Elements of Geometry and Trigonometry |
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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
... triangle ABC , let the side BC be greater than AC : then will the angle A be greater than the angle B. For , if the ... polar triangle of A , and the polar triangle of B : then , be- cause the triangles A and B are mutually ...
... triangle ABC , let the side BC be greater than AC : then will the angle A be greater than the angle B. For , if the ... polar triangle of A , and the polar triangle of B : then , be- cause the triangles A and B are mutually ...
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 D ...
... 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 D ...
Page 251
... triangle ABC is bi - rectan- gular , that is , has two right angles Band 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. B III . , C. 4 ) . The ...
... triangle ABC is bi - rectan- gular , that is , has two right angles Band 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. B III . , C. 4 ) . The ...
Page 84
Adrien Marie Legendre Charles Davies. QUADRANTAL SPHERICAL TRIANGLES . 77. A QUADRANTAL SPHERICAL TRIANGLE is one in which one side is equal to 90 ° . To solve such a triangle , we pass to its polar triangle , by subtracting each side ...
Adrien Marie Legendre Charles Davies. QUADRANTAL SPHERICAL TRIANGLES . 77. A QUADRANTAL SPHERICAL TRIANGLE is one in which one side is equal to 90 ° . To solve such a triangle , we pass to its polar triangle , by subtracting each side ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a 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 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 semi-circumference similar sine 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
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...