Prior Analytics - Book I   

by means of the first figure. For all are brought to a conclusion

either ostensively or per impossibile. In both ways the first figure

is formed: if they are made perfect ostensively, because (as we saw)

all are brought to a conclusion by means of conversion, and conversion

produces the first figure: if they are proved per impossibile, because

on the assumption of the false statement the syllogism comes about

by means of the first figure, e.g. in the last figure, if A and B

belong to all C, it follows that A belongs to some B: for if A

belonged to no B, and B belongs to all C, A would belong to no C:

but (as we stated) it belongs to all C. Similarly also with the rest.

It is possible also to reduce all syllogisms to the universal

syllogisms in the first figure. Those in the second figure are clearly

made perfect by these, though not all in the same way; the universal

syllogisms are made perfect by converting the negative premiss, each

of the particular syllogisms by reductio ad impossibile. In the

first figure particular syllogisms are indeed made perfect by

themselves, but it is possible also to prove them by means of the

second figure, reducing them ad impossibile, e.g. if A belongs to

all B, and B to some C, it follows that A belongs to some C. For if it

belonged to no C, and belongs to all B, then B will belong to no C:

this we know by means of the second figure. Similarly also

demonstration will be possible in the case of the negative. For if A

belongs to no B, and B belongs to some C, A will not belong to some C:

for if it belonged to all C, and belongs to no B, then B will belong

to no C: and this (as we saw) is the middle figure. Consequently,

since all syllogisms in the middle figure can be reduced to

universal syllogisms in the first figure, and since particular

syllogisms in the first figure can be reduced to syllogisms in the

middle figure, it is clear that particular syllogisms can be reduced

to universal syllogisms in the first figure. Syllogisms in the third

figure, if the terms are universal, are directly made perfect by means

of those syllogisms; but, when one of the premisses is particular,