Land-area mensuration for the division and collection of taxes was among the principal administrative functions in the Islamic period, and mathematicians produced practical instructions to meet these needs; understanding these instructions helps clarify the numerical and spatial logic of architecture across different eras. This study proceeds from the premise that one path to understanding Islamic architecture is to trace the relation among geometry, the workshop, and the dīwān, with ʿilm al-masāḥa (mensuration) serving as the mediating language. The core problem is that, despite abundant work on geometry and ornament, the role of mensuration in design, construction, and fiscal auditing has not been examined as an integrated, manuscript-based narrative. Drawing on first-hand manuscripts and treatises from the third to the ninth Islamic centuries, the research analyzes how mensuration functioned as the intermediary link between “geometric forms” and “operational and administrative numbers.” The method is manuscript-driven and analytical in three steps: (1) close reading and content comparison of mathematical and administrative texts with emphasis on chapters concerning the mensuration of buildings; (2) reconstruction of computational procedures and numerical examples using historical units and measuring tools (e.g., dhirāʿ, qaṣaba, jarīb, and scale rules); and (3) mapping these procedures onto three architectural arenas: modular design, estimation of construction quantities, and administrative recording. Findings indicate that, in the Islamic period, mensuration supplied a precise computational apparatus across three interlinked levels: in design, a criterion for specifying profiles and aligning them with modular grids; in construction, a basis for converting lengths, areas, and volumes into real quantities of materials and work time; and in administration, a foundation for standardizing reports, estimating wages, and assessing taxes. Accordingly, mensuration is not merely a calculative science; it provides a conceptual framework for the spatial and administrative organization of Islamic architecture and proposes a methodological bridge between mathematical texts, workshop procedures, and quantitative evaluations of historic buildings.
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