Gripla - 2021, Blaðsíða 76
GRIPLA74
the Indian calculus widely throughout Western Europe.4 It describes the
methods, or algorithms, for the operations of addition, subtraction, dupla-
tion (that is, the doubling of a number), mediation (that is, the halving of
a number), multiplication, division, and the extraction of both square and
cube roots. To this the Old Norse Algorismus adds a section on a geometric
progression between the cubes 8 and 27, connecting the sequence 8, 12, 18,
27 with the four elements of earth, water, air, and fire. The latter is an echo
of a theme which dates back to at least the Timaeus of Plato. Although
widely discussed in neoplatonic writings during late antiquity, as well as
during the revival of platonism in the High Middle Ages, the connection
between this geometric progression and the four elements has not been
found in any other known versions of the Indian calculus.5
Numerous scholars have analyzed the text of the Old Norse Algorismus
and, in particular, explicated the algorithms which it presents. Although
similar to our modern methods for arithmetic, the presentation of these
algorithms in the Algorismus, typically given without examples, is often
obscure. In recent years, Kristín Bjarnadóttir and Bjarni V. Halldórsson have
written extensively on the text itself and comparisons between the manu-
scripts in which it appears,6 Otto Bekken has written on the historical and
educational value of studying old arithmetical texts such as the Algorismus,7
4 Suzan Rose Benedict, A Comparative Study of the Early Treatises Introducing into Europe
the Hindu Art of Reckoning (Concord: The Rumford Press, 1914), 12; André Allard, “The
Influence of Arabic Mathematics in the Medieval West,” Encyclopedia of the History of
Arabic Science, ed. Roshdi Rashed, vol. 2 (London: Taylor & Francis, 1996), 523–24.
5 See, for example, William of Conches, Guillelmi de Conchis: Glosae Super Platonem, ed.
Édouard A. Jeaneau (Turnhout: Brepols, 2006), 110–11. For a discussion of the sequence
itself in the context of the Indian calculus, without reference to the four elements, see,
for example, Petri Philomeni de Dacia in Algorismum Vulgarem Johannis de Sacrobosco
Commentarius, ed. Maximilianus Curtze (Copenhagen: A. F. Høst & Fil. Bibliop. Reg.,
1897), 74–75. For a more recent edition, see Petrus de Dacia, Petri Philomenae de Dacia
et Petri de S. Audomaro Opera quadrivialia, ed. Fridericus Saaby Pedersen (Copenhagen:
Societas Linguae & Litterarum Danicarum, 1983).
6 See, for example, Kristín Bjarnadóttir and Bjarni V. Halldórsson, “Ritgerðin Algorismus
– samanburður handrita,” Vísindavefur: Ritgerðasafn til heiðurs Þorsteini Vilhjálmssyni sjö-
tugum 27. september 2010 (Reykjavík: Hið íslenska bókmenntafélag, 2010) and “Algorismus:
Hindu-Arabic Arithmetic.”
7 See, for example, Otto B. Bekken, “Algorismus of ‘Hauksbók’: An Old Norse Text of 1310
on Hindu-Arabic Numeration and Calculation” (Agder: Agder distriktshøgskole, 1986).