Powers of the Unknown

The original version of algebra as translated by Gerard of Cremona only knows two powers of the unknown, the root or thing, and the census (its square). Fibonacci adds the cube, and other powers formed by multiplication (the “cube of cube” thus being the sixth, not the ninth power). This system returns in 14th-century abbacus algebra, but a first crack is introduced by Antonio de’ Mazzinghi late in the century, who introduces cubo relato for the fifth power, leaving the other powers untouched. Gradually over the next century, the system changes, and composition is made by embedding, the “cube of cube” thus becoming the ninth power, and prime powers “first”, “second” and “third relato” (etc.). Late in the fifteenth century, some writers also try naming by number in the sequence of powers (Chuquet, Pacioli, and others) Β sometimes our exponents, sometimes counting number as the first. When algebra matures as Coß in German lands after 1500, it takes over the composition by embedding, together with the resulting need for particular names for prime powers (in 1518 Heinrich Schreyber names them by exponents but has no followers). Peletier in France adopts the system (and introduces the term “exponent”, just meant as “identifier”), and so does even Guillaume Gosselin, who otherwise follows Xylander’s translation of Diophantos. With Viète and Descartes, the notion of a single or primary unknown and its powers has disappeared.