Section IV.
Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given.
Lemma XV.
If from the two foci S, H, (Pl. 7. Fig, 1.) of any ellipiſis 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 ſituated, the other SV is biſected in T by the perpendicular TR let fall upon it; that perpendicular TR will ſomewhere touch the conic ſection: and vice verſa 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. Becauſe
