Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1869 - 455 páginas |
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Términos y frases comunes
ABCD altitude apothem Applying logarithms centre chord circle circumference circumscribed complement cone consequently convex surface cosec cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex vertices volume whence write the following
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 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.
Página 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 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.
Página 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...
Página 154 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Página 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.
Página 16 - A DIAGONAL of a polygon is a line joining the vertices of two angles, not consecutive.