Treccani History of Science
Science in Islamic civilization
C3 – Mathematics
Edited by Roshdi Rashed
Mathematical traditions
• The arithmetization of algebra
• Algebraic geometry
• Number theory and geometry
• Problem solving by conic sections
Plane geometry: Euclid re-examined
• Introduction
• The transmission of the Euclidean Corpus
• The tradition of the Elements
• The division of figures
• The tradition of Data
The theory of parallels
• The Hellenistic period
• The theory of parallels in Arabic mathematics
• The theory of parallels in the Latin tradition
Book V of Elements. Arabic commentary on theory of proportion
The Arabic tradition of Book X of the Elements
• Book X and the Pappus commentary
• Arabic commentaries: arithmetic treatment of the continuum
• Book X in Arabic mathematics of the 11th–12th centuries
• Fate of Arab commentaries on Book X after the 13th century
Archimedeans and the problems of infinitesimals
• Calculation of infinitesimal areas and volumes
• Quadrature of the lunulae
• Isoperimetric problems and Extrema
• Theory of the solid angle
The traditions of the conics and the beginnings of research on projections
• The cylindrical projections
• The conical projections
The geometry of conics, problems of loci, contacts and constructions
• The problems of construction
• Geometric analysis from lost treatises of Apollonius
• Focal properties and conic path
Continuous tracing of the conics and the curve classification
• Ibn Sahl: mechanical device for conical sections
• Al-Qūhī: the perfect compass
• Al-Sijzī: improved perfect compass
• Continuous path and curve classification
Trigonometry
• From geometry to trigonometry
• The spherical calculation of zīj
• Formulas of triangle
• Theorems of Abū Naṣr ibn ʿIrāq and Abū ’l-Wafāʾ al-Būzjānī
• The tangent function
• Treatises on trigonometry
• The sines table
Euclidean, neo-Pythagorean and Diophantine arithmetic: new methods in number theory
• Classical number theory
• Indeterminate analysis
Algebra and its unifying role
• Beginnings of algebra: al-Khwārizmī
• Successors of al-Khwārizmī: geometric interpretation and algebraic calculus
• Arithmetization of algebra: al-Karajī and successors
• Geometrization of algebra: al-Ḥayyām
• Transformation of algebraic equations: Sharaf al-Dīn al-Ṭūsī
• Fate of the theory of equations
Algorithmic methods
• Numerical equations
• Interpolation methods
Philosophy of mathematics
• Mathematics as model of philosophical activity
• Mathematics in philosophical synthesis and ontological shift
• From ars inveniendi to ars analytica
Arithmetic
• Written numbering systems
• Needs of administration and civil society
• The Indian calculation
• The ‘aerial’ calculation [ḥawāʾī]
• Fractions
Practical geometry
• Geometric constructions for craftsmen
• Measurements in ḥisāb treatises
• Ibn al-Haytham’s treatise and stereometric procedures
The science of music in Arabic writings
• Development of literary category of music
• Philosophical-metaphoric approach
• Speculative and systematic approach
Mathematics applied to astrology
• The beginnings
• The astrolabe
• Trigonometric functions in medieval astronomy
• Genethlialogy and divinatory astrology
• Conjunction astrology
The revival of geometric studies in the Latin world
• The Euclidean tradition
• The Archimedean tradition and measurement treatises
• The conical sections
• Geometry applied to astronomical problems
Hebrew mathematics
• The oldest mathematical book in Hebrew: Mīznat ha-Middot
• Rise of Jewish mathematics in Spain
• Translation movement in 13th–14th centuries
• Euclid and Euclidean tradition
• Spherical treatises
• Arithmetic and number theory
• Arabic algebra and Jewish mathematics
• Archimedean tradition and Apollonius
• Translators: their environment and motivations