"Geometry" in Early Geometrical Disciplines: Representations and Demonstrations

Elaheh Kheirandish
Bridges London: Mathematics, Music, Art, Architecture, Culture (2006)
Pages 315–318


This paper discusses various manifestations of geometry in early geometrical disciplines with reference to specific cases from the Islamic “Middle Ages”, a period of intense scientific activity falling intermediately between the initial reception of Greek scientific material in the early Islamic period (8th-9th centuries AD), and their subsequent diffusion within both Islamic and to European lands (12-13th centuries AD). The paper begins with the classification of mathematical sciences in ancient Greek and early Arabic sources, and proceeds with the identification and distinction of aspects of geometry such as geometrical “representation” and “demonstration” through a case study of specific geometrical disciplines. The case study covers sample problems from four early geometrical disciplines: optics, mechanics, surveying and algebra: optics and mechanics are subdivisions of plane and solid geometry in Aristotelian classifications, surveying and algebra are the respective subdivisions of each in early Arabic Classifications. The samples include geometrical representations (definitions, figures, models) and geometrical demonstrations (illustrations, constructions, proof), as representatives of a range of Arabic and Persian scientific sources from the Islamic Middle Ages.