we cannot abstract C and infer
A = B;
but from
AC ꖌ Ac = BC ꖌ Bc
we may abstract all reference to the term C.
It ought to be carefully remarked, however, that alternatives which seem to be without meaning often imply important knowledge. Thus if I say that “a triangle is a three-sided rectilinear figure, with or without three equal angles,” the last alternatives really express a property of triangles, namely, that some triangles have three equal angles, and some do not have them. If we put P = “Some,” meaning by the indefinite adjective “Some,” one or more of the undefined properties of triangles with three equal angles, and take
A = triangle
B = three-sided rectilinear figure
C = with three equal angles,
then the knowledge implied is expressed in the two propositions
PA = PBC
pA = pBc.
These may also be thrown into the form of one proposition, namely,