\_ \_/ _/
\_____/ \_____/ \_____/

11
_____ _____ _____
_/ \_/ \_/ \_
/ / \ / \ \
| x | | y | | m |
\_ \_/ \_/ _/
\_____/ \_____/ \_____/

12
_____ _____
_/___ \_/ \_
/ / x \ / \ \
| \___/| | m |
\_ y \_/ _/
\_____/ \_____/

Figs. 1 and 4 give

13
_____ _____
_/ \_ _/ ___ \_
/ \ / / y \ \
| x | | \___/ |
\_ _/ \_ m _/
\_____/ \_____/

From this group (Figs. 5 to 13) we have, by disregarding m, to find the
relation of x and y. On examination we find that Figs. 5, 10, 13 express
the relation of entire mutual exclusion; that Figs. 6, 11 express
partial inclusion and partial exclusion; that Fig. 7 expresses
coincidence; that Figs. 8, 12 express entire inclusion of x in y; and
that Fig. 9 expresses entire inclusion of y in x.
pg182
We thus get five Biliteral Diagrams for x and y, viz.

14
_____ _____
_/ \_ _/ \_
/ \ / \
| x | | y |
\_ _/ \_ _/
\_____/ \_____/

15
_____ _____
_/ \_/ \_
/ / \ \
| x | | y |
\_ \_/ _/
\_____/ \_____/

16
_____
_/ \_
/ \
| xy |
\_ _/
\_____/

17
_____
_/ ___ \_
/ / x \ \
| \___/ |
\_ y _/
\_____/

18
_____
_/ ___ \_
/ / y \ \
| \___/ |
\_ x _/
\_____/

where the only Proposition, represented by them all, is "Some not-y are
not-x," i.e. "Some persons, who are not gamblers, are not
philosophers"----a result which Euler would hardly have regarded as a
_valuable_ one, since he seems to have assumed that a Proposition of
this form is _always_ true!

(4) _Solution by Venn's Method of Diagrams._

The following Solution has been kindly supplied to me Mr. Venn himself.

"The Minor Premiss declares that some of the constituents in my' must be
saved: mark these constituents with a cross.