Robert Steele's 1922 edition brings together five early English arithmetic texts, the earliest dating from the 14th century. The opening excerpt from 'The Crafte of Nombrynge' immediately confronts the reader with a foreign orthography: 'ȝ' for yogh, 'ſ' for long s, and the numeral '0' sometimes printed as Greek φ (phi). The editor's introduction notes that until the mid-15th century, most arithmetic was studied in Latin, and even simple division could be a challenge. This collection, then, represents a crucial shift toward vernacular mathematical instruction.

The Challenge of Reading Early English Arithmetic

The excerpts demand careful attention to spelling and typography. In 'The Crafte of Nombrynge,' the word 'withdraw' appears inconsistently hyphenated as 'w i t h draw,' and the letter 'd' for pence sometimes has a curl. The editor preserves these features, noting that 'the first few occurrences of d were printed with a curl.' Readers must also navigate marginal notes, brackets that are original, and diagrams that may not align perfectly in all browsers. The text includes at least five types of marginal note, detailed at the end of the e-text. This is not a modernized edition; it reproduces the historical artifacts as faithfully as possible.

Procedures Explained in Vernacular Terms

The excerpts show a step-by-step approach to operations like subtraction and mediation (halving). For subtraction, the text advises working from right to left, though it notes that 'me may wele fro the lift side begynne.' The proof of subtraction is to add the subtracted figures back to the original. Mediation begins at the rightmost digit: if the first figure is unity, it is written as a cipher and the unity is resolved into '60 mynvtes' (minutes), half set aside. If the figure is odd, the next even number is taken, and the remaining unity is worth 10, added to the preceding figure. These instructions mix Latin-derived terms ('vnyte,' 'cifre') with practical examples.

Duplation and the Direction of Work

Duplation (doubling) is described as 'aggregacion of nombre to itself.' Unlike subtraction and mediation, duplation begins at the left side, 'of the more figure.' The text explains that if one started from the right, 'omwhile me myght double oo thynge twyes.' This attention to the order of operations reflects a pedagogical concern: the method must avoid redundant doubling. The examples use a tabular format with columns of digits, and the reader is expected to 'write and worch' until the total is doubled. The excerpts do not provide complete worked examples, but the pattern of instruction is clear.

The Role of the Editor and the Reader's Task

Robert Steele's introduction frames the texts as rare survivals, noting that 'the number of English arithmetics before the sixteenth century is very small.' The editor has added an Index of Technical Terms and a Glossary, which are essential for navigating terms like 'algorism' (the Arabic numeral system) and 'cifre' (zero). The reader is advised to consult these aids when encountering unfamiliar words. The excerpts also include a 'Carmen de Algorismo' in Latin, showing the bilingual context of early arithmetic. The edition is not a narrative but a collection of primary sources; the reader must engage actively with the original forms.

This edition rewards a patient, methodical reading. Focus on the procedural language rather than the numerical results: the texts are as much about the logic of calculation as about the answers. Use the glossary and index to track terms across the different treatises. The variations in spelling and notation are not errors but evidence of a living, evolving mathematical language. Approach the work as a historical document of how arithmetic was taught and learned in medieval and early modern England.