Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
From inside the book
Results 1-5 of 9
Page 242
... triangle ABC , may be described by means of DEF , as DEF is described by means of ABC . Triangles thus related are called polar triangles , or supple- mental triangles . PROPOSITION VI . THEOREM . Any angle , in one of two polar triangles ...
... triangle ABC , may be described by means of DEF , as DEF is described by means of ABC . Triangles thus related are called polar triangles , or supple- mental triangles . PROPOSITION VI . THEOREM . Any angle , in one of two polar triangles ...
Page 249
... triangles A and B , be mutually equi- ' angular then will they also be mutually equilateral . For , let P be the polar triangle of A , and the polar triangle of B : then , be- cause the triangles A and B are mutually equiangular , their ...
... triangles A and B , be mutually equi- ' angular then will they also be mutually equilateral . For , let P be the polar triangle of A , and the polar triangle of B : then , be- cause the triangles A and B are mutually equiangular , their ...
Page 250
... triangle , and DEF its polar triangle then will the sum of the angles A , B , and C , be less than six right angles and greater than two . For , any angle , as A , be- ing measured by a semi - cir- cumference , minus the side EF ( P. VI ...
... triangle , and DEF its polar triangle then will the sum of the angles A , B , and C , be less than six right angles and greater than two . For , any angle , as A , be- ing measured by a semi - cir- cumference , minus the side EF ( P. VI ...
Page 251
... triangle ABC is bi - rectan- gular , that is , has two right angles B and C , the opposite sides of the polar triangle will be quadrants , and their point of intersec- tion will be the pole of the other side ( P. III . , C. 4 ) . The ...
... triangle ABC is bi - rectan- gular , that is , has two right angles B and C , the opposite sides of the polar triangle will be quadrants , and their point of intersec- tion will be the pole of the other side ( P. III . , C. 4 ) . The ...
Page 84
... triangle , we pass to its polar triangle , by subtracting each side and each angle from 180 ° ( B. IX . , P. VI . ) . The resulting polar tri- angle will be right - angled , and may be solved by the rules already given . The polar ...
... triangle , we pass to its polar triangle , by subtracting each side and each angle from 180 ° ( B. IX . , P. VI . ) . The resulting polar tri- angle will be right - angled , and may be solved by the rules already given . The polar ...
Other editions - View all
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