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 vi
... Solution of Right - angled Triangles ,. Solution of Oblique - angled Triangles , Problems of Application , PAGE . 210 TRIGONOMETRY . ANALYTICAL Analytical Trigonometry Defined , Definitions and General Principles , .. Rules for Signs of ...
... Solution of Right - angled Triangles ,. Solution of Oblique - angled Triangles , Problems of Application , PAGE . 210 TRIGONOMETRY . ANALYTICAL Analytical Trigonometry Defined , Definitions and General Principles , .. Rules for Signs of ...
Page vii
... Solution of Right - angled Spherical Triangles , 80-83 Quadrantal Triangles , 84 Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , 85-92 92-104 MENSURATION . Mensuration Defined , 105 The Area of a ...
... Solution of Right - angled Spherical Triangles , 80-83 Quadrantal Triangles , 84 Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , 85-92 92-104 MENSURATION . Mensuration Defined , 105 The Area of a ...
Page 11
... solution . 9. A POSTULATE is a problem whose solution is self- evident . Theorems , Axioms , Problems , and Postulates , are all called Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence ...
... solution . 9. A POSTULATE is a problem whose solution is self- evident . Theorems , Axioms , Problems , and Postulates , are all called Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence ...
Page 88
... solution . When the side opposite the given angle is shorter than the distance from E to DG , there will be no solution . D PROBLEM XII . Given , two adjacent sides of a parallelogram and their included angle , to construct the ...
... solution . When the side opposite the given angle is shorter than the distance from E to DG , there will be no solution . D PROBLEM XII . Given , two adjacent sides of a parallelogram and their included angle , to construct the ...
Page 90
... solutions . For , the angles ABC and ADC are right angles ( P. XVIII . , C. 2 ) : hence , each of the lines AB and AD is perpendicular to a radius at its extremity ; and consequently , they are tangent to the given circle ( P. IX ...
... solutions . For , the angles ABC and ADC are right angles ( P. XVIII . , C. 2 ) : hence , each of the lines AB and AD is perpendicular to a radius at its extremity ; and consequently , they are tangent to the given circle ( P. IX ...
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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