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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Results 6-10 of 66
Page 120
... similar . But , EDF is equal to BGH : hence , it is also similar to BAC ; which was to be proved . ! Ym PROPOSITION XXI . THEOREM . Triangles which have their sides parallel , each to each , or perpendicular , each to each , are similar ...
... similar . But , EDF is equal to BGH : hence , it is also similar to BAC ; which was to be proved . ! Ym PROPOSITION XXI . THEOREM . Triangles which have their sides parallel , each to each , or perpendicular , each to each , are similar ...
Page 121
... similar ( P. XVIII . ) ; which was to be proved . 2o . Let the triangles ABC and DEF have the side AB perpendicular to DE , BC to EF , and CA to FD : then they are similar . is For , prolong the sides of the tri- angle DEF till they ...
... similar ( P. XVIII . ) ; which was to be proved . 2o . Let the triangles ABC and DEF have the side AB perpendicular to DE , BC to EF , and CA to FD : then they are similar . is For , prolong the sides of the tri- angle DEF till they ...
Page 122
... similar ( P. XXI . ) , we have , AI : AF :: DI : BF ; and , the triangles AIK and AFG , being similar , we have , KL AI : AF :: IK FG ; hence ( B. II . , P. IV . ) , we have , DI : BF :: IK : FG . In like 122 GEOMETRY .
... similar ( P. XXI . ) , we have , AI : AF :: DI : BF ; and , the triangles AIK and AFG , being similar , we have , KL AI : AF :: IK FG ; hence ( B. II . , P. IV . ) , we have , DI : BF :: IK : FG . In like 122 GEOMETRY .
Page 123
... similar to the given triangle , and to each other : 2 ° . Each side about the right angle is a mean propor- tional ... similar to ABC , and consequently , similar to each other . The triangles ADB and ABC have B the angle B common , and ...
... similar to the given triangle , and to each other : 2 ° . Each side about the right angle is a mean propor- tional ... similar to ABC , and consequently , similar to each other . The triangles ADB and ABC have B the angle B common , and ...
Page 124
... similar ; and since ADB and ADC are each similar to ABC , they are similar to each other ; which was to be proved . 2o . AB is а mean proportional between BC and BD ; and AC is a mean proportional between CB and CD . For , the triangles ...
... similar ; and since ADB and ADC are each similar to ABC , they are similar to each other ; which was to be proved . 2o . AB is а mean proportional between BC and BD ; and AC is a mean proportional between CB and CD . For , the triangles ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence