Elements of Geometry and Trigonometry, from the Works of A.M. Legendre

A.S. Barnes & Company, 1869 - 455 σελίδες

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Σελίδα 83 - 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Σελίδα 56 - 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.
Σελίδα 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...
Σελίδα 154 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Σελίδα 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.
Σελίδα 16 - A DIAGONAL of a polygon is a line joining the vertices of two angles, not consecutive.

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