Jacopo da Firenze's Tractatus Algorismi and Early Italian Abbacus CultureSpringer Science & Business Media, 2007/12/24 - 482 ページ This book examines a Tractatus algorismi written in 1307 in Montpellier by Jacopo da Firenze. It is one of the earliest surviving "abbacus" treatises and the first to contain a presentation of algebra. This current book includes the text in late medieval Italian with an English translation. The author offers extensive discussions of the contents and its place within early abbacus culture. Historians, mathematicians, and students interested in the history of mathematics will find this text provides a fascinating glimpse into the field’s early development and evolution. |
目次
| 3 | |
The Abbacus Tradition 27 | 26 |
The Contents of Jacopos Tractatus | 45 |
Algebra | 147 |
Jacopos Material and Influence | 183 |
The Text 193 | 192 |
9 Graphic Schemes Illustrating the Arithmetic of Fractions | 228 |
10 Examples Explaining the Arithmetic of Fractions | 230 |
Introduction | 379 |
The text 383 | 382 |
2 Introduction of the Numerals and the Role of Zero | 385 |
4 Explanation and Exemplification of the PlaceValue Principle | 387 |
6 Multiplication Tables | 389 |
7 Tables of Higher Squares and Products | 395 |
8 Divisions a regolo and a danda | 408 |
9 Graphic Schemes Illustrating the Arithmetic of Fractions | 415 |
11 The Rule of Three with Examples | 236 |
12 Computations of NonCompound Interest | 242 |
13 Problems involving metrological shortcuts | 246 |
14 Mixed Problems Including Partnership Exchange and Genuine Recreational Problems | 251 |
15 Practical Geometry with Approximate Computation of Square Roots | 284 |
16 Rules and Examples for Algebra until the Second Degree | 304 |
17 Rules without Examples for Reducible Third and FourthDegree Equations | 320 |
18 A Grain Problem of Alloying Type | 323 |
19 Second and ThirdDegree Problems about Continued Proportions Dressed as Wage Problems and Solved without the Use of cosacensus Algebra | 324 |
20 Tabulated Degrees of Fineness of Coins | 331 |
21 Alloying Problems | 337 |
22 Further Mixed Problems Including Practical Geometry | 347 |
THE REVISED VERSION MILAN AND FLORENCE | 377 |
10 Examples Explaining the Arithmetic of Fractions | 416 |
11 The Rule of Three with Examples | 419 |
12 Computations of NonCompound Interest | 422 |
13 Problems Involving Metrological Shortcuts | 423 |
14 Mixed Problems Including Partnership Exchange and Genuine Recreational Problems | 426 |
15 Practical Geometry with Approximate Computation of Square Roots | 440 |
20 Tabulated Degrees of Fineness of Coins | 448 |
21 Alloying Problems | 452 |
Sigla | 457 |
| 458 | |
| 467 | |
| 475 | |
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多く使われている語句
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ii ページ - Edited by Eberhard Knobloch and Erhard Scholz Editorial Board: K. Andersen, Aarhus R. Halleux, Liege D. Buchwald, Pasadena S. Hildebrandt, Bonn HJM Bos, Utrecht Ch. Meinel, Regensburg U. Bottazzini, Roma J- Peiffer, Paris JZ Buchwald, Cambridge, Mass. W. Purkert, Leipzig K. Chemla, Paris D. Rowe, Mainz SS Demidov, Moskva AI Sabra, Cambridge, Mass. EA Fellmann, Basel Ch. Sasaki, Tokyo M. Folkerts, Munchen RH. Stuewer, Minneapolis P. Galison, Cambridge, Mass. H.
463 ページ - I-III. (Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung A: Quellen.
3 ページ - ... d'ahhaco. Originally the term ahhaco referred to a device for calculating by means of disks, beads, counters, etc.; but in Italy after the introduction of the use of arabic numerals and the mathematical work on computations with them by Leonardo Fibonacci in the early thirteenth century, the term ahhaco came to be used in a general sense for instruments, methods, manuals, schools, teachers or anything else related to the skill of doing computations, especially with reference to practical applications...
3 ページ - ... wonder that Alberti in generalizing about the society as, a whole felt compelled to lament the lack of interest in letters among these merchants of Florence.6 In this process of growing up a boy's formal secondary education was in most cases limited to the scuola d'ahhaco. Originally the term ahhaco referred to a device for calculating by means of disks, beads, counters, etc.; but in Italy after the introduction of the use of arabic numerals and the mathematical work on computations with them...