Page:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu/141

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SECTION A]
THE LOGICAL PRODUCT OF TWO PROPOSITIONS
119

*3·45.

This principle shows that we may multiply both sides of an implication by a common factor; hence it is called by Peano the "principle of the factor." We shall refer to it as "Fact." It is the analogue, for multiplication, of the primitive proposition *1·6.

Dem.

*3·47.

This proposition, or rather its analogue for classes, was proved by Leibniz, and evidently pleased him, since he calls it "præclarum theorema[1]."

Dem.

*3·48.

This theorem is the analogue of *3·47.

Dem.

  1. Philosophical works, Gerhardt's edition, Vol. vii. p. 223.