Elements of Geometry and Trigonometry |
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Page 77
... measured by one - half or two - thirds of a quadrant , it will two - thirds of a right angle . be equal to one - half or PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There ...
... measured by one - half or two - thirds of a quadrant , it will two - thirds of a right angle . be equal to one - half or PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There ...
Page 78
... 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 by half of the arc BED . For , draw the diameter AE . Then , from what ...
... 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 by half of the arc BED . For , draw the diameter AE . Then , from what ...
Page 79
... measured by half of the same are 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 ...
... measured by half of the same are 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 ...
Page 80
... measured by half the sum of the arcs AC and DB . For , draw AD : then , the angle DEB , being an exterior angle of ... measured by D B half the arc AC , and EAD by half the are DB ( P. XVIII . ) : hence , the angle DEB is measured by ...
... measured by half the sum of the arcs AC and DB . For , draw AD : then , the angle DEB , being an exterior angle of ... measured by D B half the arc AC , and EAD by half the are DB ( P. XVIII . ) : hence , the angle DEB is measured by ...
Page 81
... measured by half the included arc . Let BE be tangent to the circle AMC , and let AC be a chord drawn from the point of contact A : then will the angle BAC be measured by half of the arc AMC . M For , draw the diameter AD . The angle ...
... measured by half the included arc . Let BE be tangent to the circle AMC , and let AC be a chord drawn from the point of contact A : then will the angle BAC be measured by half of the arc AMC . M For , draw the diameter AD . The angle ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence