Elements of Geometry and Trigonometry Translated from the French of A.M. Legendre, by David Brewster: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Results 1-5 of 43
Page 21
... suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC , BAC , we have BD = AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common ...
... suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC , BAC , we have BD = AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common ...
Page 22
... suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and D- draw FC . Then , the two triangles CAB , CBF , will be equal : for , the angles CBA , and CBF are right angles ...
... suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and D- draw FC . Then , the two triangles CAB , CBF , will be equal : for , the angles CBA , and CBF are right angles ...
Page 23
... suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side AB is common , and the angle CBA ABE ; hence the sides AC and AE are equal ( Prop . V. Cor . ) : therefore , two oblique , lines ...
... suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side AB is common , and the angle CBA ABE ; hence the sides AC and AE are equal ( Prop . V. Cor . ) : therefore , two oblique , lines ...
Page 24
... suppose these two sides to be unequal , and that BC is the greater . On BC take BG = EF , and draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side BA = ED by hypothesis , and the ...
... suppose these two sides to be unequal , and that BC is the greater . On BC take BG = EF , and draw AG . Then , in the two triangles BAG , DEF , the angles B and E are equal , being right angles , the side BA = ED by hypothesis , and the ...
Page 47
... Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D M A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is ...
... Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D M A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and the side AF , the half of AB , is ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine Sine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater hence homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex