 | Mathematics - 1865 - 132 pages
...B6, Cc are drawn. A straight line AR meets Cc in B ; EB meets Ao, in P ; PC meets B& in Q ; QA meets Cc in r ; and so on. Prove that, after going twice...quadrilateral in space, and of a polygon of n sides in a plane ................ 63 1653. Let t be the distance between the point of contact of any tangent plane to... | |
 | Arthur Cayley - Mathematics - 1892 - 662 pages
...Bb, Oc are drawn. A straight line AR meets Cc in R; RB meets A a in P ; PC meets Bb in Q; QA meets Cc in r; and so on. Prove that, after going twice...and of a polygon of n sides in a plane. Solution by PROFESSOR CAYLEY. 1. The theorem may be thus stated : Given three lines x, y, z, and in these lines... | |
 | American Mathematical Society - Mathematics - 1906 - 750 pages
...Hii. C<; are drawn. A straight line AR meets Cc in K ; KB meets Aa in P ; PC cats Bb in M ; MA meets Cc in r ; and so on. Prove that after going twice...in this way, we always come back to the same point. ( Cayley's Collected Math. Papers, volume 5, p. 589) has shown that if the vertices of the inscribed... | |
 | W. J. C. Miller, D. Biddle - Mathematics - 1901 - 128 pages
...Bi, Cc are drawn. A straight line AR meets Cc in R ; RB meets Aa in P; PC meets Bi in Q; QA meets Co in r; and so on. Prove that, after going twice round...a skew quadrilateral in space, and of a polygon of » sides in a plane. Solution by PEOIESSOB CAÏI.EY. 1. The theorem may be thus stated: Given three... | |
 | American Mathematical Society - Mathematics - 1907 - 682 pages
...Bb, Ce, are drawn. A straight line AH meets Cc in K ; KB meets Aa in P ; PC cuts Bb in M ; MA meets Cc in r • and so on. Prove that after going twice...in this way, we always come back to the same point. ( Cayley 's Collected Math. Papers, volumes, p. 589) has shown that if the vertices of the inscribed... | |
| |
Cc in r; and so on. Prove that, after going twice round the triangle in this way, we always come back to the same point. Show that the theorem is its own reciprocal. Find the analogous properties of a skew quadrilateral in space, and of a polygon of n... 