A treatise on special or elementary geometry (1877)
Olney, Edward, 1827-1887, Olney, Edward, 1827-1887. Elements of trigonometry, plane and spherical · New York : Sheldon · leaf 121
lt;?., an angle at the centre is measured by its intercepted arc. PROPOSITION TI. 214, Theorem.—An angle formed ly two secants meeting zvith-out the circle is measured hy one-half the difference of the interceptedarcs, Dem.—Let APB be an angle formed by the two se-cants AP and PB ; then is it… … 215, ScH.—This case passes into that of an in-scribed angle, by conceiving P to move toward C, thusdiminishing the arc CD. When P reaches C, the anglebecomes inscribed; and, as CD is then 0, i(AB — CD)= ^AB. Also, by conceiving P to continue to movealong PA, CD will reappear oil the other side of…
Geometry · Trigonometry
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