Clavius’ unified solutions by the method of twofold double false positions. (Chinese. English summary) Zbl 1449.01012

Liu, Di; Zhao, Jiwei

J. Northwest Univ., Nat. Sci. Ed. 49, No. 6, 970-976 (2019).

Summary: In 1202, the Italian mathematician Fibonacci (ca.1170 – ca.1250) published Liber Abaci, in which the system of linear equations was solved by multi-fold double false positions for the first time in Europe. This method became the standard algorithm until the late 16th century when European mathematicians treated with such problems. In 1583, the German mathematician Clavius (1538–1612) dealt with the system of 3-variable linear equations by the method of twofold double false positions in his Epitome Arithmeticae Practicae, he discovered the consistence of the solution formula of double false positions, which became the earliest simplification to Fibonacci’s method. By comparing the similarities and differences between the two methods, this paper presents a quantitative analysis of how Clavius’ simplified method works, and explains the mathematical principles of Clavius’ consistence of the solution formula, and proposes that Clavius’ discovery of the consistency of solution formula may be based on analysis and induction of the concrete mean results during his solution of 4 special systems of 3-variable linear equations.

MSC:

01A40

History of mathematics in the 15th and 16th centuries, Renaissance

Keywords:

method of twofold double false positions; Fibonacci; consistence; system of linear equations