Praeclarum Theorema

Leibniz' Proof
The praeclarum theorema was noted and named by G. W. Leibniz, who stated and proved it in the following manner:


 * If $a$ is $b$ and $d$ is $c$, then $ad$ will be $bc$.
 * This is a fine theorem, which is proved in this way:
 * $a$ is $b$, therefore $ad$ is $bd$ (by what precedes),
 * $d$ is $c$, therefore $bd$ is $bc$ (again by what precedes),
 * $ad$ is $bd$, and $bd$ is $bc$, therefore $ad$ is $bc$.
 * Q.E.D.


 * (Leibniz, Logical Papers, p. 41).

Linguistic Note
Praeclarum Theorema is Latin for splendid theorem.

It was so named by Gottfried Wilhelm von Leibniz.

Also see
Compare the Constructive Dilemma, which is similar in appearance.