| Description |
1 online resource (506 p.) |
| Series |
Frontiers in the History of Science |
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Frontiers in the history of science.
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| Contents |
Intro -- Preface -- Table of contents -- Introduction -- I. The Home of Abbacus Mathematics: the Abbacus School -- II. An Example: Jacopo da Firenze's Tractatus Algorismi, the Short Version -- The Introduction -- About the Numerals and the Place-Value System -- Multiplication, Division, Fractions -- The Rule of Three -- Basic Commercial Techniques -- Mixed Problems -- Practical Geometry with Approximate Determination of Square Roots -- The Coin List -- Alloying Problems -- III. Fibonacci and the Fibonacci Story -- The Liber Abbaci, the Autobiography, and the Meaning of the Title |
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Some General Characteristics of Fibonacci's Project -- Chapter 1 -- Introducing the Hindu-Arabic Numerals -- Chapter 2 -- Multiplication of Integers -- Chapters 3-4 -- Addition and Subtraction -- Chapter 5 -- Division -- Chapter 6 -- Multiplication of Mixed Numbers -- Chapter 7 -- Addition, Subtraction and Division of Mixed Numbers -- Chapter 8 -- the Rule of Three -- Chapter 9 -- Barter -- Chapter 10 -- Partnership -- Chapter 11 -- Alloying -- Chapter 12 -- Mixed "Abbacus Questions" -- 12.1, Summation of Series -- 12.2, "Proportions of Numbers" -- 12.3, "Questions of Trees ..." -- 12.4, Finding a Purse |
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12.5, Buying a Horse -- 12.6, Repeated Travels with Gain and Expenses -- 12.7, "Rambling Problems" -- 12.8, Divinations -- 12.9, Chess-Board and Other Geometric Series -- Chapter 13 -- Elchatayn Rule -- 13.1, Problems Already Dealt With -- 13.2, New Problems -- Chapter 14 -- Square and Cube Roots -- A Puzzling Preamble -- 14.1, Extraction of Square Roots -- 14.2a, the Multiplication of Roots and Binomials -- 14.2b, Multiplying Roots by Roots -- 14.3, Addition and Subtraction of Monomials, Binomials and Apotomes -- 14.4a, Mutual Division of Monomials -- 14.4b, Division of Binomials and Apotomes |
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14.5, Cube Roots -- Chapter 15 -- Theory of Means, Rules of Geometry, and Algebra -- 15.1, An Investigation of Means -- 15.2, Geometric and Other Questions -- 15.3, Introduction to Algebra -- 99 Questions with Interspersed Theory -- IV. The Real Story in Select Detail -- "Generation 1": "Generation 1": Livero de l'Abbecho, Pisan Libro di Ragioni, "Columbia Algorism" and Liber Habaci -- The Livero de l'Abecho -- The Pisa Libro di Ragioni -- The "Columbia Algorism" -- The Liber Habaci -- An Ibero-Provençal aside -- The "Second Generation": Crystallization of a Tradition, and the Arrival of Algebra |
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Jacopo's Tractatus -- Paolo Gherardi -- Tutta l'Arte -- The Lucca Libro d'Abaco -- Giovanni di Davizzo -- Biagio il Vecchio -- The Second Generation -- Summary Observations -- Further into the 14th Century -- Dardi da Pisa and the Aliabraa Argibra -- Alcibra Amuchabile -- Antonio de' Mazzinghi -- The Florentine Tratato sopra l'Arte della Arismetricha -- The Abbacus Encyclopedias -- The Ottoboniano and Palatino -- Benedetto -- Summary Observations Concerning the Florentine Encyclopedias -- V. Abbacus Goes into Print and Abroad -- Early Prints in Italy -- The Basic to Intermediate Levels |
| Summary |
The abbacus was a thorough and complete system of arithmetical calculations, which saw its dawn in the Indian and Arabic tradition of the Middle Ages, but which was developed in its fully fledged aspects especially in Italy, between Genoa, Milan, Venice and the region of Umbria. In this monograph, Hyrup explores how the abbacus tradition has developed in Europe, with a focus on Italy and Germany between the 14th and the 17th Century. With the analysis of texts from Fibonacci, Pacioli, and Stifel to name but a few, this book offers a critical historical analysis of the development and diffusion of a tradition of calculus that has deeply influenced the way in which mathematics has developed in the West. The primary purpose of the book is to present a fairly detailed portrait of the abbacus tradition as it developed historically; as will be argued, Fibonacci was much less important for the emergence of this tradition than mostly assumed but since his importance is broadly taken for granted, that argument needs to be made, for which reason Fibonaccis Liber Abbaci is also described and analyzed in some depth. A secondary purpose is to show how the adoption of abbacus mathematics in German lands gave rise to the creation of a different tradition. The end of the book investigates the interplay of abbacus algebra with other intellectual currents which turned the whole mathematical undertaking upside-down in the 17th Century |
| Notes |
The Higher Level |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed April 9, 2024) |
| Subject |
Fibonacci, Leonardo, approximately 1170-approximately 1240. Liber abaci
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Abacus -- History
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| Form |
Electronic book
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| ISBN |
9783031251641 |
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3031251644 |
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