Elements of Geometry and Trigonometry |
From inside the book
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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 ; B4 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 ; B4 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 De 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 De 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 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 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 centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex