Boethius, De institutione arithmetica


Written by the sixth-century Roman philosopher Boethius, De institutione arithmetica (On Arithmetic) was the principal mathematical textbook of pre-12th century Western Europe. Rather than a practical manual of calculation, it comprises a philosophical discussion of numbers, their relationships and meanings. One of the text’s most influential features was its division of the mathematical sciences into arithmetic, music, geometry, and astronomy, which it together designated as the quadrivium.

This idea was widely adopted as the basis of the medieval curriculum, together with the trivium of literary arts: grammar, dialectic (critical investigation of truth through reasoned argument) and rhetoric (classical techniques of eloquent and persuasive language). This manuscript copy of De institutione arithmetica was made in England in the third quarter of the 12th century. The text is illustrated with mathematical diagrams, including a multiplication table for Roman numerals decorated with fish and animals in colours and gold.

This manuscript was digitised with the support of The Polonsky Foundation.

Full title:
Boethius, De institutione arithmetica
3rd quarter of the 12th century, England or Northern France
Usage terms

Public Domain in most countries other than the UK.

Held by
British Library
Harley MS 549

Full catalogue details

Related articles

Medieval science and mathematics

Article by:
Taylor McCall
Science and nature, History and learning

Taylor McCall discusses early medieval approaches to various types of knowledge we might consider today to be ‘scientific’, as well as those subjects taught in the earliest universities, including mathematics and astronomy.