§ 11. Euler's diagrams are used to illustrate the syllogism, though not very satisfactorily, thus:

Fig. 5.

Fig. 6.

Fig. 7.

Remembering that 'Some' means 'It may be all,' it is plain that any one of these diagrams in Fig. 7, or the one given above for Barbara, may represent the denotative relations of P, M and S in Darii; though no doubt the diagram we generally think of as representing Darii is No. 1 in Fig. 7.

Remembering that A may be U, and that, therefore, wherever A occurs there may be only one circle for S and P, these syllogisms may be represented by only two circles, and Barbara by only one.