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 , ANALYTICAL Analytical Trigonometry Defined , Definitions and General Principles , .. Rules for Signs of the Functions ...
... Solution of Right - angled Triangles , . Solution of Oblique - angled Triangles , Problems of Application , ANALYTICAL Analytical Trigonometry Defined , Definitions and General Principles , .. Rules for Signs of the Functions ...
Page vii
... Solution of Right - angled Spherical Triangles , Quadrantal Triangles , ... ..... Formulas for Oblique - angled Triangles , .. Solution of Oblique - angled Triangles , MENSURATION . PAGE . 55 57-59 60-62 63 61--66 67 68-72 71 73 73 74 ...
... Solution of Right - angled Spherical Triangles , Quadrantal Triangles , ... ..... Formulas for Oblique - angled Triangles , .. Solution of Oblique - angled Triangles , MENSURATION . PAGE . 55 57-59 60-62 63 61--66 67 68-72 71 73 73 74 ...
Page 11
... solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all called Propositions . 10 : A LEMMA is an auxiliary proposition . 11 . A COROLLARY is an obvious consequence of one more ...
... solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all called Propositions . 10 : A LEMMA is an auxiliary proposition . 11 . A COROLLARY is an obvious consequence of one more ...
Page 88
... solution . When the side opposite the given angle is shorter than the distance from E to DG , there will be no solution . 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 . 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 ) : B 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 ) : B 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 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