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GP: Fachverband Geschichte der Physik

GP 7: Practices and Experiments

GP 7.3: Talk

Wednesday, March 18, 2026, 14:45–15:15, KH 02.019

Between geometry and physics: revisiting Torricelli's Opera geometrica (1644) as a foundational framework for early modern mechanics — •Raffaele Pisano — HOPAST team, IEMN, Department of Phsysics, University of Lille, France

My talk revisits the physical-mathematical foundations of Evangelista Torricelli's Opera geometrica (1644) within the context of seventeenth-century mechanics and geometry. Marking the 380th anniversary of the work, it draws on the historical-scientific analysis developed in Homage to Evangelista Torricelli's Opera Geometrica (1644-2024) (Springer, 2024), which presents a critical transcription of the original text alongside interpretative essays. Torricelli stands at a crucial transition between classical Archimedean geometry and early modern infinitesimal methods, deeply shaped by Galilean mechanics. Like Cavalieri, he relied on geometrical proportions rather than algebraic equations and worked without an explicit notion of limit. Yet Torricelli advanced beyond the geometry of indivisibles by seeking the logical and physical structure underlying geometrical reasoning. His mathematics is inseparable from physical-mechanical meaning, especially in problems concerning motion, statics, and the determination of areas and volumes of curvilinear solids. For example, Torricelli's proofs on finite volume of the solido acutissimo, illustrating early infinitesimal reasoning at the boundary between geometry and mechanics, and his analysis of the logarithmic spiral, revealing a refined conception of geometrical motion.The Opera geometrica is examined as a synthesis of geometry, infinitesimals, and mechanics.

Keywords: Torricelli’s Opera geometrica (1644); Geometry–Physics Interplay; Archimedean–Galilean Tradition; Infinitesimal Reasoning & Methods; Early Modern Mechanics