## The Ciphers of the Monks: A Forgotten Number-notation of the Middle AgesThis is the first comprehensive study of an ingenious number-notation from the Middle Ages that was devised by monks and mainly used in monasteries. A simple notation for representing any number up to 99 by a single cipher, somehow related to an ancient Greek shorthand, first appeared in early-13th-century England, brought from Athens by an English monk. A second, more useful version, due to Cistercian monks, is first attested in the late 13th century in what is today the border country between Belgium and France: with this any number up to 9999 can be represented by a single cipher. The ciphers were used in scriptoria - for the foliation of manuscripts, for writing year-numbers, preparing indexes and concordances, numbering sermons and the like, and outside the scriptoria - for marking the scales on an astronomical instrument, writing year-numbers in astronomical tables, and for incising volumes on wine-barrels. Related notations were used in medieval and Renaissance shorthands and coded scripts. This richly-illustrated book surveys the medieval manuscripts and Renaissance books in which the ciphers occur, and takes a close look at an intriguing astrolabe from 14th-century Picardy marked with ciphers. With Indices. "Mit Kings luzider Beschreibung und Bewertung der einzelnen Funde und ihrer Beziehungen wird zugleich die Forschungsgeschichte - die bis dato durch Widerspruechlichkeit und Diskontinuit t gepr gt ist - umfassend aufgearbeitet." Zeitschrift fuer Germanistik. |

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### Contents

Preface | 15 |

Acknowledgements | 21 |

Introduction | 27 |

The English ciphers | 49 |

The horizontal ciphers of the Cistercians | 91 |

The astrolabe of Berselius | 131 |

The French vertical ciphers in manuscript sources | 152 |

The fate of the monastic ciphers in the Renaissance and thereafter | 189 |

Jean Fusoris and his workshop | 397 |

Three astronomical instruments related to the Picard astrolabe with ciphers | 398 |

The Picard astrolabe with monastic ciphers | 406 |

The stars on the rete | 408 |

The names of the zodiacal signs and the months | 410 |

The plates and the latitudes they serve | 411 |

The calendrical scale | 416 |

The alidade radial rule and nut and bolt | 419 |

The ciphers falling between the cracks of modern scholarship | 262 |

Appendix A General bibliographical notes | 275 |

B The survival of the Roman numerals in medieval Europe | 281 |

Ancient Greek and medieval alphanumerical notations | 290 |

The introduction of the HinduArabic numerals in Europe | 309 |

E Sundry numeral notations and symbols in medieval and later sources | 318 |

F Aspects of medieval astronomy | 355 |

H On medieval European astronomical instruments | 364 |

J The quatrefoil on medieval astrolabe retes | 380 |

K Astronomical instrumentation in Northern France in the 14th century | 391 |

The textual tradition | 396 |

MThe Virgin of Berselius | 420 |

N Nonhistorical reflections on the ciphers | 427 |

On the morphology and aesthetics of the ciphers | 428 |

Ciphers to bases other than 10 | 429 |

Arithmetic with ciphers | 432 |

Manuscripts cited | 435 |

Astronomical instruments cited | 438 |

Bibliography and bibliographical abbreviations | 442 |

502 | |

505 | |

### Common terms and phrases

13th century 14th-century Agrippa alphabet alphanumerical notation Amerotius appendages Appendix Arabic numerals astrolabe astronomical astronomical instruments astronomical tables attested basic Basingstoke ciphers Beaujouan Berselius Bibliotheque Bischoff Bruges Brussels Cardano century Chaldean chiffres Cistercian copied courtesy Damme dated Dict ecliptic English European astrolabes example Exhibition Catalogue featured forms France French astrolabe Fusoris Geheimschriften German Geschichte Greek Gunther Hindu-Arabic numerals horizontal ciphers idem illustrated inscriptions Islamic John of Basingstoke Johnen King known Latin latitudes letters Library Liege London Louvain M. R. James magic marks mathematics Matthew Paris medieval medieval European mentioned Middle Ages monastery monastic ciphers monks Munich Museum Muzerelle notaria notes Noviomagus numbers numerical ciphers numerical notation Oxford Photo Picard astrolabe plates published quatrefoil Renaissance rete Roman numerals runes scale Science script Section Sesiano shorthand sources Stenographie symbols Systeme artificiel tion Tironian notes treatise various vertical ciphers wine-gauging written Zahlzeichen Zeichen

### Popular passages

Page 463 - Rara Mathematica ; or a Collection of Treatises on the Mathematics and Subjects connected with them, from ancient inedited MSS. by JO HALLIWELL, 8vo.

Page 448 - The Controversy over the Boundary between the English and Picard Nations in the University of Paris," Etudes d'histoire dediees a la memoire de Henri Pirenne (Brussels, 1937).