Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States
A.S. Barnes & Company, 1869 - Geometry - 455 pages
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ABCD altitude base Book called centre chord circle circumference circumscribed coincide common cone consequently construct corresponding Cosine Cotang cylinder denote described diameter difference distance divided draw drawn edges equal EXAMPLES extremity faces feet figure formed Formula four frustum given greater half height hence homologous included inscribed intersection less logarithm lower base manner mean measured meet multiplied opposite parallel parallelogram parallelopipedon pass perpendicular placed plane polyedron polygon position principle prism proportional PROPOSITION proved pyramid radii radius rectangle regular remaining right angles RULE Scholium segment shown sides similar sine solution sphere spherical triangle square straight line surface taken Tang tangent THEOREM third triangle triangle ABC unit vertex vertices volume whence
Page 85 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 28 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 90 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 58 - ABM'" ; that is, the functions of — a are the same as the functions of 360° — a. From an inspection of the figure, we shall discover the following relations, viz. : sin (— a) = — sin a ; cos (— a) = cos a ; tan (—a) = — tan a ; cot (— a) = — cot a ; sec ( - a) = sec a ; cosec ( — a) = — cosec a.
Page 243 - AD c, have two sides, and the included angle of the one equal to two sides and the included angle of the other, each \ to each, and are equal in all their parts...
Page 154 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Page 57 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 16 - A DIAGONAL of a polygon is a line joining the vertices of two angles, not consecutive.