The Earliest Arithmetics in English
1922

Before the Renaissance brought algebra and Hindu-Arabic numerals to English shores, calculation was a mysterious art guarded by Latin scholars. This 1922 scholarly compilation recovers the rare English arithmetic texts that survive from the 15th century, revealing a time when most mathematical literature was written in Latin and an English reader seeking to learn calculation would find almost nothing in their own language. Editor Robert Steele reconstructs two major treatises that formed the backbone of early English mathematical education, tracing how schoolmasters taught counting, computation with counting boards, and algorithmic procedures to students who would become merchants, craftsmen, and navigators. The introduction illuminates the fascinating transition from Roman numerals to more efficient systems, the cultural dominance of figures like Sacro Bosco and Alexander de Villa Dei, and the practical anxieties that drove ordinary people to learn arithmetic beyond simple record-keeping. For anyone curious about the material history of ideas, these fragile texts offer something remarkable: a glimpse into the mental toolbox that built the English-speaking world, one calculation at a time.
About The Earliest Arithmetics in English
Chapter Summaries
- Introduction
- Steele provides comprehensive background on early English arithmetic texts, explaining the rarity of vernacular mathematical works before the 16th century and detailing the manuscript sources. He traces the development from Roman calculation methods through medieval abacus systems to the revolutionary algorism.
- The Crafte of Nombrynge
- A 15th-century English translation of commentaries on Alexander de Villa Dei's arithmetic, teaching the seven rules of algorism: addition, subtraction, duplation, mediation, multiplication, division, and root extraction. The text explains Hindu-Arabic numerals and place-value notation.
- The Art of Nombryng
- An English translation of John of Holywood's 'de arte numerandi', covering the nine operations of arithmetic including numeration, the four basic operations, duplation, mediation, progression, and extraction of square and cube roots.
Key Themes
- Mathematical Evolution
- The text traces the evolution of arithmetic from ancient Roman methods through medieval abacus systems to the revolutionary Hindu-Arabic algorithmic approach, showing how mathematical knowledge progressed through cultural transmission.
- Cultural Translation
- The work demonstrates how mathematical knowledge traveled from India through the Islamic world to medieval Europe, with each culture adapting and translating methods to suit their needs and understanding.
- Practical vs. Theoretical Mathematics
- The texts reveal the tension between practical calculation needs (commerce, taxation, astronomy) and theoretical mathematical understanding, showing how practical demands drove mathematical innovation.
Characters
- Robert Steele(major)
- The editor and scholar who compiled and introduced this collection of early English arithmetic texts. He provides extensive historical context and analysis of medieval mathematical practices.
- Alexander de Villa Dei(major)
- Medieval mathematician (c. 1220) who wrote the foundational verse treatise 'Carmen de Algorismo' that influenced all subsequent arithmetic texts. His work forms the basis for several treatises in this collection.
- John of Holywood (Sacrobosco)(major)
- Medieval mathematician whose 'de arte numerandi' was translated into English as 'The Art of Nombryng'. His work represents one of the key sources for medieval arithmetic instruction.
- Robert Record(major)
- 16th-century English mathematician whose 1543 'Arithmetic' contains the treatise 'Accomptynge by Counters', representing the transition from medieval to early modern mathematical instruction.
- Al-Khowarazmi(major)
- 9th-century Arabic mathematician whose work 'de numeris Indorum' was the first arithmetic treatise translated from Arabic, giving its name to 'Algorism' and introducing Hindu-Arabic numerals to Europe.
- Adelard of Bath(minor)
- 12th-century translator who made the first Latin translation of Al-Khowarazmi's arithmetic around 1120, introducing Arabic mathematical methods to medieval Europe.













