Commentary on Proposition II.1¶
Back to Proposition II.1.
This proposition, the geometrical equivalent of the algebraical formula [ a(b + c + d + dots) = ab + ac + ad + dots, ] can, of course, easily be extended so as to correspond to the more general algebraical proposition that the product of an expression consisting of any number of terms added together and another expression also consisting of any number of terms added together is equal to the sum of all the products obtained by multiplying each term of one expression by all the terms of the other expression, one after another. The geometrical proof of the more general proposition would be effected by means of a figure showing all the rectangles corresponding to the partial products, in the same way as they are shown in the simpler case of II. 1; the difference would be that a series of parallels to BC would have to be drawn as well as the series of parallels to BF.