{"page_number":146,"title":"Page 146","overview":"This page discusses the life and contributions of Joseph-Louis Lagrange, particularly his work in analytical mechanics and his efforts to reform the foundations of calculus, set against the backdrop of the French Revolution and the establishment of the École Polytechnique.","text_summary":"The page details the career and intellectual contributions of Lagrange, a prominent mathematician. It begins by noting that despite the turmoil of the French Revolution, Lagrange was continually honored and well-regarded in Paris. His seminal work, *Mécanique analytique*, is highlighted as a comprehensive synthesis of a century of research in mechanics since Newton. This work introduced the concept of \"generalized coordinates\" and derived the Lagrangian equations, which describe the motion of a classical mechanical system by relating kinetic energy to these coordinates, corresponding forces, and time. A notable aspect of *Mécanique analytique* is Lagrange's explicit statement in its preface that it contains no figures.\n\nThe text then shifts to the period of the French Revolution, which began in 1789. Lagrange participated in the committee to reform the metric system. The execution of the chemist Antoine-Laurent Lavoisier deeply affected Lagrange, who lamented the immense loss to science. The page also mentions the founding of the École Centrale des Travaux Publics (later known as the École Polytechnique) in 1794, where Gaspard Monge became the leading mathematics professor. Lagrange's lectures at this institution were published as *Théorie des fonctions analytiques* (1797) and *Leçons sur le calcul des fonctions* (1804). These works are identified as the first textbooks on real analytic functions, in which Lagrange attempted to establish an algebraic basis for calculus, aiming to replace the then-problematic analytic foundations, though this endeavor was ultimately unsuccessful.","content_markdown":"# Page 146\n\n### Page Overview\nThis page discusses the life and contributions of Joseph-Louis Lagrange, particularly his work in analytical mechanics and his efforts to reform the foundations of calculus, set against the backdrop of the French Revolution and the establishment of the École Polytechnique.\n\n### Text Content Summary\nThe page details the career and intellectual contributions of Lagrange, a prominent mathematician. It begins by noting that despite the turmoil of the French Revolution, Lagrange was continually honored and well-regarded in Paris. His seminal work, *Mécanique analytique*, is highlighted as a comprehensive synthesis of a century of research in mechanics since Newton. This work introduced the concept of \"generalized coordinates\" and derived the Lagrangian equations, which describe the motion of a classical mechanical system by relating kinetic energy to these coordinates, corresponding forces, and time. A notable aspect of *Mécanique analytique* is Lagrange's explicit statement in its preface that it contains no figures.\n\nThe text then shifts to the period of the French Revolution, which began in 1789. Lagrange participated in the committee to reform the metric system. The execution of the chemist Antoine-Laurent Lavoisier deeply affected Lagrange, who lamented the immense loss to science. The page also mentions the founding of the École Centrale des Travaux Publics (later known as the École Polytechnique) in 1794, where Gaspard Monge became the leading mathematics professor. Lagrange's lectures at this institution were published as *Théorie des fonctions analytiques* (1797) and *Leçons sur le calcul des fonctions* (1804). These works are identified as the first textbooks on real analytic functions, in which Lagrange attempted to establish an algebraic basis for calculus, aiming to replace the then-problematic analytic foundations, though this endeavor was ultimately unsuccessful.\n\n### Visual Elements (Diagrams, Figures, Graphs, Portraits, Illustrations)\n*No visual elements on this page.*","has_visuals":0,"visual_count":0,"visuals":[]}