Several Algebraic Unknowns – The Road from Pacioli to Descarte

By : Jens Hoyrup

Page No: 177-198

Abstract
At the Annual conference of the Indian Society for History of Mathematics in 2020 I spoke about the scattered use of several algebraic unknowns in Italian algebra from Fibonacci to Pacioli, and in 2021 about Benedetto da Firenze’s introduction of symbolic algebraic calculations with up to five unknowns in 1463 – the latter having no impact whatsoever on future developments. Here I shall complete what was not originally planned to become a triptych, looking at the development of the technique from Pacioli onward in the writings of Rudolff, Stifel and Mennher. In the end I shall consider the likely influence on Viete’s and Descartes’ algebras, together with the reasons for their unprecedented introduction of abstract coefficients.

DOI: https://doi.org/10.32381/GB.2021.43.2.5