Elements of Geometry and Trigonometry |
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Page 53
... shown . that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc intercepted by its ...
... shown . that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc intercepted by its ...
Page 57
... shown , by taking the difference between the an- gles DAE , DAC , that the angle CAE is measured by half the arc AC , included between its sides . PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS . PROBLEM I. To divide a given straight ...
... shown , by taking the difference between the an- gles DAE , DAC , that the angle CAE is measured by half the arc AC , included between its sides . PROBLEMS RELATING TO THE FIRST AND THIRD BOOKS . PROBLEM I. To divide a given straight ...
Page 65
... shown that the two triangles BOD , BOE , are equal ; therefore OD is equal to OE ; therefore the three perpendiculars OD , OE , OF , are all equal . Now , if from the point O ' as a centre , with the radius OD , a circle be described ...
... shown that the two triangles BOD , BOE , are equal ; therefore OD is equal to OE ; therefore the three perpendiculars OD , OE , OF , are all equal . Now , if from the point O ' as a centre , with the radius OD , a circle be described ...
Page 71
... shown that we shall still have ABCD AEFD ' :: AB : AE . For if not , the first three terms continuing the same , the fourth must be greater or less A than AE . Suppose it to be greater , and that we have ABCD AEFD :: AB : AO . : FK C ...
... shown that we shall still have ABCD AEFD ' :: AB : AE . For if not , the first three terms continuing the same , the fourth must be greater or less A than AE . Suppose it to be greater , and that we have ABCD AEFD :: AB : AO . : FK C ...
Page 72
Adrien Marie Legendre Charles Davies. Exactly in the same manner , it may be shown that the fourth term of the proportion cannot be less than AE ; therefore it is equal to AE . Hence , whatever be the ratio of the bases , two rectangles ...
Adrien Marie Legendre Charles Davies. Exactly in the same manner , it may be shown that the fourth term of the proportion cannot be less than AE ; therefore it is equal to AE . Hence , whatever be the ratio of the bases , two rectangles ...
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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 consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex