Algorismus in GKS 1812

Abstract

In the ninth century, the Persian mathematician Muḥammed ibn Mūsā al-Khwārizmī wrote a short treatise on the methods for performing the operations of arithmetic with what we now refer to as the Indo-Arabic system for denoting numbers. From the 12th century on, Latin translations of this work, known as the De Numero Indorum, would help spread these techniques throughout Western Europe. In the 13th century, vernacular translations began to appear, including, by the early part of the 14th century, a version in Old Norse, known as the Algorismus. This treatise, a paraphrastic translation of a well-known Latin verse version, the Carmen de Algorismo, is preserved in three manuscripts: AM 544 4to, a part of Hauksbók, and GKS 1812 4to, both from the 14th century, and AM 685 d 4to from the 15th century. There is also a fragment of the treatise preserved ina 16th manuscript, AM 736 III 4to. This paper looks primarily at the GKS 1812 witness of the Algorismus, and includes a transcription and English translation in Appendix A. We compare this version with the copy in AM 544 and with the Carmen de Algorismo. Having accounted for the background of the work, we look at the descriptions of the operations of arithmetic which make up the bulk of the Algorismus, and then discuss the final section, a digression into the Platonic description of the creation of the four elements and the numerical relationships between them. In particular, we trace this theme from the Timaeus of Plato through neoplatonic elaborations in late antiquity to the revival of platonism in the school of Chartres in the 12th century.