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
... measure of the angle . In Geometry , the right angle which is 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 ...
... measure of the angle . In Geometry , the right angle which is 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 ...
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 arc BOC . 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 . 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
... half the sum of the included arcs . Let DEB be an the chords AB and angle formed by the intersection of CD : then will it be measured by half the sum of the arcs AC and DB . For , draw AF parallel to DC : then , the arc DF will be equal ...
... half the sum of the included arcs . Let DEB be an the chords AB and angle formed by the intersection of CD : then will it be measured by half the sum of the arcs AC and DB . For , draw AF parallel to DC : then , the arc DF will be equal ...
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
AB² 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence