Sacrobosco and Mathematical Techniques

Sacrobosco's Algorismus, sometimes called the Algorismus de integris or Algorismus vulgaris, is a brief and rather elementary mathematical treatise. Like Sacrobosco's other texts, however, it was widely used in the middle ages and reproduced into the early-modern period, with several printed editions between the first in 1488 and the last early printing of 1582. The work seems to have been the first widely-adopted university text-book which introduced Arabic numerals into the curriculum, thereby greatly simplifying the procedures of practical calculation. Moreover, Sacrobosco discussed in it the operations of addition, subtraction, mediation (the finding of the arithmetical mean), duplication (i.e doubling), mutiplication, division, the summation of arithmetical series, and the extraction of square and cube roots.

In his commentary on the Algorismus of 1291, Peter Nightingale (Petrus Philomenus), expressed the belief that Sacrobosco had written the text with the good of astronomy in mind. This opinion finds some support in the fact that, although the work did not in general discuss fractions, the concept of one half was used, and said to be equal to thirty minutes - a reference to the sexagesimal system of fractions used in astronomy. Sexagesimals, called astronomical fractions, were also discussed in Sacrobosco's Compotus with respect to the reckoning of time; to the extent that these texts introduced Arabic numerals and sexagesimals to later students of astronomy they may be considered important to further assimilation in the Latin West of Arabic astronomical knowledge and the production of more sophisticated original work in the field.

Recommended Reading

J. Moreton, 'John of Sacrobosco and the Calendar', Viator 25 (1994), pp. 229-244

O. Pedersen, 'In quest of Sacrobosco', Journal for the History of Astronomy 16 (1985), pp. 175-221

Full Bibliography