P23: He who imagines what he hates to be affected with Sadness will rejoice; if, on the other hand, he should imagine it to be affected with Joy, he will be saddened. And both these affects will be the greater or lesser, as its contrary is greater or lesser in what he hates.

Dem.: Insofar as a hateful thing is affected with Sadness, it is destroyed, and the more so, the greater the Sadness by which it is affected (by P11 S). Therefore (by P20), he who imagines a thing he hates to be affected with Sadness will on the contrary be affected with Joy, and the more so, the greater the Sadness with which he imagines the hateful thing to have been affected. This was the first point.

Next, Joy posits the existence of the joyous thing (by P11 S), and the more so, the greater the Joy is conceived to be. {Therefore} if someone imagines him whom he hates to be affected with Joy, this imagination (by P13) will restrain his striving, i.e. (by P11 S), he who hates will be affected with Sadness, etc., q.e.d.

Schol.: This Joy can hardly be enduring and without any conflict of mind. For (as I shall show immediately in P27) insofar as one imagines a thing like oneself to be affected with an affect of Sadness, one must be saddened. And the opposite, if one imagines the same thing to be affected with Joy. But here we attend only to Hate.