| A = Ac | (1) |
| B = BC | (2) |
Now, by the process of contraposition we obtain from the second premise
c = bc
and we can substitute this expression for c in (1), obtaining
A = Abc
or “Whales are not true fish, not respiring water.”
The mood Cesare does not really differ from Camestres except in the order of the premises, and it could be exhibited in an exactly similar manner.
The mood Baroko gave much trouble to the old logicians, who could not reduce it to the first figure in the same manner as the other moods, and were obliged to invent, specially for it and for Bokardo, a method of Indirect Reduction closely analogous to the indirect proof of Euclid. Now these moods require no exceptional treatment in this system. Let us take as an instance of Baroko, the argument
| All heated solids give continuous spectra | (1) |
| Some nebulæ do not give continuous spectra | (2) |
| Therefore, some nebulæ are not heated solids | (3) |
Treating the little word some as an indeterminate adjective of selection, to which we assign a symbol like any other adjective, let