It does not seems to be a tradition, since contrarily to Heath (as quoted
by Eisso), Paul Ver Eecke writes (in "Les Coniques d'Apollonius de Perge",
p. XVIII-XIX, my poor translation, "off the bat"):
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The fourth book contains fifty-seven propositions. The first twenty-three,
demonstrated by the method of reductio ab absurdo, are not else, in fact,
than the reciprocal of third book's propositions XXX to XL, and we shall
mention only the IXth, which gives a means to draw from one point two
tangents to a conic. The thirty-four other propositions all concern the
exact number of encountings between the conic sections and the circle's
circumference. These last propositions were not new; indeed Apollonius tells
us, in his introduction {for the French: "pre/ambule"}, that quite many of
them had been already exposed by Conon of Samos: that their demonstrations
had been criticised by the geometer Nicoteles, and that Nicoteles himself
had added other questions of the same kind, without demonstration. Although
Conon of Samos has to be considered as Apollonius' precursor in the theory
of the intersection of second degree curves, he essentially missed the
notion of the two branches of the hyperbole, forming only one curve, to have
this matter progress, in a way where the ancient geometer would find, to
some extent, the resources that gives us the discussion of the complete
second degree equation. This theory can thus be considered in great part as
an Apollonius' original work, not only because of the rigorous way he
demonstrate propositions known before him, the beautiful displaying as he
present them, and the particular cases he treats of, but above all for
being the first one to have recognized the great utility of this theory for
the synthesis and for the discussion of a large scale of problems in
geometry.
***********
Udai Venedem
also find about Apollonius at
http://perso.wanadoo.fr/alta.mathematica/ancient.html#_Toc442366787