Irrational “Coefficients” in Renaissance Algebra
Bibliographic Data
| ID | 11658258 |
|---|---|
| Authors | Jeffrey Oaks (0000-0001-7528-9759, University of Indianapolis, corresponding author) |
| Year | 2017 |
| Volume | 30 |
| Issue | 2 |
| Pages | 141-172 |
| Publication date | 2017-06-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Science in Context (JOURNAL) |
| Journal identifiers | ISSN: 0269-8897 • E-ISSN: 1474-0664 |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1017/s0269889717000096 |
| PMID | 28699571 |
| OpenAlex | W2734555219 |
| Language | EN |
| Citations received | 1 |
| References cited | 14 |
Argument From the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply $\sqrt {18} $ by x , for instance, the result was expressed as the rhetorical equivalent of $\sqrt {18{x^2}} $ . The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or “number,” of a term was thought of as how many of that term are present, and not as the scalar multiple that we work with today. Then, in sixteenth-century Europe, a few algebraists began to allow for irrational coefficients in their notation. Christoff Rudolff (1525) was the first to admit them in special cases, and subsequently they appear more liberally in Cardano (1539), Scheubel (1550), Bombelli (1572), and others, though most algebraists continued to ban them. We survey this development by examining the texts that show irrational coefficients and those that argue against them. We show that the debate took place entirely in the conceptual context of premodern, “cossic” algebra, and persisted in the sixteenth century independent of the development of the new algebra of Viète, Decartes, and Fermat. This was a formal innovation violating prevailing concepts that we propose could only be introduced because of the growing autonomy of notation from rhetorical text
Algebra over a field · Archaeology · Argument (complex analysis · Arithmetic · Art · Art history · Context (archaeology · Epistemology · Fermat's Last Theorem · Irrational number · Literature · Monomial · Notation · Pure mathematics · Rhetorical question · The Renaissance · Historical and Literary Studies · Historical Philosophy and Science · History · History and Theory of Mathematics · Mathematics · Philosophy
| Citations per year | 0.13 |
|---|---|
| Citation span | 2018 - 2018 (1) |
| Highly cited | No |