Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 , and , BC : AB :: AB : BD , ВС : AC :: AC : DC , we have ( B. II . , P. I. ) , and , AB2 = BC x BD , AC2 = BC DC ...
... homologous sides are proportional ; hence , BD AD :: AD : DC ; which was to be proved . Cor . 1. From the proportions , and , BC : AB :: AB : BD , ВС : AC :: AC : DC , we have ( B. II . , P. I. ) , and , AB2 = BC x BD , 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 , ADE : ABE :: ABE : ABC ; that is , ABE is a mean proportional be- tween ADE and ABC . B E PROPOSITION XXV ...
... homologous , DE will be parallel to BC , and we shall have , AD : AB :: AE AC ; : hence ( B. II . , P. IV . ) , we have , ADE : ABE :: ABE : ABC ; that is , ABE is a mean proportional be- tween ADE and ABC . B E 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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AB² ABCD altitude apothem Applying logarithms centre chord circle circumference 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 linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar 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 volume whence write the following