Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 7
... Half Arcs , Additional Formulas , Method of Computing a Table of Natural Sines , .... SPHERICAL TRIGONOMETRY . PAGE . 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right ...
... Half Arcs , Additional Formulas , Method of Computing a Table of Natural Sines , .... SPHERICAL TRIGONOMETRY . PAGE . 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right ...
Page 34
... 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 side BC equal to BE , by hypothesis , the side AB com- mon , and the included angles ABC and and ABE equal ...
... 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 side BC equal to BE , by hypothesis , the side AB com- mon , and the included angles ABC and and ABE equal ...
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
... half of the arc BED . Then , from what has just measured by half of DE , EB : hence , BAD , which For , draw the diameter AE . been proved , the angle DAE is and the angle EAB by half of is the sum of EAB and DAE , is measured by half ...
... half of the arc BED . Then , from what has just measured by half of DE , EB : hence , BAD , which For , draw the diameter AE . been proved , the angle DAE is and the angle EAB by half of is the sum of EAB and DAE , is measured by half ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following