The World of the Abbaco: Abbacus Mathematics Analyzed and Situated Historically Between Fibonacci and Stifel (Frontiers in the History of Science)

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
	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
		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
		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
		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
		The Higher Level
		Luca Pacioli
	The German-Speaking Area
		Wolack’s Lecture
		The Regensburg Practica, Friedrich Amann – and Regiomontanus
		Two Manuscripts, a University Lecture, and the First Prints
		Rechenmeister Culture Attains Maturity
		Coß
		Stifel’s Arithmetica Integr
VI. A Double Conclusion
	A Mathematical Practice Sui Generis
	The Zilsel Thesis and the Transformation of Mathematics
		12th-13th-Century Reception of Algebra
		The 14th Century – Early Abbacus Algebra, and First Interaction
		The 15th Century – the Beginnings of a Ménage à Trois
		1500–1575: a Changing Scenery
		The Take-Off of modern Algebra
Sigla
Bibliography
Source Index
	Sources referred to by author, title or modern designation
	Manuscripts referred to as such
Name and Subject Index