Ball, W. W. Rouse (Walter William Rouse), 1850-1925 · London, Macmillan · leaf 337
from a point on one of them tothe other remains finite. On these assumptions the postulatecan be proved. But just as we cannot assume that two con-verging lines (ex. gr. a curve and its asymptote) will ultimatelymeet, so we must not assume that the distance between twodiverging lines will be… … CH. XV] THE PARALLEL POSTULATE 315 his argument may be put thus*. It is desired to prove that iftwo lines AB, CD meet a transversal HACK, so that the sumof the angles BAG, ACD is less than two right angles, then ABand CD must (if produced) meet. One of the angles BAG, ACDmust be acute; suppose it…
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