ch is
equivalent, and to which it is to be reduced: as Bramantip to Barbara,
Camestres to Celarent, and so forth.

The vowels A, E, I, O, occurring in the several names, give the quantity
and quality of major premise, minor premise, and conclusion in the usual
order.

The consonants s and p, occurring after a vowel, show that the
proposition which the vowel stands for is to be converted either (s)
simply or (p) _per accidens_; except where s or p occurs after the third
vowel of a name, the conclusion: then it refers not to the conclusion of
the given Mood (say Disamis), but to the conclusion of that Mood of the
first Figure to which the given Mood is reduced (Darii).

M (_mutare_, metathesis) means 'transpose the premises' (as of
Ca_m_estres).

C means 'substitute the contradictory of the conclusion for the
foregoing premise,' a process of the Indirect Reduction to be presently
explained (see Baroco, Sec. 8).

The other consonants, r, n, t (with b and d, when not initial),
occurring here and there, have no mnemonic significance.

What now is the problem of Reduction? The difference of Figures depends
upon the position of the Middle Term. To reduce a Mood of any other
Figure to the form of the First, then, we must so manipulate its
premises that the Middle Term shall be subject of the major premise and
predicate of the minor premise.

Now in Fig. II. the Middle Term is predicate of both premises; so that
the minor premise may need no alteration, and to convert the major
premise may suffice. This is the case with Cesare, which reduces to
Celarent by simply converting the major premise; and with Festino, which
by the same process becomes Ferio. In Camestres, however, the minor
premise is negative; and, as this is impossible in Fig. I., the premises
must be transposed, and the new major premise must be simply converted:
then, since the transposition of the premises will have transposed the
terms of the conclusion (according to the usual reading of syllogisms),
the new conclusion must be simply converted in order to prove the
validity of the original conclusion. The process may be thus represented
(_s.c._ meaning 'simply convert')

Camestres. Celarent.

All P is M; ----\ /---> No M is S;
\ c/
\/
s/\
/ \
No S is M: ----/ \---> All P is M:

s.c.
.'. No S is P. <----------- No P is S.

T