_Begging the Question_ (Vol. viii., p. 640.).--This is a common logical
fallacy, _petitio principii_; and the first known use of the phrase is to
be found in Aristotle, [Greek: to en archê aiteisthai] (Topics, b. VIII.
ch. xiii., Bohn's edition), where the five ways of "begging the question,"
as also the contraries thereof, are set forth. In the _Prior Analytics_ (b.
II. ch. xvi.) he gives one instance from mathematicians--
"who fancy that they describe parallel lines, for they deceive
themselves by assuming such things as they cannot demonstrate unless
they are parallel. Hence it occurs to those who thus syllogise to say
that each thing is, if it is; and thus everything will be known through
itself, which is impossible."