Cartesian Mechanics Sophie Roux
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Calcul Différentiel Et Intégral De Leibniz Et Newton
Master de Mathématiques – Sorbonne Université (M1) UE 4M039 : Histoire des mathématiques (Alexandre Guilbaud et Laurent Mazliak) Semaine 4 La naissance du calcul différentiel et intégral : un pas décisif vers l’émergence du concept de fonction Le jeudi 15 février 2018 M1 - Histoire des mathématiques 1 Prologue (1/3) – Les académies Jean-Baptiste Colbert présentant les membres de l'Académie royale des sciences à Louis XIV (H. Testelin, d'après une gravure de Lebrun) Le jeudi 15 février 2018 M1 - Histoire des mathématiques 2 Prologue (1/3) – Les académies § Les académies qui naissent au XVIIe siècle signent l'abandon du travail solitaire. § Les savants s'y réunissent de leur plein gré et de façon informelle pour : échanger des idées et réfléchir de façon collective sur un certain nombre de sujets / soumettre leurs travaux à la critique des autres membres / réaliser des observations et les commenter. § Les « académies privées » : ü L'Académie dei Lincei, fondée à Rome en 1603 (Galilée en est membre à partir de 1611) ü L'Académie del Cimento à la brève existence (1657-1667) ü L'académie napolitaine des Investiganti (1663-1670) ü L'Académie par correspondance de Marin Mersenne (1588-1648) met en relation une quarantaine de savants (dont Descartes, Fermat, Galilée, Gassendi, Roberval, Huygens) ü etc. Le jeudi 15 février 2018 M1 - Histoire des mathématiques 3 Prologue (1/3) – Les académies § La Royal Society de Londres : existe depuis 1661, elle ne reçoit aucun financement de la couronne et vit des cotisations de ses membres (qui devinrent fort nombreux). § L'Académie royale des sciences de Paris, créée par Colbert en 1666 : - l'Observatoire de Paris naît en 1667 sous l'impulsion de l'Académie. -
Le Calcul Différentiel Et Intégral Dans L'analyse Démontrée De Charles
Recherches sur Diderot et sur l'Encyclopédie 38 | avril 2005 La formation de D'Alembert Le calcul différentiel et intégral dans l’Analyse démontrée de Charles René Reyneau Jean-Pierre Lubet Édition électronique URL : https://journals.openedition.org/rde/304 DOI : 10.4000/rde.304 ISSN : 1955-2416 Éditeur Société Diderot Édition imprimée Date de publication : 1 juin 2005 ISBN : 2-9520892-4-8 ISSN : 0769-0886 Référence électronique Jean-Pierre Lubet, « Le calcul différentiel et intégral dans l’Analyse démontrée de Charles René Reyneau », Recherches sur Diderot et sur l'Encyclopédie [En ligne], 38 | avril 2005, mis en ligne le 30 mars 2009, consulté le 30 juillet 2021. URL : http://journals.openedition.org/rde/304 ; DOI : https:// doi.org/10.4000/rde.304 Propriété intellectuelle 151-176 21/06/05 16:07 Page 151 Jean-Pierre LUBET Le calcul différentiel et intégral dans l’Analyse démontrée de Charles René Reyneau Le premier mémoire envoyé par Jean Le Rond D’Alembert à l’Académie royale des sciences avait pour objectif essentiel de rectifier une erreur contenue dans l’Analyse démontrée de Charles René Reyneau. Avec d’autres travaux de D’Alembert sur le calcul intégral, cette question1 a été présentée en détail par Christian Gilain dans un article récent . Nous proposons de revenir ici sur l’ensemble du traité de Reyneau, pour essayer de caractériser les éléments de calcul différentiel et intégral qu’il contient. Publié pour la première fois en 1708, l’ouvrage a été largement diffusé au point qu’une seconde édition, comportant peu de modifications, a été nécessaire en 1736-1738. -
A Study on University Education of Medieval European Mathematicians 1K
International Journal of Pure and Applied Mathematics Volume 116 No. 22 2017, 265-273 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu A Study on University Education of Medieval European Mathematicians 1K. Rejikumar and 2C.M. Indukala 1Deptment of Mathematics, N.S.S. College, Pandalam, Kerala, India. [email protected] 2University of Kerala, Palayam, Thiruvananthapuram, Kerala, India. [email protected] Abstract Higher educational institutions in a country play an important role in the cultural transformation of people. Its role in the coordination and strengthening of new knowledge and its proper dissemination in the community is an important factor in the development of any country. In this paper we compare the importance of role played by higher educational institutions in the development of Kerala School of Mathematics and European School of Mathematics. Key Words:Kerala school of mathematics, european school of mathematics, institutions of higher learning. 265 International Journal of Pure and Applied Mathematics Special Issue 1. Introduction The word university is originated from the Latin word “Universitas”, means the whole, the world or the universe. Before Universities were established, the main centers for education were monastic schools. Because of the increasing necessity for acquisition of knowledge, there happened the migration of cathedral schools to large cities. At the early stage Universities were consisted of a group of individuals assembled at some available spaces such as church or homes. Gradually Universities were established in secluded buildings and teachers were granted remuneration [1]. This paper deals with a cursory overview on the education details of eminent European scholars who made significant contributions in mathematics and other fields of interest during the period from 1300 to 1700. -
The Point Mass As a Model for Epistemic Representation
Dipartimento di Scienze Pure e Applicate Corso di Dottorato di Ricerca in Scienze di Base e Applicazioni Ph.D. Thesis THE POINT MASS AS A MODEL FOR EPISTEMIC REPRESENTATION. A HISTORICAL & EPISTEMOLOGICAL APPROACH Tutor: Candidate: Chiar.mo Prof. Vincenzo Fano Dott.ssa Antonella Foligno Curriculum Scienze della Complessità Ciclo XXX – A. A. 2016/2017 Settore Scientifico Disciplinare: M-FIL/02 To Martina and Giada If our highly pointed Triangles of the Soldier class are formidable, it may be readily inferred that far more formidable are our Women. For, if a Soldier is a wedge, a Woman is a needle; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a Female, in Flatland, is a creature by no means to be trifled with. But here, perhaps, some of my younger Readers may ask how a woman in Flatland can make herself invisible. This ought, I think, to be apparent without any explanation. However, a few words will make it clear to the most unreflecting. Place a needle on the table. Then, with your eye on the level of the table, look at it side-ways, and you see the whole length of it; but look at it end-ways, and you see nothing but a point, it has become practically invisible. Just so is it with one of our Women. When her side is turned towards us, we see her as a straight line; when the end containing her eye or mouth – for with us these two organs are identical – is the part that meets our eye, then we see nothing but a highly lustrous point; but when the back is presented to our view, then – being only sublustrous, and, indeed, almost as dim as an inanimate object – her hinder extremity serves her as a kind of Invisible Cap. -
Deux Moments De La Critique Du Calcul Infinitésimal
Séminaire de philosophie et mathématiques MICHEL BLAY Deux moments de la critique du calcul infinitésimal Séminaire de Philosophie et Mathématiques, 1987, fascicule 12 « Deux moments de la critique du calcul infinitésimal », , p. 1-32 <http://www.numdam.org/item?id=SPHM_1987___12_A1_0> © École normale supérieure – IREM Paris Nord – École centrale des arts et manufactures, 1987, tous droits réservés. L’accès aux archives de la série « Séminaire de philosophie et mathématiques » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Deux moments de la critique du calcul infinitésimal: Michel Rolle et George Berkeley par Michel BLAY 1) La critique de Michel Rolle 1-1) La critique des concepts et des principes fondamentaux. 1-2) Le nouveau calcul conduit à l'erreur. 1-2-1) Le cadre général de l'argumentation. 1-2-2) Le privilège accordé à la méthode de Hudde. 1-2-3) La construction des exemples. 2) La critique de George Berkeley 2-1) L'absence de rigueur. 2-2) L'heureuse compensation des erreurs. 2-2-1) Première détermination de la sous-tangente. 2-2-2) Deuxième détermination de la sous-tangente. Deux moments de la critique du calcul infinitésimal: Michel Rolle et George Berkeley C'est en 1684, dans le tout nouveau périodique des Acta Eruditorum, que Leibniz publie son texte fondateur du nouveau calcul différentiel: "Nova Methodus pro Maximis et Minimis, itemque, Tangentibus, quae nec Fractas nec Irrationales Quantitates moratur, et singulare pro illis calculi genus" (1). -
GALILEO CREATION and COSMOGONY a Study on the Interplay Between Galileo’S Science of Motion and the Creation Theme [M-STO/05, M-FIL/06]
DOCTORAL DISSERTATION GALILEO CREATION AND COSMOGONY A Study on the Interplay between Galileo’s Science of Motion and the Creation Theme [M-STO/05, M-FIL/06] Ph.D. Candidate Ph.D. Coordinator IVAN MALARA Prof. ANDREA PINOTTI Registration number: R11933 JOINT PH.D. SUPERVISORS Università degli Studi di Milano Prof. LUCA BIANCHI Doctoral course in Philosophy and Human Sciences – XXXIII Cycle Prof. ELIO NENCI (Dipartimento di Filosofia “Piero Martinetti”) Gent Universiteit Prof. MAARTEN VAN DYCK Academic Year 2019/2020 È chiaro che il pensiero dà fastidio anche se chi pensa è muto come un pesce anzi è un pesce e come pesce è difficile da bloccare perché lo protegge il mare Com’è profondo il mare LUCIO DALLA, Com’è profondo il mare (1977) Non ’mbrischiare a calia ca ’nzudda (Calabrian saying) Table of contents Abstract English .........................................................................................................VII Italian ..........................................................................................................VIII Dutch.............................................................................................................IX Introduction .............................................................................................................XI PART ONE: CREATION I. Anno 1607: Galileo and Castelli 1. Galileo in 1607..............................................................................................3 2. Castelli in 1607. The epistulae Cavenses....................................................... -
Knowledge, Freedom, and Brotherly Love: Homosociality and the Accademia Dei Lincei Mario Biagioli Special Cluster: Gender and Early-Modern Science
Copyright © 1995, The Johns Hopkins University Press and the Society for Literature and Science. All rights reserved. Configurations 3.2 (1995) 139-166 ../toc Knowledge, Freedom, and Brotherly Love: Homosociality and the Accademia dei Lincei Mario Biagioli Special Cluster: Gender and Early-Modern Science The Accademia dei Lincei, often considered the earliest of scientific organizations, was established in 1603 by Federico Cesi, a young Roman aristocrat who was soon to become prince of San Polo and Sant'Angelo, duke of Aquasparta, and marquis of Monticelli. 1 After a period of very limited activity, which lasted until 1609, the academy quickly revived its membership and visibility, and by 1611 it included prestigious figures like Galileo and Giovanbattista della Porta. Its ranks continued to increase until 1625, when it listed thirty-two members, most of them located in Rome, Naples, and Florence. 2 The Lincei became an important reference point in the fledgling Italian philosophical community and played a relevant role in Galileo's later career, but it collapsed shortly after the prince's death in 1630. Cesi left behind a vast, elaborate, and well-documented academic project that usually bore little more than a family resemblance to the [End Page 139] actual academy. This essay analyzes the gender dimensions of Cesi's project and traces them into some aspects of the academy's historical record. Unlike all other seventeenth-century scientific academies that excluded women from their membership without making that ban explicit or providing reasons for their policies, the Lincei's oath stated that the academy was a "philosophical army" whose recruits were exclusively male. -
The Birth of Calculus: Towards a More Leibnizian View
The Birth of Calculus: Towards a More Leibnizian View Nicholas Kollerstrom [email protected] We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. We are to a considerable extent agreeing with the mathematics historians Tom Whiteside in the 20th century and Augustus de Morgan in the 19th. By way of introduction we recall two apposite quotations: “After two and a half centuries the Newton-Leibniz disputes continue to inflame the passions. Only the very learned (or the very foolish) dare to enter this great killing- ground of the history of ideas” from Stephen Shapin1 and “When de l’Hôpital, in 1696, published at Paris a treatise so systematic, and so much resembling one of modern times, that it might be used even now, he could find nothing English to quote, except a slight treatise of Craig on quadratures, published in 1693” from Augustus de Morgan 2. Introduction The birth of calculus was experienced as a gradual transition from geometrical to algebraic modes of reasoning, sealing the victory of algebra over geometry around the dawn of the 18 th century. ‘Quadrature’ or the integral calculus had developed first: Kepler had computed how much wine was laid down in his wine-cellar by determining the volume of a wine-barrel, in 1615, 1 which marks a kind of beginning for that calculus. The newly-developing realm of infinitesimal problems was pursued simultaneously in France, Italy and England. -
PIERRE VARIGNON and the CALCULUS of MOTION Michael S
PIERRE VARIGNON AND THE CALCULUS OF MOTION Michael S. Mahoney Princeton University The new currents of scientific thought that reshaped the Académie des Sciences in the 1690s flowed from sources outside France and met in Paris during the period 1689-92. From England came Newton's Principia, familiar in style perhaps to those who knew Huygens' work, but novel in substance surely to those schooled in Cartesian mechanics. From Germany1 by way of the Acta eruditorum came Leibniz' "Tentamen de motuum coelestium causis", familiar in its vortex cosmology but strange in its use of a new "differential calculus" to analyze the motion of bodies. From Basel came Johann Bernoulli, an unknown young mathematician skilled in that calculus and in the even newer and more mysterious "method of integrals", which his brother Jakob and he had recently be developing. Though the last of the new currents to arrive in Paris, the Bernoullis' infinitesimal analysis was the first to influence the direction of mathematics there. It opened the way to Leibniz' recent work on dynamics and thereby provided the tools with which a new generation of Academicians would recast and reorganize Newton's mechanics, integrating it into a program of research that would remain essentially Cartesian for another half-century. Hence, we shall consider the new currents in reverse order. Although Leibniz had worked out the essentials of his new calculus while still in Paris in the mid-1670s,2 he waited almost a decade before publishing an account of it in the May 1684 number of Acta eruditorum. The article, "Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractis, nec irrationales quantitates moratur, & singulare pro illis calculi, genus"3 set forth only the bare algorithms of differentiation, with no explanation or demonstration to speak of and with the sketchiest of illustrative examples. -
How a Dangerous Mathematical Theory Shaped the Modern World
it. As Clavius points out in the “Prolegomena,” it was the sturdiest edifice in the kingdom of knowledge. For a taste of the Euclidean method, consider Euclid’s proof of proposition 32 in book 1: that the sum of the angles of any triangle is equal to two right angles—or, as we would say, 180 degrees. Euclid, at this point, has already proven that when a straight line falls on two parallel lines, it creates the same angles with one parallel line as with the other (book 1, proposition 29). He makes good use of this theorem here: Proposition 32: In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. Proof: Let ABC be a triangle and let one side of it be produced to D. I say that the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC, and the three interior angles of the triangle, ABC, BCA, CAB, are equal to two right angles. Figure 2.1. The sum of the angles in a triangle. 92 This was Salviati’s (Galileo’s) theory of matter, and as he himself admitted, it was a difficult one. “What a sea we are slipping into without knowing it!” Salviati exclaims at one point. “With vacua, and infinities, and indivisibles … shall we ever be able, even by means of a thousand discussions, to reach dry land?” Indeed, can a finite amount of material be composed of an infinite number of atoms and an infinite number of empty spaces? To prove his point that it could, he turned to mathematics. -
NUN 30 Ribouillault Proofs 1.REV.Pdf (1.888Mb)
2014224 [NUN-2015-30.1] 006-Ribouillault-proof-01 [date 1412151024 : version 1412031345] page 124 Nuncius 30 (2015) 124–160 brill.com/nun Atlas and Hercules in the Garden Scientific Culture and Literary Imagination at the Villa Aldobrandini at Frascati Denis Ribouillault University of Montréal, Canada [email protected] Abstract This essay explores the interplay in early modern Roman gardens between the iconog- raphy of instruments and fountains and scientific culture, especially astronomy. Exam- ining the sundials that adorned the garden at the Villa Aldobrandini at Frascati, it suggests a new reading of the garden and its iconographic programme, centred on the iconography of Atlas and Hercules holding the celestial sphere. It stresses the impor- tance of scientific culture for both the conception and the subsequent reception of the programme. Several themes are developed: the relevance of wonder and curiosity in the process of understanding nature, the multiple links between nature and artefacts in the space of the garden, and the scientific interests of the patron, Cardinal Pietro Aldobrandini, and his main adviser, the letterato Giovanni Battista Agucchi. Keywords gardens – Giovanni Battista Agucchi – sundials … For Volker Remmert ∵ In Galileo as a Critic of the Arts (1954), Erwin Panofsky famously advanced the contention that it was Galileo’s aesthetic taste that explained his refusal to con- © koninklijke brill nv, leiden, 2015 | doi: 10.1163/18253911-03001006 2014224 [NUN-2015-30.1] 006-Ribouillault-proof-01 [date 1412151024 : version 1412031345] page 125 atlas and hercules in the garden 125 sider Kepler’s discovery of the elliptical orbit. The ellipse, he argued, was too foreign to the idea of perfection represented by the circle. -
Cum Ferme Omnes Ante Cartesium Arbitrarentur, Primam Humanae
General Theses from Physics As Taught in the Clementine College Don Alexandro Malaspina of the Imperial Marquisate of Mulazzo, Member of the said College. Facta cuilibet singulas impugnandi facultate. [Great deeds are achieved by attacking them singly.] ____________________________________________________________________ Rome 1771 From the Press of Lorenzo Capponi. ___________________________________________ With the Sanction of the Higher Authorities. 1 Of the Principles of Education in Physics Since the serious study of a philosophical man looks above all to this end, that he might achieve certainty and clear knowledge of things, we ourselves have taken pains at the outset to render an account according to reason, so that through our careful investigation of physics, the mind might thus be drawn towards Nature. Of physicists, we consider, with John Keill,a,1 four schools to be pre-eminent among the rest, the first being the Pythagoreans and Platonists; another has its origin in the Peripatetic School;2 the third tribe of Philosophisers pursues the experimental method; and the final class of physicists is commonly known as the Mechanists. While not all that is propounded by these schools is worthy of assent, yet in each there are certain things of which we approve, abhorring as we do the fault with which Leibniz charges the Cartesians,b,3 namely that of judging the ancient authors with contempt, punishing them, as it were, according to one’s own law. And since Those things last long, and are fixed firmly in the mind, Which we, once born, have imbibed from our earliest years, we select what will be of most use in the future, and of all this we present to our scholars an ordered account: no one would think it suitable for us to hear or read anything contrary to method,c,4 for in general it is through habit, and especially through philosophical habit, that youth is first instructed in the colleges.