History of fractions, parts of history (Q1345405)

The articles of this volume will be reviewed individually. The articles of the book base on lectures given at a colloquium at Paris in 1987. Editors and authors intended to make a contribution to the history of fractions. Till now a history of fractions doesn't exist. The particular articles give an insight into the role played by fractions in various historical epochs. The topics of the several articles are as follows: \textit{J. Ritter}, Metrology and the prehistory of fractions; \textit{M. Caveing}, Le statut arithmétique du quantième égyptien (The arithmetic status of the Egyptian quantième); \textit{M. Guillemot}, Les notations et les pratiques opératoires permettent-elles de parler de ``fractions égyptiennes''? (Do notational and operational practices allow us to speak of Egyptian fractions?); \textit{E. M. Bruins}, La construction des tables numériques en Mésopotamie (The construction of numerical tables in Mesopotamia); \textit{C. Michel}, Les fractions dans les tablettes économiques du début du second millénaire en Assyrie et en Babylonie (Fractions in the economic tablets of the early second millenium in Assyria and Babylonia); \textit{S. Démare}-\textit{Lafont}, Les partages successoraux paléobabyloniens (Division of inherited property in Old Babylonian times); \textit{J.-J. Glassner}, Du bon usage des fractions (On the proper use of fractions); \textit{D. Fowler}, Logistic and fractions in early Greek mathematics: a new interpretation; \textit{B. Vitrac}, Logistique et fractions dans le monde hellénistique (Logistic and fractions in the Hellenistic world); D'Orient en Occident: le Moyen Age des fractions (From the Orient to the Occident: the Middle Ages of fractions); \textit{K. Chemla}, Les fractions comme modèle formel en Chine ancienne (Fractions as a formal model in Ancient China); \textit{G. Mazars}, Les fractions dans l'Inde ancienne, de la civilisation de l'Indus à Mahāvīra (IXe siècle) (Fractions in Ancient India, from the Indus civilization to Mahāvīra (ninth century)); \textit{A. Djebbar}, Le traitement des fractions dans la tradition mathématique arabe du Maghreb (The treatment of fractions in the Arab mathematical tradition of the Maghreb); \textit{M. Aballagh}, Les fractions entre la théorie et la pratique chez Ibn al-Bannā' al-Murrākuši (1256-1321) (Fractions between theory and practice in the work of Ibn al-Bannā' al- Murrākuši (1256-1321)); \textit{K. Chemla}, \textit{A. Djebbar} and \textit{G. Mazars}, Mondes arabe, chinois, indien: quelques points communs dans le traitement des nombres fractionnaires (The Arab, Chinese and Indian worlds: some common points in the treatment of fractional numbers); \textit{T. Lévy}, Notes sur le traitement des fractions dans les premiers écrits mathématiques rédigés en hébreu (The treatment of fractions in the earliest mathematical writings in Hebrew); \textit{A. Allard}, Le traitement des fractions dans les premiers textes latins du XIIe siècle influencés par l'arithmétique arabe (The treatment of fractions in the earliest Latin texts of the twelfth century influenced by Arabic arithmetics); \textit{P. Benoit}, Arithmétiques commerciales et compatibilités dans la France médiévale (Commercial arithmetics and accounts in medieval France); \textit{R. Franci}, Des fractions arithmétiques aux fractions algébriques dans les trattati d'abaco du XIVe siècle (From arithmetical fractions to algebraic fractions in the trattati d'abaco of the fourteenth century); \textit{J. Cassinet}, La relation d'ordre entre rapports dans les Eléments d'Euclide: développements au XVIIe siècle (Order relations among ratios in Euclid's Elements: seventeenth century developments); \textit{C. Jami}, Rencontre entre arithmétiques chinoise et occidentale au XVIIe siècle (The meeting between Chinese and Western arithmetics in the seventeenth century); \textit{C. Goldstein}, Fractions de naguère (Today's fractions). The entire collection demonstrates the changing importance of fractions in the history of mathematics and shows in this way the different understanding of the number concept at various times and geographical regions. Most of the articles are written in French, and some in English as indicated above. The book is completed with many illustrations, an extensive index and short biographies of the contributors. In addition each article includes a detailed bibliography of primary and secondary sources. Indexed articles: \textit{Ritter, James}, Metrology and the prehistory of fractions, 19-34, 403, 409 [Zbl 1067.01505] \textit{Caveing, Maurice}, The arithmetical status of the Egyptian ``quantieme'', 39-52, 403, 409 [Zbl 1067.01503] \textit{Guillemot, Michel}, Do operational practices and notations allow us to speak of ``Egyptian fractions''?, 53-69, 403, 409 [Zbl 1067.01504] \textit{Bruins, Evert M.}, The construction of numerical tables in Mesopotamia, 75-85, 403, 409 [Zbl 1067.01506] \textit{Michel, Cécile}, Fractions in commercial tablets of the early second millenium B.C. in Assyria and Babylonia, 87-101, 404, 409 [Zbl 1067.01509] \textit{Démare-Lafont, Sophie}, Division of inherited property in the paleo-Babylonian period, 103-114, 404, 410 [Zbl 1067.01507] \textit{Glassner, Jean-Jacques}, On the proper use of fractions, 115-127, 404, 410 [Zbl 1067.01508] \textit{Fowler, David H.}, Logistic and fractions in early Greek mathematics: a new interpretation, 133-147, 404, 410 [Zbl 1067.01511] \textit{Vitrac, Bernard}, Logistics and fractions in the Hellenistic world, 149-172, 404-405, 410 [Zbl 1067.01517] \textit{Chemla, Karine}, Fractions as a formal model in ancient China, 189-207, 405, 410 [Zbl 1067.01518] \textit{Mazars, Guy}, Fractions in ancient India, from the Indus civilization to Mahavira (IXth century), 209-218, 405, 410 [Zbl 1067.01535] \textit{Djebbar, Ahmed}, The treatment of fractions in the Arab mathematical tradition of the Maghreb, 223-245, 405, 411 [Zbl 1067.01525] \textit{Aballagh, Mohamed}, Fractions between theory and practice in Ibn al-Banna al-Murrakusi (1256--1321), 247-258, 405-406, 411 [Zbl 1067.01520] \textit{Chemla, Karine; Djebbar, Ahmed; Mazars, Guy}, The Arab, Chinese and Indian worlds: some common points in the treatment of fractional numbers, 263-276, 406, 411 [Zbl 1067.01523] \textit{Lévy, Tony}, Notes on the treatment of fractions in the first mathematical writings in Hebrew (IXth and XIIth centuries), 277-289, 406, 411 [Zbl 1067.01538] \textit{Allard, André}, The treatment of fractions in the first Latin texts of the XIIth century influenced by Arab arithmetic, 291-302, 406, 412 [Zbl 1067.01536] \textit{Benoit, Paul}, Commercial arithmetiques and accounts in medieval France, 307-323, 406, 412 [Zbl 1067.01537] \textit{Franci, Raffaella}, From arithmetical fractions to algebraic fractions in the abacus treatises of the XIVth century, 325-334, 407, 412 [Zbl 1067.01527] \textit{Cassinet, Jean}, Order relations among ratios in Euclid's \textit{Elements}: XVIIth-century developments, 341-350, 407, 412 [Zbl 1067.01541] \textit{Jami, Catherine}, The meeting of Chinese and Western mathematics in the XVIIth century, 351-373, 407, 413 [Zbl 1067.01519] \textit{Goldstein, Catherine}, Fractions lately, 375-389, 407, 413 [Zbl 1067.01557]