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konkrétní realizace používá pseudosphere, což je plocha vytvořená revoluce z traktrix o její asymptota.
the concrete realisation uses the pseudosphere, a surface generated by the revolution of a tractrix about its asymptote .
v knize jeden vztahy spokojen s průměry a tečen na conics jsou studovány, zatímco v knize dvě apollóniovi zkoumá, jak hyperbolas jsou spojené s jejich asymptotes, a on také studie, jak k tomu tečny k dané conics.
in book one the relations satisfied by the diameters and tangents of conics are studied while in book two apollonius investigates how hyperbolas are related to their asymptotes , and he also studies how to draw tangents to given conics.