ing the mind, and establishing a habit of close thinking and just reasoning, in every enquiry after truth, is far fuperior to all the dialectical principles that have yet been invented; the fimplicity of its firft principles; the clearness and certainty of its demonftrations; the regular concatenation of its parts; and the univerfality of its application being fuch as no other fubject can boast. For thefe reafons, it was judged neceffary to adhere as closely as poffible to the plan of the original Elements; this being, in many refpects, much more natural and judicious than any of those which have fince been propofed by other writers. But as the work was rather defigned as a regular Inftitution of the most useful principles of the fcience, than a ftrict abridgment of EUCLID, fome alterations have been made, both in the arrangement of the propofitions and the mode of demonstration; the latter of which, in particular, it is prefumed, will be found confiderably 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 demonftrated with a fcrupulous accuracy; and it was at firft defigned that the fame method fhould have been obferved throughout; but this, in treating of the folids, was found incompatible with the plan of the work, it being here fcarcely poffible 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 perfpicuous than the former, and equally fatisfactory and convincing to the mind; efpecially in the way it is here given, which is fomething lefs exceptionable than that of CAVALERIUS, by whom it was first intro*duced! vi 1 Many other particulars might be mentioned, in which this performance 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 efcape the notice of the reader, any further account of them would be unneceffary. It is fufficient to obferve that much time and attention 1 |