Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 93
... sides about the equal angles , taken in the same order , proportional . 2. In similar polygons , the parts which are similarly placed in each , are called homologous . The corresponding angles are homologous angles , the corresponding sides ...
... sides about the equal angles , taken in the same order , proportional . 2. In similar polygons , the parts which are similarly placed in each , are called homologous . The corresponding angles are homologous angles , the corresponding sides ...
Page 118
... sides are homo- logous . Cor . 2. The homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- licular , each to each , they may have a ...
... sides are homo- logous . Cor . 2. The homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- licular , each to each , they may have a ...
Page 120
... angles ; they are , there fore , similar ( P. XVIII . , C ) . In like manner , it may be shown that the triangles ADC ... homologous sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . and , Cor . 1. From the ...
... angles ; they are , there fore , similar ( P. XVIII . , C ) . In like manner , it may be shown that the triangles ADC ... homologous sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . and , Cor . 1. From the ...
Page 123
... homologous sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F. then will the triangles be to each other as the squares of any two homologous sides . Because the angles A and D ...
... homologous sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F. then will the triangles be to each other as the squares of any two homologous sides . Because the angles A and D ...
Page 124
... homologous with A , draw the diagonals FH , FI , to the ver- tices H and I , hom- B A E K ologous with C and D. Because the polygons are similar , the triangles ABC and FGH have the angles B and G equal , and the sides about these angles ...
... homologous with A , draw the diagonals FH , FI , to the ver- tices H and I , hom- B A E K ologous with C and D. Because the polygons are similar , the triangles ABC and FGH have the angles B and G equal , and the sides about these angles ...
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Common terms and phrases
ABē ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence