Elements of Geometry and Trigonometry |
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Page 54
... difference BAD will be measured by the half of BE minus the half of ED , or by the B half of BD . Hence every inscribed angle is measured by half of the arc included between its sides . C DE Cor . 1. All the angles BAC , BDC , 54 GEOMETRY .
... difference BAD will be measured by the half of BE minus the half of ED , or by the B half of BD . Hence every inscribed angle is measured by half of the arc included between its sides . C DE Cor . 1. All the angles BAC , BDC , 54 GEOMETRY .
Page 56
... difference of BEC and EC , or half the difference of BEC and DF . B A. E F PROPOSITION XXI . THEOREM . The angle formed by a tangent and a chord , is measured by half of the arc included between its sides . Let BE be the tangent , and ...
... difference of BEC and EC , or half the difference of BEC and DF . B A. E F PROPOSITION XXI . THEOREM . The angle formed by a tangent and a chord , is measured by half of the arc included between its sides . Let BE be the tangent , and ...
Page 57
... 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 line into two equal ...
... 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 line into two equal ...
Page 76
... difference , AC - AB must be equal to the difference AE - AF , which gives BC = EF ; but IG is equal to BC , and DG to EF , since the lines are parallel ; therefore IGDH is equal to a square described on BC . And those two squares being ...
... difference , AC - AB must be equal to the difference AE - AF , which gives BC = EF ; but IG is equal to BC , and DG to EF , since the lines are parallel ; therefore IGDH is equal to a square described on BC . And those two squares being ...
Page 77
... difference ; then is . AC , or ( AB - BC ) 2 = AB + BC2-2AB x BC . Describe the square ABIF ; take AE L F = AC ... difference of two lines , is equivalent to the difference of the squares of those lines . Let AB , BC , be two lines ...
... difference ; then is . AC , or ( AB - BC ) 2 = AB + BC2-2AB x BC . Describe the square ABIF ; take AE L F = AC ... difference of two lines , is equivalent to the difference of the squares of those lines . Let AB , BC , be two lines ...
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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