Themistius illustrates this obscure passage, p. 89. The definitions
of [Greek: eu)thei=a grammê/, keklasme/nê grammê/, peripherê\s
grammê/], must each of them contain the definition of [Greek: grammê/
(= mê=kos a)plate/s)], since it is in the Category [Greek: Poso/n
(poso\n mê=kos a)plate/s)]. But the derivative properties of the
circle ([Greek: peripherê\s grammê/]) are deduced from the definition
of a circle, and belong to it in the first instance _quâ_ [Greek:
peripherê\s grammê/], in a secondary way _quâ_ [Greek: grammê/].]
[Footnote 40: Analyt. Post. II. xiii. p. 96, b. 25-p. 97, a. 6.]
Some contemporaries of Aristotle, and among them Speusippus,
maintained that it was impossible either to define, or to divide
logically, unless you knew all particulars without exception. You
cannot (they said) know any one thing, except by knowing its
differences from all other things; which would imply that you knew
also all these other things.[41] To these reasoners Aristotle
replies: It is not necessary to know _all_ the differences of every
thing; you know a thing as soon as you know its essence, with the
properties _per se_ which are derivative therefrom. There are many
differences not belonging to the essence, but distinguishing from
each other two things having the same essence: you may know the
thing, without knowing these accidental differences.[42] When you
divide a genus into two species, distinguished by one proximate
specific difference, such that there cannot be any thing that does
not fall under one or other of these _membra condividentia_, and when
you have traced the subject investigated under one or other of these
members, you can always follow this road until no lower specific
difference can be found, and you have then the final essence and
definition of the subject; even though you may not know how many
_other_ subjects each of the two members may include.[43] Thus does
Aristotle reply to Speusippus, showing that it is not necessary, for
the definition of one thing, that you should know _all_ other things.
His reply, as in many other cases, is founded on the distinction
between the Essential and the Accidental.
[Footnote 41: Ibid. p. 97, a. 6-10; Themistius, p. 92. Aristotle does
not here expressly name Speusippus, but simply says [Greek: phasi/
tines]. It is Themistius who names Speusippus; and one of the
Scholiasts refers to Eudemus as having expressly indicated Speusippus
(Schol. p. 248, a. 24, Br.).]
[Footnote 42: Analyt. Post. II. xiii. p. 97, a. 12: [Greek: pollai\
ga\r diaphorai\ u(pa/rchousi toi=s au)toi=s tô=| ei)/dei, a)ll' ou)
kat' ou)si/an ou)de\ kath' au(ta/.]]
[Footnote 43: Ibid. a. 18-22: [Greek: phanero\n ga\r o(/ti a)\n
ou(/tô badi/zôn e)/lthê| ei)s tau=ta ô(=n mêke/ti e)sti\ diaphora/,
e(/xei to\n lo/gon tê=s ou)si/as.]]