Sentence Examples

  • By drawing Ac and Ad parallel to BC and BD, so as to meet the plane through CD in c and d, and producing QP and RS to meet Ac and Ad in q and r, we see that the area of Pqrs is (x/h - x 2 /h 2) X area of cCDd; this also is a quadratic function of x.
  • In order to find the difference of optical distances between the courses QAQ', QPQ', we have to express QP-QA, PQ'-AQ'.
  • To find the former, we have, if OAQ=4), AOP=w, QP 2 =u 2 +4a 2 sin 2 2w - 4au sin la) sin (2w-4)) = (u +a sin 4) sin w) 2 -a 2 sin 2 4)sin 2 c0+4a sin 2 2w(a-u cos 0).
  • (8); 4 sin 2 2w=sin 2 cw+ sin4w, and thus to the same order QP 2 = (u-{-a sin 0 sin w)2 - a cos 0(u - a cos 4) sin 2 o+- a(a - u cos 0) sin 4(.0.
  • But if we now suppose that Q lies on the circle u= a cos 0, the middle term vanishes, and we get, correct as far as w4, QP= (u+a sin 4) sin w) 1 ' 3 1 {- a sin2c?sin4w V 4u so that QP - u=asin0sinw -Ft asin¬ĘtanOsin 4 w..

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