Elements of Geometry and Trigonometry |
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Page 53
... measurement of angles by arcs of a circle is in any degree indirect , it is still equally easy to obtain the direct and absolute measure by this method ; since , on comparing the arc which serves as a measure to any an- gle , with the ...
... measurement of angles by arcs of a circle is in any degree indirect , it is still equally easy to obtain the direct and absolute measure by this method ; since , on comparing the arc which serves as a measure to any an- gle , with the ...
Page 54
... measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that ... measured by the arc BE ; hence BAC will be measured by the half of BE . For a like reason , the angle CAD will be ...
... measured by half the arc included between its sides . Let BAD be an inscribed angle , and let us first suppose that ... measured by the arc BE ; hence BAC will be measured by the half of BE . For a like reason , the angle CAD will be ...
Page 55
... measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ... measured by half of the arc BOC , less than a semicircumference . And every angle BOC , inscribed in a segment less ...
... measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ... measured by half of the arc BOC , less than a semicircumference . And every angle BOC , inscribed in a segment less ...
Page 56
... measured by half the arc FDB ( Prop . XVIII . ) ; therefore , DEB A E D B is measured by half of FDB ; that is , by half of DB + DF , or half of DB + AC . In the same manner it might be proved that the angle AED is measured by half of ...
... measured by half the arc FDB ( Prop . XVIII . ) ; therefore , DEB A E D B is measured by half of FDB ; that is , by half of DB + DF , or half of DB + AC . In the same manner it might be proved that the angle AED is measured by half of ...
Page 57
... measured by o half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half of DC , or by half the whole arc AMDC . It might be shown , by taking ...
... measured by o half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half of DC , or by half the whole arc AMDC . It might be shown , by taking ...
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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