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 34
... equal : 3 ° . Of two oblique lines that meet the given line at points unequally distant from the foot of the ... half of AF , is shorter than AC , the half of ACF ; which was to be proved . 2o . In the triangles ABC and ABE , we have the ...
... equal : 3 ° . Of two oblique lines that meet the given line at points unequally distant from the foot of the ... half of AF , is shorter than AC , the half of ACF ; which was to be proved . 2o . In the triangles ABC and ABE , we have the ...
Page 35
... half of ADF , is greater than AC , the half of ACF ; which was to be proved . Cor . 1. The perpendicular is the shortest distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight ...
... half of ADF , is greater than AC , the half of ACF ; which was to be proved . Cor . 1. The perpendicular is the shortest distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight ...
Page 77
... half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There may be three cases ...
... half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides . There may be three cases ...
Page 78
... equal to the sum of the opposite interior angles CAD and CDA ( B , L , P. XXV . , C. 6 ) . But , the triangle DCA ... 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 ...
... equal to the sum of the opposite interior angles CAD and CDA ( B , L , P. XXV . , C. 6 ) . But , the triangle DCA ... 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 ...
Page 79
... equal ; because they are each 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 ...
... equal ; because they are each 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 ...
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Common terms and phrases
ABē ACē 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