Next, take a syllogism in Bocardo. The application of the diagrams is now more complicated. The premisses are
| Some M is not P, |
| All M is S. |
The major premiss yields three cases, namely,
and the minor premiss two cases, namely,
343 Taking them together we have six combinations, some of which themselves yield more than one case:—
344 So far as S and P are concerned (M being left out of account) these nine cases are reducible to the following three:
