 ... of the hodograph. Then Sp' is parallel to the tangent at p, which again is parallel to SP. Hence PSp' is a straight line. Also, since p belongs (by hypothesis) to a central orbit, the tangent at p' is parallel to Sp, ie, to the tangent at P. Hence...  Mathematical Questions and Solutions - Page 921865Full view - About this book
 | 1865 - 128 pages
...circle through A and M. If p be on a circle whose centre is C and diameter BM, M^' is parallel to Bp and bears a constant ratio to it ; hence the locus of p' is similar to that ofp, and is therefore a circle having its centre on BM produced. 1690. (Proposed by WA WHITWOETH, MA)—... | |
 | Peter Guthrie Tait, William John Steele - Dynamics of a particle - 1871 - 462 pages
...(by hypothesis) to a central orbit, the tangent at p is parallel to Sp, i, e., to the tangent at P. Hence the locus of p is similar to that of P, and therefore Sp' is proportional to SP. But Sp' represents the acceleration at P. Hence the proposition.... | |
 | Peter Guthrie Tait - 1878 - 480 pages
...belongs (by hypothesis) to a central orbit, the tangent at p is parallel to Sp, ie to the tangent at P. Hence the locus of p. is similar to that of P, and therefore Sp. is proportional to Sp. But Sp' represents the acceleration at P. Hence the proposition.... | |
 | Peter Guthrie Tait - Kinetic theory of gases - 1898 - 548 pages
...belongs (by hypothesis) to a central orbit, the tangent at p' is parallel to Sp, ie, to the tangent at P. Hence the locus of p' is similar to that of P, and therefore Sp' is proportional to SP. But Sp' represents the acceleration at P. Hence the proposition.... | |
 | W. J. C. Miller, D. Biddle - Mathematics - 1901 - 128 pages
...circle through A and M. If p be on a circle whose centre is C and diameter BM, Wp' is parallel to Kp and bears a constant ratio to it ; hence the locus...having its centre on BM produced. 1690. (Proposed by WA WHITWOBTH, MA)— If ABC be the triangle formed by the three diagonals aci', bb', cc' of a complete... | |
 | Royal Society of Edinburgh - Science - 1869 - 640 pages
...hypothesis) to a central orbit, the tangent at p' is parallel to Sp, »'. «., to the tangent at P. Hence the locus of p' is similar to that of P, and therefore Sp' is proportional to SP. But Sp' represents the acceleration at P. Hence the proposition.... | |
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