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Besides the alterations in the enunciation of the propositions, others of considerable importance have also been made in the present edition. The proposition in Book V., which proves that a polygon and circle may be made to coincide so nearly, as to differ from each other by less than any assignable quantity, has been taken from the Edinburgh Encyclopedia. It is proved in the corollaries that a polygon of an infinite number of sides becomes a circle, and this principle is made the basis of several important demonstrations in Book VIII.
Book II.,on Ratios and Proportions, has been partly adopted from the Encyclopedia Metropolitana, and will, it is believed, supply a deficiency in the original work.
Very considerable alterations have also been made. in the manner of treating the subjects of Plane and Spherical Trigonometry. It has also been thought best to publish with the present edition a table of logarithms and logarithmic sines.
West Point, March, 1834.
The Circle and the Measurement of Angles,
Problems relating to the First and Third Books,
Division of the Circumference,
General Ideas relating to the Trigonometrical Lines,
Theorems and Formulas relating to the Sines, Cosines, Tan-
Construction and Description of the Tables,
Description of Table of Logarithms,
Principles for the Solution of Rectilineal Triangles,
Solution of Rectilineal Triangles by Logarithms,
Solution of Right angled Triangles,
Solution of Right angled Spherical Triangles by Logarithms,
SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO THE PRINCIPAL PROPOSITIONS OF THE FIRST SIX BOOKS OF EUCLID.