• Corpus ID: 16682432

The Abbacus Tradition : the Missing Link between Arabic and Early Symbolic Algebra ?

@inproceedings{June2009TheAT,
  title={The Abbacus Tradition : the Missing Link between Arabic and Early Symbolic Algebra ?},
  author={Albrecht Heeffer June},
  year={2009}
}

• Albrecht Heeffer June
• Published 2009
• History

Abbaco algebra is a coherent tradition of arithmetical and algebraic problem solving, mostly based in the merchant cities of fourteenth and fifteenth-century Italy. This period is roughly situated between two important works dealing with algebra: the Liber Abbaci by Fibonacci (1202) [5] and the Summa di Arithmetica et Geometria by Luca Pacioli (1492) [20]. Such continuous tradition of mathematical practice was hardly known before the first transcriptions of extant manuscripts by Gino Arrighi from the 1960’s (most notably [1], [2], [3] and [4]) and the ground-breaking work by Warren van Egmond [28]. After some decades of manuscript study and the recent assessment of Jens Høyrup [10] we now have a better understanding of this tradition. Here we provide an overview of the basic characteristics of the abbaco tradition and discuss the role it played towards the new symbolic algebra as it emerged in sixteenth-century Europe. 1 Abbacus algebra: a brief characterization With some exceptions, algebraic practice was completely absent from the scholarly tradition or university curriculum before the mid-sixteenth century. It took until the late seventeenth century before algebra became taught at universities. Instead, algebra flourished within the vernacular tradition of the abbacus schools in Italian cities during the fourteenth and fifteenth century. We call this the abbacus or abbaco tradition, spelled as in the Liber abbaci of Fibonacci (1202) to distinguish it from the abacus as a calculating tool. The abbacists practised calculation with hindu-arabic numerals as opposed to calculation using material means such as the tavola or the abacus. The abbaco masters were hardly known before the first transcriptions of their manuscript treatises by Gino Arrighi during the 1960s and 1970s. It is only with Warren van Egmond’s 1This paper was presented at the International Seminar on History of Mathematics in memory of Subhash Handa, New Delhi, India, December 17-18, 2007. 2One such exception is the Quadripartitum numerorum of Jean de Murs (1343) [17], which provides evidence that algebra, as known from Fibonacci’s Liber abbaci, was studied in scholarly circles in Paris. However, it is unlikely that it was ever taught within the quadrivium.