What Did the Abbacus Teachers Really Do When They (Sometimes) Ended Up Doing Mathematics?

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Abstract

Italian fourteenth- and fifteenth-century abbacus algebra presents us with a number of deviations from what we would consider normal (or 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 treating roots as negative powers. In both 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, and developed safeguards against the latter misconception. The paper analyses both phenomena, and correlates them with the general norm system of abbacus mathematics as this can be extracted from the more elementary level of the abbacus treatises.

Original languageEnglish
Place of PublicationRoskilde
PublisherRoskilde Universitet
Number of pages28
Publication statusPublished - 2007

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