Vll

PREFACE.

quainted with the Elements of Geometry,and yet know but very little of their Appli-cation, without which it is in vain to expectto make any great Advances, I have alsogiven a large Variety of Geometrical Pro-blems with their Constructions; which, I flat-ter myself, cannot fail of pleasing, being mostof them entirely new, and such as tend verymuch to elucidate and shew the Utility ofthat important Science : And it may be pro-per to hint, that these Problems may be fur-ther useful, as Exercises for the young Be-ginner to solve algebraically; whence he willlikewise see the Advantages which the anci-ent synthetic Method of Reasoning has, inmany Cafes, over the modern Analysis, espe-cially in what regards Neatness and Perspi-cuity.

But, after all, I cannot help suggestingmy Suspicions, that the Pains I have takento reduce the most difficult, as well as themore easy Parts of the Subject to a Demon-stration, may not prove altogether agreeableto the Taste of one Part of my Readers, be-ing sensible, that there are Many who had-much rather take a Thing upon Trust, thanbe at the Trouble of examining it, even by

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