Üsna

Üsna (also transliterated as usna or usnâ) is a historical term used in Ottoman Turkish mathematical literature to denote a compilation of practical calculation methods. In many manuscripts, üsna refers to a dedicated section or genre that collects rules, algorithms, and worked examples for performing arithmetic operations and elementary algebra. The scope can vary by author, but typical üsna content includes operations with integers and fractions, proportion and the rule of three, roots and powers, decimal notation, and methods for solving linear and quadratic equations. The emphasis is practical computation, with applications in commerce, taxation, land measurement, and engineering.

The term is part of a broader tradition of 'usul' or 'usna' in Islamic and Central Asian mathematical literature, where mathematical knowledge was organized into curricula with practical and theoretical components. Üsna treatises were written in Ottoman Turkish and Persianate literary Persian, and they circulated in manuscript form from the 16th through the 19th centuries, often used by students and professionals for instruction and reference. Some works embedded üsna sections within larger arithmetic or algebra manuals.

Etymology is linked to Turkish vocabulary for calculation, related to Arabic-derived mathematical terms. In modern scholarship, üsna is studied as evidence of how arithmetic was taught and systematized in pre-modern Turkish-speaking worlds.