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
... homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS are those which ...
... homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS are those which ...
Page 118
... homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- dicular , each to each , they may have a different relative position from that ...
... homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- dicular , each to each , they may have a different relative position from that ...
Page 120
... homologous sides are proportional ; hence , BD AD :: AD : DC ; which was to be proved . Cor . 1. From the proportions , BC : AB :: AB : BD , and , BC : AC :: AC : DC , we have ( B. II . , P. I. ) , AB2 = BC × BD , and , AC2 BC × DC ...
... homologous sides are proportional ; hence , BD AD :: AD : DC ; which was to be proved . Cor . 1. From the proportions , BC : AB :: AB : BD , and , BC : AC :: AC : DC , we have ( B. II . , P. I. ) , AB2 = BC × BD , and , AC2 BC × DC ...
Page 122
... homologous , DE will be parallel to BC , and we shall have , AD : AB :: AE : AC ; hence ( B. II . , P. IV . ) , we have , A ADE : ABE :: ABE : ABC ; D E that is , ABE is a mean proportional be- tween ADE and ABC . B PROPOSITION XXV ...
... homologous , DE will be parallel to BC , and we shall have , AD : AB :: AE : AC ; hence ( B. II . , P. IV . ) , we have , A ADE : ABE :: ABE : ABC ; D E that is , ABE is a mean proportional be- tween ADE and ABC . B PROPOSITION XXV ...
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 ...
... 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 ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence