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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Page 51
... supplement of an angle is the difference between that E angle and two right angles ; thus , EOC is the supplement of AOE . 13. An angle is of a right angle ; what is its com- plement ? and what its supplement ? 14. Show that any two ...
... supplement of an angle is the difference between that E angle and two right angles ; thus , EOC is the supplement of AOE . 13. An angle is of a right angle ; what is its com- plement ? and what its supplement ? 14. Show that any two ...
Page 187
... supplement of the diedral angle . 6. Show that if a plane meets another plane , the sum of the adjacent diedral angles is equal to two right angles . 7. Show that if two planes intersect each other , the opposite or vertical diedral ...
... supplement of the diedral angle . 6. Show that if a plane meets another plane , the sum of the adjacent diedral angles is equal to two right angles . 7. Show that if two planes intersect each other , the opposite or vertical diedral ...
Page 258
... supplemental tri- angles , any part of either being the supplement of the part opposite it in the other . Cor . 2. Arcs of great circles , drawn from corresponding vertices of two supplemental polar triangles perpendicular to the ...
... supplemental tri- angles , any part of either being the supplement of the part opposite it in the other . Cor . 2. Arcs of great circles , drawn from corresponding vertices of two supplemental polar triangles perpendicular to the ...
Page 265
... supplemental triangles P and Q must be mutually equilateral ( P. VI . ) , and conse- quently mutually equiangular ( P. X. ) . But , the triangles P and Q being mutually equiangular , their supplemental triangles A and B are mutually ...
... supplemental triangles P and Q must be mutually equilateral ( P. VI . ) , and conse- quently mutually equiangular ( P. X. ) . But , the triangles P and Q being mutually equiangular , their supplemental triangles A and B are mutually ...
Page 266
... supplemental triangle , the measure of the sum of the three angles is equal to three semi - circumferences , minus the sum of the sides of the sup- plemental triangle DEF . But the latter sum is less than a circum- · ference ...
... supplemental triangle , the measure of the sum of the three angles is equal to three semi - circumferences , minus the sum of the sides of the sup- plemental triangle DEF . But the latter sum is less than a circum- · ference ...
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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