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 vii
... Half Arcs , 67 Additional Formulas , 68-70 Method of Computing a Table of Natural Sines , 71 SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , 73 ... General Principles , ..... 73 Formulas for Right - angled Triangles , 74-76 ...
... Half Arcs , 67 Additional Formulas , 68-70 Method of Computing a Table of Natural Sines , 71 SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , 73 ... General Principles , ..... 73 Formulas for Right - angled Triangles , 74-76 ...
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 angles ABC and ABE ...
... 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 angles ABC and ABE ...
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 . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by half of EB : hence , BAD , which is the sum of EAB and DAE , is measured by half ...
... half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by half of EB : hence , BAD , which is the sum of EAB and DAE , is measured by half ...
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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