Institutio Oratoria

An ἀπόδεξις is a clear proof; hence the use of the term γραμμικαὶ ἀποδείξεις,

linear demonstrations

[*](See I. x. 38.) by the geometricians. Caecilius holds that it differs from the epicheireme solely in the kind of conclusion arrived at and that an apodeixis is simply an incomplete epicheireme for the same reason that we said an enthymeme differed from a syllogism. For an epicheireme is also part of a syllogism. Some think that an apodeixis is portion of an epicheireme, namely the part containing the proof.

But all authorities, however much they may differ on other points, define both in the same way, in so far as they call both a method of proving what is not certain by means of what is certain. Indeed this is the nature of all arguments, for what is certain cannot be proved by what is uncertain. To all these forms of argument the Greeks give the name of πίστεις , a term which, though the literal translation is fides

a warrant of credibility,

is best translated by probatio

proof.

But argument has several other meanings.