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.

The Ostensive Reduction of Baroco also needs special explanation; for as it used to be reduced indirectly, its name gives no indication of the ostensive process.  To reduce it ostensively let us call it Faksnoko, where k means ‘obvert the foregoing premise.’  By thus obverting (k) and simply converting (s) (in sum, contrapositing) the major premise, and obverting the minor premise, we get a syllogism in Ferio, thus: 

Baroco or Faksnoko.  Ferio.
                           contrap
    All P is M; -----------------------> No m (not-M) is P;

obv
Some S is not M:   ----------------------->  Some S is m (not-M): 
.’.  Some S is not P.                            .’.  Some S is not P.

In Fig.  III. the middle term is subject of both premises; so that, to reduce its Moods to the First Figure, it may be enough to convert the minor premise.  This is the case with Darapti, Datisi, Felapton, and Ferison.  But, with Disamis, since the major premise must in the First Figure be universal, we must transpose the premises, and then simply convert the new minor premise; and, lastly, since the major and minor terms have now changed places, we must simply convert the new conclusion in order to verify the old one.  Thus: 

Disamis.  Darii.

Some M is P; ——­\ /—–­> All M is S;
\s./
\/
/\c.
/ \
All M is S:  ——­/ \—–­> Some P is M: 

s.c.
.’.  Some S is P. <------------- .’.  Some P is S.

Bocardo, like Baroco, indicates by its name the indirect process.  To reduce it ostensively let its name be Doksamrosk, and proceed thus: 

Bocardo or Doksamrosk.  Darii.