Quelques probl\`emes issus des Arithmetica Philosophica de Peter Roth

TL;DR

This paper provides a French translation and commentary on 17 problems from Roth's 1608 Arithmetica Philosophica, focusing on complex algebraic equations, stereometry, and polygonal numbers, highlighting their unique combination in the text.

Contribution

It offers the first detailed translation and analysis of these problems, emphasizing their interdisciplinary nature in early modern mathematics.

Findings

14 problems combine algebra, stereometry, and polygonal numbers

Problems involve equations of degree 5 or 6

Highlights unique mathematical intersections in Roth's work

Abstract

Here is a French translation and commentary of 17 problems in Peter Roth's Arithmetica Philosophica (1608). These problems are dealing with algebraic equations of degree 5 or 6; moreover, among these problems, 14 are also dealing with stereometry and polygonal numbers. These 14 problems are the only ones, in the Arithmetica Philosophica, to combine these three distinct topics in a single setting (algebra, stereometry, polygonal numbers).