiry after truth, is far superior to all the dialectical principles that have yet been invented; the fimplicity of its first principles ; the clearness and certainty of its demonftrations; the regular concatenation of its parts; and the univerfality of its application being such as no other subject can boast. - For these reasons, it was judged neceffary to adhere as closely as possible to the plan of the original Elements, this being, in many respects, much more natural and judicious than any of those which have since been proposed by other writers. But as the work was rather designed as a regular Institution of the most useful principles of the science, than a strią abridgment of EUCLID, fome alterations have been made, both in the arrangement of the propositions and the mode

of demonstration; the latter of which, in particular, it is presumed, will be found considerably improved, being here delivered in a more convenient form, and rendered as

clear and explicit as the nature of the subject would admit.

In the first fix books, every thing has been demonstrated with a fcrupulous accuracy; and it-was at first designed that the same method fhould have been observed throughout; but this, in treating of the folids, was found incompatible with the plan of the work, it being here scarcely possible to follow the strict principles of EUCLID without becoming' prolix and obfcure. It was therefore thought proper, in this part of the performance, to adopt a mode of proof, which though not geometrically exact, is far more perspicuous than the former, and equally fatisfactory and convincing to the mind; especially in the way it is here given, which is fomething less exceptionable than that of CAVALERIUS, by whom it was first introduced. «1» Many other particulars might be mentioned, in which this performante will be found to differ from most others of the like nature; but' as they confift chiefly of improvements and emendations which are too obvious to escape the notice of the reader, any further account of them would be unnecessary. It is sufficient to observe that much time and



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