Jacopo da Firenze's Tractatus Algorismi and Early Italian Abbacus Culture

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Springer Science & Business Media, 24 dic 2007 - 482 pagine

This book deals with one of the earliest surviving "abbacus" treatises, one that is by far more orderly than any of the extant predecessors and is also the first to contain a presentation of algebra. The book contains an edition and an English translation of a manuscript from c. 1450. In addition, it features an extensive discussion of the contents of the treatise and its location within early abbacus culture.

 

Sommario

Introduction
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
Bibliography
458
Source Index
467
Geographical Locations
475
Copyright

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Pagina ii - 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.
Pagina 463 - I-III. (Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung A: Quellen.
Pagina 3 - ... 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...
Pagina 3 - ... 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...

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