Author : Blaise Pascal
Publisher : LP
ISBN 13 : 3689384664
Total Pages : 243 pages
Book Rating : 4.6/5 (893 download)
Book Synopsis The Geometry of Thought: Pascal’s Early Mathematical and Scientific Writings by : Blaise Pascal
Download or read book The Geometry of Thought: Pascal’s Early Mathematical and Scientific Writings written by Blaise Pascal and published by LP. This book was released on 2024-05-09 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new translation of Pascal's core mathematical and geometrical works, which include commentary on scientific progress, Morality, Theology and Sociological topics. This new Reader's Edition from LP contains a new Afterword by the translator on Pascal's personal relationship with Descartes and his intellectual objections to the new Cartesian rationality which fundamentally changed the course of both Science and Philosophy. Additional materials include a short biography on Pascal's life and impact, a useful timeline of his life and relationships, an index of his core Philosophic terminology, a chronological summary of all of his published and posthumous works, and the text of Pascal's Memorial, a poetic, fragmented account of his divine vision in 1654. These extra materials introduce the reader to Pascal's metaphysical works and his environment- bringing to life Pascal's witness of the dawn of a new Scientific age. This is volume 1 of the 7-part Complete Works of Pascal by LP. This volume covers Pascal’s groundbreaking contributions to mathematics, science, and engineering, as well as his Scientific-Philosophical commentary on the Enlightenment's Scientific progress. This translation of Pascal's 1648 "The History of the Roulette Line, Otherwise known as the Trochoid or Cycloid" contains Pascal's two additions to the text- "Continuation of the History of Roulette" (December 1658) and "Addition Following the History of Roulette" (January 1659). The 1647 work "Treatise on Emptiness & New Experiments Concerning the Vacuum" is Pascal's paper proving the existence of Vacuums (something his contemporary Descartes and the Scientific world believed impossible) along with a treatise on the philosophic ramifications of new scientific discoveries. The original French title of his paper on vacuums is "Expériences nouvelles touchant le vide" and the fragment of the unfinished "preface to the Treatise on Emptiness" (Fragment de préface pour le traité du vide) first written in October 1647. Together, these two papers provide a fascinating view into the mind of the Scientist-Theologian Pascal. In September 1647 in Pais, René Descartes met with Pascal over this topic of the vacuum. Descartes' mechanistic understanding of Physics led to his skepticism over the possibility of a vacuum, but Pascal almost convinced him.This meeting was arranged by Father Mersenne, a mutual acquaintance who was deeply involved in the intellectual circles of the time. Pascal and Descartes discussed various scientific and philosophical issues, particularly focusing on physics and the nature of the vacuum, a subject both were deeply interested in. Pascal had been conducting experiments on atmospheric pressure and the vacuum, and he sought Descartes' opinion on his findings. Descartes later read this work, evolving his understanding of Physics. Pascal's Theorem, also known as the Hexagrammum Mysticum Theorem, is found first here in his 1639 Essay on Conic Sections. This theorem is one of Pascal's early contributions to projective geometry, dealing with the properties of hexagons inscribed in conic sections. The lemma mentioned in this work is Pascal's famous theorem related to a hexagon inscribed in a conic section. It states that the intersection points of the opposite sides of such a hexagon lie on a straight line. Pascal referred to this inscribed hexagon as the "mystic hexagram" but would later be called Pascal's Theorem. Originally written in 1640 "Essai pour les coniques" is one of Pascal's earliest existing works on Geometry, displaying his particularly advanced understanding and extension of conic sections, inspired by Desargues' pioneering work. Pascal's definition of the arrangement of straight lines is closely borrowed from Girard Desargues, particularly from his work "Brouillon Project" (Project Draft). Desargues' influence is evident in Pascal's studies, especially in the properties and projections of conic sections. Pascal's work also reflects Desargues' theorem, which deals with the intersections of a transversal with a conic section and the sides of an inscribed quadrilateral. Following Girard Desargues' methods, Pascal studied the properties of conic sections by considering them as projections of a circle. This approach was to form part of his comprehensive work on conics, "Conicorum opus completum." Pascal's propositions often involve relationships that can be understood using this concept. A fragment from Pascal's complete treatise on conics, titled "Generatio Conisectionum," develops these considerations further, however this manuscript has been lost, save for handwritten copies of parts of it copied by Leibnitz. This volume contains: 1640: Essay on Conic Sections 1645: The Arithmetic Machine 1647: Treatise on Emptiness & New Experiments Concerning the Vacuum 1648: The History of the Roulette Line, Otherwise known as the Trochoid or Cycloid 1654: Treatises on the Equilibrium of Liquors and the Gravity of the Mass of Air 1871: On the Geometric Mind
