Leibniz

1689 · 61446 — 1689. Acta Eruditorum 1689. - Leipzig Grossium & Gleditsch 1689 4° 8 653 7 pp. mit 15 z.T. gefalt. Kupfertafeln feiner Pappand im Stil d.Zt.: frisches Expl. First printing of these extremely important papers in which Gottfried Wilhelm Leibniz 1646-1716 claimed that he independently of Newton had discovered the principal propositions of his "Principia" and which present us with Leibniz's fundamental physico-mathematical theory his dynamics his concepts of force space and time. 1. : De Lineis Opticis et alia; Excerpta ex literis ad pp.36-38 Tab. I Fig. 1 2. : Schediasma de Resistentia Medii Motu projectorum gravium in medio resistente pp.38-46 Tab. I Fig. 2-4. 3. : Tentamen de Motuum Coelestium causis pp.82-96 Tab.II Fig. 1. 4. : De Linea Isochrona in qua grave sine acceleratione descendit & de controversia cum Dn. Abbate D.C. pp.195-198 Tab. IV Fig. 3. The "Tentamen." constitutes Leibniz's response to Newton's theories about the motion of the celestial bodies. Leibniz can be said to have anticipated the modern mathematical principle of relativity as it is his idea of individual co-ordinate systems and his practical rejection of the Galilean co-ordinate system that Newton adopted. Leibniz opposes Newton's ideas of attractions gravitational forces and calls them "occult qualities". The task of the "Tentamen." was to attain a theory mathematically equivalent to Newton's in accounting for planetary motion and especially for the inverse-square law of Kepler's laws but physically sound and capable of explaining the causes of phenomena. Newton attacked Leibniz's claim of priority in his anonymously published paper "Commercium epistolicum" Phil. Transactions 1714 and states that "in those tracts the principal propositions of that book are composed in a new manner and claimed by Mr. Leibniz as if he had found them himself before the publishing of the said book. But Mr. Leibniz cannot be a witness in his own cause. It lies upon him either to prove that he had found them before Mr. Newton or to quit his claim." The features of Leibniz's mathematical representation of motion as put forward in "Tentamen." are -Empty space does not exist. The world is filled with a variety of fluids which are responsible for physical actions including gravity. - Living force and its conservation are the fundamental notion and principle respectively in the investigation of nature however they do not figure prominently in the study of planetary motion. - Finite and infinitesimal variables are regularly employed in the study of motion and of other physical phenomena. Living force and velocity are finite; solicitation and conatus are infinitesimal. - Accelerated motion whether rectilinear or curvilinear is represented as a series of infinitesimal uniform rectilinear motions interrupted by impulses. I call this 'polygonal representation'. Usually the polygon is chosen in such a way that each side is traversed in an equal element of time dt. In polygonal representations accelerations are reduced to a macroscopic phenomenon. - Propositions are often used to safeguard dimensional homogeneity. Constant factors - such as numerical factors mass and the element of time - are usually ignored in the calculations. -cf. D.B. Meli: Equivalence and Priority. Newton versus Leibniz. pp. 90-91. Further we find in this important volume following Papers by Denis Papin - 1. : Descriptio Torcularis cujus in Actis Anni 1688 pag. 646 mentio facta a suit. pp. 96-101 Tab. II Fig. 2 2. : De Gravitatis Causa et proprietatibus Observationes pp.183-188. 3. : Examen Machinæ Dn. Perrault pp.189-195 Tab. IV Fig. 1-3. 4. : Rotatilis Suctor et Pressor Hasciacus in Serenissima Aula Cassellana demonstratus & detectus pp.317-322 Tab. VII Fig. 3-6. This paper describes and depicting Papin's famous invention of the CENTRIFUGAL PUMP 5.: In J.B. Appendicem Illam Ad Perpetuum Mobile Actis Novemb.A. 1688 p. 592. pp.322-324. 6. : Excerpta et Litteris Dn. Dion Papini ad --- de Instrumentis ad flammam sub aqua conservandam pp.485-489 Tab. XI Fig. 2-3. - and 3 papers by Jakob Bernoulli: 1. : De Invenienda Cujusque Plani Declinatione ex unica observatione projectæ a flylo umbræ pp.311-316 Tab. VII Fig. 1-2. 2. : Bernoulli Jakob : Vera Constructio geometrica Problematum Solidorum & Hypersolidorum per rectas lineas & circulos pp.454-459 Tab. X. 3.: Bernoulli Jakob : Novum Theorema Pro Doctrina Sectionum Conicarum. pp.586-588 Tab. XIV. See - Thomas Sonar : The History of the Priority Dispute between Newton and Leibniz: Mathematics . 2018 Ravier 101102103104 unknown