Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 76
... similar manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB which was to be proved . arc AD Cor . 1. The intercepted arcs are ...
... similar manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB which was to be proved . arc AD Cor . 1. The intercepted arcs are ...
Page 93
... similar polygons , the parts which are similarly placed in each , are called homologous . The corresponding angles ... SIMILAR ARCS , SECTORS , or SEGMENTS are those which correspond to equal angles at the centre . Thus , if the angles A ...
... similar polygons , the parts which are similarly placed in each , are called homologous . The corresponding angles ... SIMILAR ARCS , SECTORS , or SEGMENTS are those which correspond to equal angles at the centre . Thus , if the angles A ...
Page 113
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
Page 114
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equal to two angles in the other , each to each , they will be similar · ( B. I. , · P . XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles ...
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in one , equal to two angles in the other , each to each , they will be similar · ( B. I. , · P . XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles ...
Page 115
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH . Then , because BG is equal to DE , and BH to EF , we have , G B E ВА BG :: BC : BH ; D hence , GH is parallel to AC ( P. XVI . ) ; and ...
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH . Then , because BG is equal to DE , and BH to EF , we have , G B E ВА BG :: BC : BH ; D hence , GH is parallel to AC ( P. XVI . ) ; and ...
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Common terms and phrases
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