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 Hud’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribi’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references.

Summary:

Chapter 1. The Latin Mathematics of Medieval Europe

I. Latin Schools, 800-1140

I-2. Numbering

I-3. Arithmetic

I-4. Geometry

I-5. Recreational Mathematics

II. A School becomes a University : 1140-1480

II-1. Translations

II-2. Arithmetic

II-3. Algebra

II-4. Geometry

II-5. Trigonometry

II-6. Mathematics of the infinite

II-7. Statics, dynamics, and kinematics

III. Abbacist schools : 1300-1480

III-1. Foreign exchange

III-2. Geometry

III-3. Algebra

Chapter 2. Mathematics in Hebrew in medieval Europe

I. Practical and scholarly arithmetic

II. Numerology, combinatorics, and number theory

III. Measurement and practical geometry

IV. Scharlarly geometry

V. Algebra

Chapter 3. Mathematics in the Islamic world in medieval Spain and North Africa

I. Arithmetic

II. Algebra

III. Combinatorics

IV. Geometry

V. Trigonometry

Appendices