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(Article II.12.) What did the Abbacus Teachers Aim at when they (sometimes) Ended Up doing Mathematics?

In: Selected Essays on Pre- and Early Modern Mathematical Practice

Author

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  • Jens Høyrup

    (Roskilde University, Section for Philosophy and Science Studies)

Abstract

Italian 14th- and 15th-century abbacus algebra presents us with a number of deviations from what we would consider normal mathematical practice and proper mathematical behaviour: the invention of completely false algebraic rules for the solution of cubic and quartic equations, and of rules that pretend to be generally valid but in fact only hold in very special cases; and (in modern terms) an attempt to expand the multiplicative semi-group of non-negative algebraic powers into a complete group by identifying roots with negative powers. In both false-rule cases, the authors of the fallacies must have known they were cheating. Certain abbacus writers seem to have discovered, however, that something was wrong, and devised alternative approaches to the cubics and quartics; they also developed safeguards against the misconceived extension. The paper analyses both phenomena, and correlates them with the general practice and norm system of abbacus mathematics as this can be extracted from the more elementary level of the abbacus treatises.

Suggested Citation

  • Jens Høyrup, 2019. "(Article II.12.) What did the Abbacus Teachers Aim at when they (sometimes) Ended Up doing Mathematics?," Springer Books, in: Selected Essays on Pre- and Early Modern Mathematical Practice, chapter 0, pages 795-822, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-19258-7_29
    DOI: 10.1007/978-3-030-19258-7_29
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