Old algebraical treatises (Q2767832)

The author gives a number of examples showing that, for a long time, until the end of the 18th century, algebra was only a language for geometry, very useful in the applications, but only a language. This is compared to the situation of set theory at the beginning of the 20th century: by that time set theory was a useful language in mathematics, but only few were convinced that it was, in fact, a new branch of mathematics. The author's examples start with Euclid and Diophantus. Further examples are taken from Islamic algebra (Al-Khwarizmi, Omar Khayyam, al-Kashi), Indian algebra (Mahaviracarya), medieval Europe (Leonardo Pisano, Jordanus Nemorarius), Europe in the 16th century (Stifel, Cardano, Tartaglia, Candella, Salignac, Viete), Europe in the 17th century (Peletier, Stevin, Descartes, Wallis), and Europe in the 18th century (Gvisnee, de l'Hospital, Newton, Sounderson, Euler). The author concludes that -- notwithstanding many efforts to become independent of geometry -- algebra remained until the 18th century only the language of geometry.NEWLINENEWLINEFor the entire collection see [Zbl 0976.00021].