A scrap-book of elementary mathematics; notes, recreations, essays (1908)
White, William Frank, 1871- · Chicago, The Open Court Pub. Co · leaf 117
MATHEMATICS. out limit.* Then PR is parallel to SQ. That is, paral- lelism is attributed to the limiting position of inter- secting lines as the point of intersection recedes with- out limit; which, for the sake of brevity, we may ex- press by the familiar sentence, "Parallels meet at in- finity."… … to Euclid's postulate PT and PR are one straight line; according to Lobachevsky's they are not; while ac- cording to Riemann's Q and S can not recede to an infinite distance (but Q comes around, so to speak, through S, to P' again) and there is no limiting posi- tion (in the terminology of the…
Mathematical recreations
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