ARISTOTLE AND THE EARLIER PERIPATETICS vol.I by Eduard Zeller, B.F.C.Costelloe 1897

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LOGIC 237
The principle that this process in its simplest form involves
no more than two assumptions; or more accurately
two judgments, from which a third is derived, and that
therefore no syllogistic
conclusion can have more than
two premisses, is nowhere expressly proved by Aristotle
in the beginning of his treatise, though he refers to it
later. Now 1 the deduction of a third judgment from two"
given judgments can only arise
out of some bringing
into connection of the concepts, which in these given
judgments were as yet unconnected. 2
This is impossi-_
ble, except a mediation be effected between them by
another concept connected with both of them. 3
syllogism must therefore necessarily contain three
Every
concepts,
no more and no less, 4 and of these the intermediate
is connected in the one premiss with the first and in
the other with the third, in such a way as to
bring out
the connection between the first and third in the confxevaiv
Q avdyfcrjs trvfifiaivet Tip
tclvtcl eivtu. (Likewise Top. i. 1,
100, a, 25, cf. Soph. El. c. 1, 165,
a, 1.) \eyco 8e l T