# A History of Algebra: From al-Khwārizmī to Emmy Noether by Prof. Dr. Bartel Leenert van der Waerden (auth.)

By Prof. Dr. Bartel Leenert van der Waerden (auth.)

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Maestro Benedetto In 1463, Benedetto of Florence completed his great work "Trattato di praticha d'arismetica", consisting of 500 large pergament pages. For us, the most interesting parts of this work are the books 13, 14, and 15, which deal with algebraic equations. Benedetto starts with the welI-known "reghola de algebra amuchable", that is, with the solution of the six types of linear and quadratic equations x 2 =px x 2 =q px=q x 2 +px=q x 2 +q=px x 2 =px+q. According to Franci and Toti Rigatelli (Historia Math.

Cajori: A History of Mathematics, p. 271. In 1240, the republic of Pisa awarded the "serious and learned Master Leonardo Bigolli" a yearly salary of 20 pounds silver "in addition to the usual From Leonardo da Pisa 10 Luca Pacioli 35 allowances, in recognition of his usefulness to the city and its citizens through his teaching and devoted services". We shall now discuss the extant works of Leonardo. 1. The "Liber Abbaci" The Italian masters of computation were called "maestri d'abbaco". In this sense the title of Leonardo's most influential work is to be understood.

I shall now describe their work, wh ich is of fundamental import an ce for the history of algebra. Scipione deZ Ferro The general cubic equation The Solution of Cubic and Biquadratic Equations 53 ean be redueed, by introdueting a new variable x'=x+ta, to the simpler form If only positive eoeffieients and positive values of x are admitted, there are 3 types x 3 +px=q (1) (2) x 3 =px+q (3) x 3 +q=px. The first to solve equation (1) was Seipione deI Ferro, who was professor at the university of Bologna until his death in 1526.