(Article II.14.) Embedding – Another Case of Stumbling Progress

At an earlier occasion I have argued that the development toward full algebraic symbolism in Europe was a case of “stumbling progress”, before Viète never really intentional. Here I shall concentrate on a particular aspect of algebraic symbolism, the one that allowed Cartesian algebraic symbolism to become the starting point not only for theoretical algebra but for the whole transformation of mathematics from his times onward: The possibility of embedding, that is, of making a symbol or an element of a calculation stand not only for a single number, determined or undetermined, but for a whole expression (which then appears as an algebraic parenthesis). From the Italian beginning in 14th century, and also in ibn al-Yāsamin’s (?) first creation of the Maghreb letter symbolism, the possibility of embedding was understood and explained in the simple case where a fraction line offered itself as defining a parenthesis; Diophantos, without a line, did something similar on at least one occasion. However, only Chuquet and Bombelli would explore some of the possibilities beyond that, and Viète still less. Even Descartes did not take full advantage. A final section argues, from the character of the mathematical practice in which medieval and Renaissance algebra participated, why this stumbling character of development should not bewilder us.