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Les Origines De La Statique

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Les Origines De La Statique LES ORIGINES DE LA STATIQUE PAR P. DUHEM correspondant de l’Institut de France, Professeur à la Faculté des Sciences de Bordeaux. TOME SECOND Alain.B lachair@ac -nancy -metz.fr Cliquez sur le lien ci -dessus pour signaler des erreurs. PRÉFACE DU TOME II ................................ ................................ ................................ ....................... 3 CHAPITRE XV : LES PROPRIETES MECAN IQUES DU CENTRE DE GRAVITE D’ALBERT DE SAXE A EVANGELISTA TORRICELLI ................................ ................................ ............................... 5 PREMIÈRE PÉRIODE : D’ALBERT DE SAXE À LA RÉVOLUTION COPERNICAINE ................... 5 1. Énoncé du Principe de Torricelli ................................ ................................ ................................ 5 2. La notion de centre de gravité dans l’Antiquité ................................ ................................ ......... 6 3. La tendance du centre de gravité vers le centre de l’Univers : Albert de Saxe (XIV e siècle) ..... 7 4. La théorie de la figure de la Terre et des mers d’Aristote à Albert de Saxe ............................ 15 5. La tradition d’Albert de Saxe dans l’École : Thimon le Juif, Marsile d’Inghen, Blaise de Parme, Pierre d’Ailly, Jean -Baptiste Capuano, Nipho, Grégoire Reisch................................ .................. 19 6. La tradition d’ Albert de Saxe et Léonard de Vinci ................................ ................................ ... 25 SECONDE PÉRIODE : DE LA RÉVOLUTION COPERNICAINE A TORRICELLI ......................... 33 7. La tradition d’Albert de Sa xe et la révolution copernicaine ................................ ..................... 33 8. La tradition d’Albert de Saxe et de Léonard de Vinci : Cardan et Guido Ubaldo. ................... 37 9. La tradi tion d’Albert de Saxe et de Léonard de Vinci : J.-B. Vilialpand et Mersenne .............. 41 10. La tradition de Léonard de Vinci :Bernardino Baldi ................................ ............................... 45 11. La tradition d’Albert de Saxe et Galilée. En quoi Galilée a contribué à l’invention du Principe de Toricelli. ................................ ................................ ................................ ................................ .. 48 CHAPITRE XVI : LA DOCTRINE D’ALBERT DE SAXE ET LES GÉOSTATICIENS ........................ 53 1. Comment s’est épurée la notion de centre de gravité ; L’influence de Képler ........................... 53 2. Comment s’est épurée la notion de centre de gravité ( suite ) - Les géostaticiens ...................... 54 CHAPITRE XVII : LA COORDINATION DES LOIS DE LA STATIQUE ................................ ............ 64 1. Le P. Marin Mersenne (1588 -1648) - Bla ise Pascal (1623 -1662) - Le P. Zucchi (1586 -1670) - Le P. Honoré Fabri (1606 - 1688) ................................ ................................ ................................ ........ 64 2. Le TRAITÉ DE MÉCANIQUE de Roberval ................................ ................................ ................ 68 3. J ohn Wallis (1616 -1703) ................................ ................................ ................................ ............ 71 4. Les grands traités de statique de l’Ecole jésuite - Le P. De Challes (1621 -1678) - Le P. Paolo Gasati (1617 -1707) ................................ ................................ ................................ ........................ 73 5. La réaction contre les méthodes des vitesses virtuelles et des travaux virtuels : Jacques Rohault (1620 -1675) - Le P. Pardies (1636 -1673) - Les TRAITEZ du P. Lamy - Le DE MOTU ANIMALIUM de Borelli ................................ ................................ ................................ ................................ ........ 78 6. Le parallélogramme des forces et la Dynamique - Les Observations de Roberval - Pierre Varigon (1654 -1722) - La Lettre du P. Lainy - Les Principes de Newton - La Néo -Statique du P. Saccheri 82 7. La lettre de Jean Bernoulli à Varignon (1717). L’énoncé définitif du principe des déplacements virtuels................................. ................................ ................................ ................................ ........... 89 CONCLUSION ................................ ................................ ................................ ................................ .. 93 NOTES ................................ ................................ ................................ ................................ .............. 97 A. SUR L’AXIOME D’ARISTOTE ................................ ................................ ................................ ... 97 B. SUR CHARISTION ET SUR LE PERI ZUGWN D’ARCHIMEDE. ................................ .............. 100 C. SUR L’ ARCHITECTURE DE VITRUVE. ................................ ................................ .................. 104 D. SUR LES MECANIQUES DE HÉRON D’ALEXANDRIE. ................................ ........................ 105 E. SUR JORDANUS DE NEMORE ................................ ................................ .............................. 107 F. SUR LE PRECURSEUR DE LEONARD DE VINCI. ................................ ................................ 107 G. SUR UN PASSAGE DU TRACTATUS DE CONTINUO DE THOMAS BRA DWARDIN. ......... 109 H. SUR LA PROGRESSION DES ÉLÉMENTS SELON THOMAS BRADWARDIN. ................... 109 I. SUR LE TRAITE DES METEORES FAUSSEMENT ATTRIBUÉ A JEA N DUNS SCOT. ......... 110 J. L’INFLUENCE D’ALBERT DE SAXE ET NICOLE ORESME. ................................ .................. 114 K. SUR QUELQUES PASSAGES DES XIV QUAESTIONES DE PIERRE D’AILL Y. .................. 114 L. SUR LE TRACTATUS DE PONDERIBUS DE BLAISE DE PARME. ................................ ....... 116 M. SUR LA FORME DE LA TERRE ET DES MERS SELON JEAN -BAPTISTE CAPUANO DE MANFREDONIA. ................................ ................................ ................................ .......................... 116 N. SUR LA THÉORIE DU PLAN INCLINÉ IMAGINEE PAR LÉONARD DE VINCI. .................... 117 O. SUR LA DECOUVERTE, FAITE PAR LEONARD DE VINCI, DE LA LOI DE COMPOSITION DES FORCES CONCOURANTES. ................................ ................................ ............................. 118 P. SUR LA FORME DE LA TERRE ET DES MERS SELON JEAN FERNEL. ............................. 118 Q. SUR LA FORME DE LA TERRE ET DES MERS SELON MELANCTHON. ............................ 119 R. SUR TARTAGLIA. ................................ ................................ ................................ ................... 119 S. SUR L’ORTHOGRAPHE DU NOM DE GUIDOBALDO DAL MONTE. ................................ .... 119 PRÉFACE DU TOME II Nous commencerons par réparer une injustice involontaire. En la préface du tome I, nous disions comment, en commençant la publication de nos recherches, nom ignorions la solution du problème du plan i ncliné empruntée par Tartaglia à l’École de Jordanus. Nous ajoutions que, de cette belle découverte, aucun historien de la Mécanique n’avait fait mention. Or, en ce point, nous nom trompions. Depuis plusieurs années, l’Académie des Sciences de Turin avait repu une importante communication1 de M. Giovanni Vailati. En cet écrit, l’auteur étudiait les diverses esquisses du principe des vitesses virtuelles que l’on peut relever dans les ouvrages des mécaniciens grecs. C’est parmi ces ouvrages qu’il rangeait l’é crit pillé par Tartaglia, et composé par l’auteur inconnu que nous avons nommé le Précurseur de Léonard. Nous ne discuterons pas ici l’âge que M. Vailati attribue à ce traité de Mécanique ; cette question sera examinée ailleurs 2. Nous nous bornerons à décl arer, pour le moment, que le savant professeur de l’Institut Technique de Florence avait très exactement apprécié l’importance de ce traité ; on en jugera par la conclusion qui terminait son exposé : « Pour rencontrer une œuvre en laquelle la statique se t rouve aussi absolument concentrée autour du principe des travaux virtuels, encore que ce principe ne soit conçu que d’une manière partielle et imparfaite, une œuvre, dirai - je, où la Statique soit assujettie d’une manière si despotique à ce principe ; une œ uvre où l’on refuse, d’une manière si rigoureuse, toute initiative, tout droit d’intervenir à l’intuition directe, dont la méthode d’Archimède faisait si largement usage ; pour rencontrer une telle œuvre, dis -je, il faut venir jusqu’à l’opuscule que Descar tes a intitulé : Explicatio machinarum atque instrumentorum, quorum ope gravissima quaeque pondera sublevantur ; cet opuscule est, en effet, la première tentative qui ait été faite, après le traité dont nous parlons, pour construire l’édifice entier de la statique sur le plan que devait réaliser la Mécanique analytique de Lagrange. » Au moyen âge, la Statique était enseignée de deux manières : Dans les Universités, les maîtres -es -arts rattachaient l’étude des lois de l’équilibre aux commentaires dont ils en richissaient les écrits cosmologiques d’Aristote ; hors des Universités, on traitait la Statique comme une science mathématique autonome, sans attache avec la Philosophie ; cette science, on en trouvait le dépôt dans des ouvrages que l’on attribuait parfois à Euclide, à Archimède, à Jordanus, dont plus souvent encore, les auteurs étaient simplement désignés par ce terme collectif : Auctores de ponderibus. Notre premier volume a eu pour principal objet de suivre, parmi mille vicissitudes, le développement des méthodes que les Auctores de ponderibus avaient créées ; de ce développement
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