An elementary treatise on analytical geometry : embracing plane co-ordinate geometry, and an introduction to geometry of three dimensions (1869)
Johnson, William Woolsey, 1841-1927 · Philadelphia : J.B. Lippincott · leaf 117
e simplest oblique equations of theparabola will be those which express the relation between thesesemi-chords and parts of the diameter cut off. Thus, let P^andPiPJ a diameter and tangent at its vertex, be taken as the co-ordi-nate axes, then the two halves of any chord, PP (which is bisectedat M),… … X == n2p -f- a ± nyrPp2 -\- 2pcr, Y == np =h ~[/n2p2 -\- 2pa, of which the rational partsare the co-ordinates of M,and the radicals are MQand PQ, the differences ofthe co-ordinates of M andP. By the right-angled tri-angle, PQM, the sum of thesquares of these quantitiesis the square of PM. AgainPXM…
Geometry, Analytic
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