B chapter.indd - Charles Babbage Institute - University of Minnesota

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This Arithmetic, dedicated to Boethius’s father-in-law, Aurelius Memmius Symmachus, was part of a project to produce a text for each of the four mathematically oriented disciplines: arithmetic, music, geometry and astronomy. He termed these four subjects the quadrivium, a term that was in use in European schools until well after the Middle Ages. There is no indication he ever managed to complete this project—as only his works on arithmetic and music survive. In this volume, Boethius adheres to the early Greek idea of arithmetic as something more akin to modern number theory than anything of a practical nature (the Greeks would have termed the process of doing arithmetical operations as logistic rather than arithmetic). This work is loosely based on the Greek Arithmetica Eisagoge of Nicomachus of Gerasa (fl.100AD). It contains little or nothing original to Boethius, but it was presented in Latin in such a way that it appealed to the medieval scholar and became the standard work from which such subjects were taught for almost 1,000 years. The subject matter originated with Pythagoras (ca. 540 BC) and his followers, who developed a philosophy based on numbers and their symbolism. Nicomachus was a Pythagorean, and we can easily trace the origins of most of this work back to Pythagoras himself (or at least to his era). The work is heavily concerned with sequences and ratios between values—something that stemmed from the Greek difficulty with fractions and fractional notation. A large, well-laid-out multiplication table is the same as in earlier manuscript copies with the exception that here, and in the rest of the text, the newer Hindu-Arabic 164 Erwin Tomash Library Boethius, Anicius Manlius Severinus Boethius, Anicius Manlius Severinus numerals are used rather than the original Roman variety. Another major topic, again stemming from Pythagoras, is figurative numbers (those that can be arranged into geometric shapes such as triangles, squares, cubes, etc). This copy ends with seven pages of early (contemporary?) manuscript notes and diagrams relating to the movements of Saturn, Jupiter, Mars, Venus, Mercury, the sun and the moon. Illustrations available: Diagram with sequences First page Multiplication table Page with triangular numbers Venus manuscript diagram and notes Colophon B 185 Boethius, Anicius Manlius Severinus (ca.480–524/525) Arithmetica, duobus discreta libris; adiecto commentario, mysticam numerorum applicationem perstríngente, declarata. Year: 1521 Place: Paris Publisher: Simon Colines [Colinaeus] Edition: 16th Language: Latin Binding: contemporary vellum Pagination: ff. 138 Collation: a–s 6 t 8 v–x 6 y 10 Size: 275x200 mm Reference: Rcrdi I, 140; DeMorgan, p. 13 This is the first edition of Boethius’ Arithmetica with the addition of the commentary by Girardus Ruffus (Gérard Roussel). Smith (Rara) indicates that This commentary greatly exceeds the text in extent, and as to ponderosity it leaves little to be desired. As a piece of typography, however, this is one of the best editions of Boethius. To a great extent, the commentary by Ruffus seems to rely on the work of Nicolaus Cusanus. For what little is known of the commentator, see the listing in this catalog for Roussel, Gérard. The work includes several diagrams, which help in the explanation. In particular, there is a large circular diagram that relates the Greek alphabetical number system to the Hindu-Arabic (on the innermost circles of the illustration) and indicates some of the properties of each value. Triangular numbers, B 184 Colophon, B 185
Erwin Tomash Library Boethius, Anicius Manlius Severinus Boethius, Anicius Manlius Severinus Illustrations available: Title page Circular diagram relating numbers Page with figurative numbers Page with numerical sequences Colophon B 185 B 186 B 186 Boethius, Anicius Manlius Severinus (CA.480–524); [Faber Stapulensis (1455–1536) and Clichtove, Josse (1472–1543), editors] In hoc libro contenta. Epitome compendiosaque introductio in libros arithmeticos divi Severini Boëtii: adjecto familiari commentario dilucidata. Praxis numerandi certis quibusdam regulis constricta. Introductio in geometriam breviusculis annotationibus explanata sex libris distincta. Primus de magnitudinibus et earum circumstantiis. Secundus de consequentibus contiguis & continuis. Tertius de punctis. Quartus de lineis. Quintus de superficiebus. Sextus de corporibus. Liber de quadratura circuli. Liber de cubicatione sphere. Perspectiva introductio. Insuper astronomicon. Year: 1503 Place: Paris Publisher: Wolfgang Hopyl [Hopilius] & Henry Estienne [Stephens] Edition: 1st Language: Latin Binding: modern suede leather Pagination: ff. 112 Collation: a–o 8 Size: 263x190 mm. Reference: Smi Rara, pp. 29, 80–81; Ada CBCE, F17 Ren, p. 1; Rcrdi BMI I, p. 142–143; DeM AB, p. 3 Jodocus Clichtoveus was born Josse Clichtove in Nieuport, Belgium but spent most of his life in France editing early books in mathematics. See the entry for Jordanus, 1514, for remarks on Faber Stapulensis. As Smith (Rara, p. 30) points out, the various early editions of Boethius’ Arithmetic differ only in the combination of works they contain. In this edition Clichtoveus and Faber Stapulensis added material that would have fitted neatly into the curriculum of the quadrivium, namely works on the basic arithmetical operations, geometry and astronomy. The work on geometry is richly illustrated with marginal diagrams. Illustrations available: Title page Geometry page Astronomy colophon Astronomy colophon, B 186 B 187 [Boethius, Anicius Manlius Severinus (CA. 480–524)]; Jacobus Faber Stapulensis (1455–1536) and Johann Jacobi Scheubel Fabri Stapulensis in arithmetica Boëthi epitome, unà cum difficiliorum locorum explicationibus & figuris (quibus antea carebat) nunc per Joannem Scheubelium adornatis & adjectis. Accessit Christierni Morsiani arithmetica practica, in quinqe partes digesta: quarum I. est de numeris integris. II. de fractionibus vulgaribus & physicis. III. de regulis quibusdam. 165
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