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Evangelista Torricelli exemplifies the use the moderns made of the ancients'mathematical methods. Celebrating Evangelista Torricelli's monumental Opera geometrica, this book marks 380 years since its publication (1644-2024). This homage to Torricelli introduces the magnificent major work in Mechanics and Mathematics of a brilliant Archimedean–and–Galilean scientist to modern readers.Opera geometrica deals with Motion & Mechanics and Geometry & Infinitesimals. In quibus Archimedis doctrina Torricelli also presents his mechanical principle of equilibrium – the foundation of the modern Principle of Virtual Work/Static.This outstanding source and research book spotlights the relevance and originality of Torricelli's Mechanics, and is the first and most profound analysis of the Opera geometrica to date. The historical study is achieved in extensive Introduction, 5 Essays and an accurate Transcription of Opera geometrica with parallel side–by–side text, including substantive explicative notes. The book is an accessible avenue to understanding this work by leading authorities who offer much-needed insights into the relationship Physics–Mathematics, Mechanics and Fundamentals. It appeals to historians, epistemologists and scientists.

This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles'extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed'parabolic,'to the graphic context, so expressing the metric properties by means of this specific polarity—a foundational argument. Beyond the celebrated'Chasles theorem,'he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles'philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles'synthetic solution for the intricate problem of ellipsoid attraction—the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles'groundbreaking contributions. Providing a comprehensive understanding of Chasles'distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.