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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.

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