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 , .. 70-71 Additional Formulas , ...... 71-73 Method of Computing a Table of Natural Sines ,. 74 SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , .. 76 General Principles , 76 ....... Formulas for Right - angled ...
... Half Arcs , .. 70-71 Additional Formulas , ...... 71-73 Method of Computing a Table of Natural Sines ,. 74 SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , .. 76 General Principles , 76 ....... Formulas for Right - angled ...
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 common , 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 common , 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 50
... half of a right angle ; what is the other angle equal to ? 4. The sum of two angles of a triangle is of a right angle ; what is the other angle equal to ? 5. One of the acute angles of a right - angled triangle is of a right angle ...
... half of a right angle ; what is the other angle equal to ? 4. The sum of two angles of a triangle is of a right angle ; what is the other angle equal to ? 5. One of the acute angles of a right - angled triangle is of a right angle ...
Page 79
... half or two thirds of a quadrant , it is 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 : the ...
... half or two thirds of a quadrant , it is 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 : the ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence