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 , Additional Formulas , ...... Method of Computing a Table of Natural Sines , .... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , ... General Principles , ...... Formulas for Right - angled Triangles , Napier's ...
... Half Arcs , Additional Formulas , ...... Method of Computing a Table of Natural Sines , .... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , ... General Principles , ...... Formulas for Right - angled Triangles , Napier's ...
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 ABE equal , because ...
... 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 ABE equal , because ...
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 DE and the angle EAB by half of EB : hence , BAD , which is the sum of EAB and DAE , is measured by half of the sum of DE and EB , or by half of BED ; which was to be proved . 3 ° . Let BAD be an inscribed angle , and let the ...
... 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 of the sum of DE and EB , or by half of BED ; which was to be proved . 3 ° . Let BAD be an inscribed angle , and let the ...
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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