Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/148



Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given.

If from the two foci S, H, (Pl. 7. Fig, 1.) of any ellipiis or hyperbola, we draw to any third point V the right lines SV, HV, whereof one HV is equal to the principal axis of the figure, that is, to the axis in which the foci are ituated, the other SV is biected in T by the perpendicular TR let fall upon it; that perpendicular TR will omewhere touch the conic ection: and vice vera if it does touch it, HV will be equal to the principal axis of the figure.

For, let the perpendicular TR cut the right line HV, produced if need be, in R; and join SR. Becaue