Isaac Newton

“ When the trajectory is an hyperbola, I do not comprehend its conjugate by hyperbola under the name of this trajectory. For a body going on with a continued motion can never pass out of one hyperbola into its conjugate hyperbola. ”

“ From the focus On those tangents let fall the perpendiculars ST, St, which produce to V, v, so that TV, tv may be equal to TS, tS. Bifect Vv in O, and erect the indefinite perpendicular OH, and cut the right Line VS infinitely produced in K and k, so that VK be to KS, and Vk to kS as the principal axe of the trajectory to be described is to the distance of it's foci. On the diameter Kk describe a circle cutting OH in H; and with the foci S, H, and principal axe equal to VH, describe a trajectory. ”

“ Wherefore the points B, C, D lie in a conic section described about the focus S, in such manner that all the right lines drawn from the focus S to the several points of the section, and the perpendicular: let fall from the same points on the right line GF are in that given ratio. ”