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 77
... measured by a quarter of a circumference , or a quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle ...
... measured by a quarter of a circumference , or a quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle ...
Page 78
... measured by the arc DE ( P. XVII . , S. ) : hence , the , angle DAE is measured by half of the arc DE ; which was to be proved . B E 2o . Let DAB be an inscribed angle , and let the centre lie within it : then will the angle be measured ...
... measured by the arc DE ( P. XVII . , S. ) : hence , the , angle DAE is measured by half of the arc DE ; which was to be proved . B E 2o . Let DAB be an inscribed angle , and let the centre lie within it : then will the angle be measured ...
Page 79
... measured by half of the same arc BOC . B D C Cor . 2. Any angle BAD , in- scribed in a semi - circle , is a right an- gle ; because it is measured by half the semi - circumference BOD , or by a quadrant ( P. XVII . , S. ) . Cor . 3. Any ...
... measured by half of the same arc BOC . B D C Cor . 2. Any angle BAD , in- scribed in a semi - circle , is a right an- gle ; because it is measured by half the semi - circumference BOD , or by a quadrant ( P. XVII . , S. ) . Cor . 3. Any ...
Page 80
... measured by half the arc FAB is FDB ( P. XVIII . ) ; therefore , DEB is measured by half of FDB ; that is , by half the sum of FD and DB , or by half the sum of AC and DB ; which was to be proved . PROPOSITION XX . THEOREM . The angle ...
... measured by half the arc FAB is FDB ( P. XVIII . ) ; therefore , DEB is measured by half of FDB ; that is , by half the sum of FD and DB , or by half the sum of AC and DB ; which was to be proved . PROPOSITION XX . THEOREM . The angle ...
Page 81
... measured by half of the arc AMC . M D For , draw the diameter AD . The angle BAD is a right angle ( P. IX . ) , and is measured by half the semi - circumference AMD ( P. XVII . , S. ) ; the angle DAC is measured by half of the arc DC ...
... measured by half of the arc AMC . M D For , draw the diameter AD . The angle BAD is a right angle ( P. IX . ) , and is measured by half the semi - circumference AMD ( P. XVII . , S. ) ; the angle DAC is measured by half of the arc DC ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence