Glossary

al-jabr — "Restoration/completion": moving a subtracted quantity to the other side of an equation as an added one. Half of the name of al-Khwarizmi's method; source of the word algebra.

al-muqabala — "Balancing/confrontation": cancelling equal terms from both sides of an equation. The other half of the method's name.

algorism — Medieval Latin term for written computation with Hindu-Arabic numerals, from Algorismi (al-Khwarizmi). Ancestor of algorithm.

astrolabe — Analog computer for astronomical problems, based on stereographic projection of the celestial sphere onto a plane; the standard scientific instrument of the era. The safiha (saphaea) of al-Zarqali is a universal (any-latitude) variant; Sharaf al-Din al-Tusi's linear astrolabe compresses one onto a rod.

dust board (takht) — Erasable computing surface on which Indian-reckoning algorithms were first performed; al-Uqlidisi advertised adapting them to ink and paper.

equant — Ptolemy's device: a point about which a planet's epicycle center moves with uniform angular speed, violating uniform circular motion and provoking the Islamic critical tradition from Ibn al-Haytham to the Maragha school.

girih — The strapwork pattern family of Islamic geometric ornament; connected to the constructional geometry of Abu al-Wafa's artisan handbook and, in modern analysis, to quasi-periodic tilings.

hisab — Practical calculation/arithmetic; hisab al-hind = Indian (decimal positional) reckoning.

ilm al-fara'id — The law/science of inheritance shares; a driver of exact fraction arithmetic and the application field of half of al-Khwarizmi's Algebra.

ilm al-miqat — The science of astronomical timekeeping (prayer times etc.); profession of the muwaqqit.

jayb — Arabic for sine (see Etymology for the mistranslation to sinus).

madrasa — Endowed teaching college; the institutional home of later mathematical instruction (Samarkand's being the most scientifically ambitious).

mal — "Wealth/property": the technical term for the square of the unknown in Arabic algebra (the unknown itself being shay, "thing," or jidhr, "root").

Maragha school — The 13th-century observatory group (Tusi, Urdi, Shirazi, al-Maghribi) and their successors (Ibn al-Shatir) who rebuilt planetary geometry from uniform circular motions.

muwaqqit — Mosque-employed astronomer/timekeeper (Ibn al-Shatir and al-Khalili held the post in Damascus).

qibla — The direction of Mecca; determining it from arbitrary coordinates is a central spherical-trigonometry problem of the tradition.

rub al-mujayyab — The sine quadrant: a quarter-circle instrument with a trigonometric grid, used to solve triangles graphically; an analog trig calculator.

shadow functions — The tangent and cotangent in their original form: shadow lengths of a standard gnomon (vertical or horizontal). Zill = shadow.

shay — "Thing": the unknown, x, of Arabic algebra.

Tusi couple — Two-circle rolling mechanism (radii in ratio 1:2) converting circular motions into straight-line oscillation; introduced by Nasir al-Din al-Tusi (1247/1261 works), used to replace the equant; reappears in Copernicus.

Urdi's lemma — Geometric equivalence (al-Urdi, before 1259) letting an eccentric-with-equant be replaced by concentric circles plus an epicyclet; a second core tool of Maragha planetary theory, also present in Copernicus's models.

zij — Astronomical handbook: theory reduced to tables plus instructions. The tradition's characteristic mathematical-astronomical publication (200+ known); ancestor, through the Toledan and Alfonsine tables, of the modern ephemeris.