Description
Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time.
Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos’s elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references.
The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.
Chapter
1. Al-Khwārizmī, Arithmetic
2. Leonardo of Pisa (Fibonacci), Liber abbaci (Book on Calculation)
3. John of Sacrobosco, Algorismus vulgaris
4. Johannes de Lineriis, Algorismus de minuciis
5. Jordanus de Nemore (Nemorarius), De elementis arithmetice artis
6. Combinatorics and probability, De Vetula
2. Leonardo of Pisa, Liber abbaci (Book on Calculation)
3. Leonardo of Pisa, Book of Squares
4. Jordanus de Nemore, De numeris datis (On Given Numbers)
5. Nicole Oresme, Algorismus proportionum (Algorithm of Ratios)
6. Nicole Oresme, De proportionibus proportionum (On the Ratio of Ratios)
1. Banū Mūsā ibn Shākir, The Book of the Measurement of Plane and Spherical Figures
2. Abū Bakr, Liber mensurationum (On Measurement)
3. Leonardo of Pisa, De practica geometrie (Practical Geometry)
4. John of Murs, De arte mensurandi
5. Jordanus de Nemore, Liber philotegni
6. Dominicus de Clavasio, Practica geometriae
1. Ptolemy, On the Size of Chords in a Circle
2. Leonardo of Pisa, De practica geometrie (Practical Geometry)
3. Johannes de Lineriis, Canones
4. Richard of Wallingford, Quadripartitum
5. Geoffrey Chaucer, A Treatise on the Astrolabe
6. Regiomontanus, On Triangles
II-6. Mathematics of the infinite
2. Thomas Bradwardine, Tractatus de continuo (On the Continuum)
3. John Duns Scotus, Indivisibles and Theology
4. Does light travel instantaneously or over time?
5. Nicole Oresme, Questiones super geometriam Euclidis (Questions on the Geometry of Euclid)
II-7. Statics, Dynamics, and Kinematics
1. Robert Grosseteste, De lineis, angulis et figuris (On lines, angles and figures)
2. Jordanus de Nemore, De ratione ponderis (On the Theory of Weights)
3. Thomas Bradwardine, Tractatus de proportionibus
4. William Heytesbury, Regule solvendi sophismata (Rules for Solving Sophisms)
5. Giovanni di Casali, De velocitate motus alterationis (On the Velocity of Motion of Alteration)
6. Nicole Oresme, De configurationibus qualitatum et motuum (On the Configurations of Qualities and Motions)
III. Abbacist Schools: 1300–1480
1. Gilio da Siena, A Lecture in Introductory Algebra
2. Paolo Girardi, Libro di Ragioni
3. Jacobo da Firenze, Tractatus algorismi
4. Master Dardi, New equations solved
Chapter 2. Mathematics in Hebrew in Medieval Europe
I. Practical and Scholarly Arithmetic
1. Abraham ibn Ezra, Sefer Hamispar (The Book of Number)
2. Aaron ben Isaac, Arithmetic
3. Immanuel ben Jacob Bonfils, On decimal numbers and fractions
4. Jacob Canpanṭon, Bar Noten Ṭaʿam
5. Elijah Mizraḥi, Sefer Hamispar (The Book of Number)
6. Levi ben Gershon, Maʿase Ḥoshev (The Art of the Calculator)
II. Numerology, Combinatorics, and Number Theory
1. Abraham ibn Ezra, Sefer Haʾeḥad (The Book of One)
2. Abraham ibn Ezra, Sefer Haʿolam (Book of the World)
3. Levi ben Gershon, Maʿase Ḥoshev (The Art of the Calculator)
4. Levi ben Gershon, On Harmonic Numbers
5. Qalonymos ben Qalonymos, Sefer Melakhim (Book of Kings)
6. Don Benveniste ben Lavi, Encyclopedia
7. Aaron ben Isaac, Arithmetic
III. Measurement and Practical Geometry
1. Abraham ibn Ezra (?), Sefer Hamidot (The Book of Measure)
2. Abraham bar Ḥiyya, Ḥibur Hameshiḥa Vehatishboret (The Treatise on Measuring Areas and Volumes)
3. Rabbi Shlomo Iṣḥaqi (Rashi), On the Measurements of the Tabernacle Court
4. Simon ben Ṣemaḥ, Responsa 165 concerning Solomon’s Sea
5. Levi ben Gershon, Astronomy
1. Levi ben Gershon, Commentary on Euclid’s Elements
2. Levi ben Gershon, Treatise on Geometry
3. Qalonymos ben Qalonymos, On Polyhedra
4. Immanuel ben Jacob Bonfils, Measurement of the Circle
5. Solomon ben Isaac, On the Hyperbola and Its Asymptote
6. Abner of Burgos (Alfonso di Valladolid), Sefer Meyasher ʿAqov (Book of the Rectifying of the Curved)
1. Quadratic word problems
3. Ibn al-Aḥ dab, Igeret Hamispar (The Epistle of the Number)
Chapter 3. Mathematics in the Islamic World in Medieval Spain and North Africa
1. Ibn al-Bannāʾ, Arithmetic
2. ʿAlī b. Muḥammad al-Qalasṣādī, Removing the Veil from the Science of Calculation
3. Muḥammad ibn Muḥammad al-Fullānī al-Kishnāwī, On magic squares
1. Aḥmad ibn al-Bannāʾ, Algebra
2. Muḥammad ibn Badr, An Abridgement of Algebra
1. Aḥmad ibn Munʿim, Fiqh al-ḥisāb (On the Science of Calculation)
2. Ibn al-Bannāʾ on Combinatorics, Raising the Veil
3. Shihāb al-Dīn ibn al-Majdī, On enumerating polynomial equations
1. Abū ʿAbd Allah Muḥammad ibn ʿAbdūn, On Measurement
2. Abū al-Qāsim ibn al-Samḥ, The Plane Sections of a Cylinder and the Determination of Their Areas
3. Abū ʿAbd Allah Muḥammad ibn Muʿādh al-Jāyyānī, On ratios
4. Al-Muʾtaman ibn Hūd, Kitāb al-Istikmāl (Book of Perfection)
5. Muḥyī al-Dīn ibn Abī al-Shukr al-Maghribī, Recension of Euclid’s Elements
1. Abū ʿAbd Allah Muḥammad ibn Muʿādh al-Jayyānī, Book of Unknowns of Arcs of the Sphere
2. Abū ʿAbd Allah Muḥammad ibn Muʿādh al-Jayyānī, On Twilight and the Rising of Clouds
3. Abū ʿAbd Allah Muḥammad ibn Muʿādh al-Jayyānī, On the qibla
4. Ibrāhīm ibn al-Zarqālluh, On a universal astrolabe
5. Abū Muḥammad Jābir ibn Aflaḥ, Correction of the Almagest
Appendix 1. Byzantine Mathematics
1. Maximus Planudes, The Great Calculation According to the Indians
2. Manuel Moschopoulos, On Magic Squares
3. Isaac Argyros, On Square Roots
4. Anonymous fifteenth-century manuscript on arithmetic
Appendix 2. Diophantus Arithmetica, Book I, #24
Appendix 3. From the Ganitasārasangraha of Mahavira
Sourcebook in the Mathematics of Medieval Europe and North Africa
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