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7 Bl., 552 S. OLwd. Sprache: Deutsch 0 gr.

OLwd. m. goldener Rücken- u. Deckelprägung u. OU. 8°, 134 S., zahlr. Abb. (tlw. auf Tafeln). Tadellos. EA. Mit Widmung des Verfassers in blauer Tinte auf Schmutztitel (datiert November 1993). Im Anhang: Christoph Bernoulli: «Von der Verfertigung des Papiers» (faksimiliert nach dem «Handbuch der Technologie [. . .]», Basel, 1834) (S. 107 ff.).

Amsterdam, Ten Brink & de Vries, 1911. Zesde druk. In verguld linnen gebonden. Hardcover. Met 483 afbeeldingen, 218 tafels en 326 voorbeelden. xxiii, 869 pag. KEURIG EXEMPLAAR [Architecture / bouwkunde ].

19cm, Halbleder. Zustand: Gut. 3. edizione volume unico. 789 pp. dorso con scritte dorate, dorso leggermente allentato, rilegatura leggermente sfregata, bugnata, fogli di fondo leggermente strappati all'interno, pagine leggermente macchiate, condizioni commisurate all'età. Sprache: Italienisch Gewicht in Gramm: 740.

240, 200 S. OHpgt. Originaler Halbpergamenteinband: Kanten leicht berieben. Sonst guter Erhaltungszustand.

4°. M. zahlr. Notenbeisp. VIII, 240 S., 1 Bl.; 200 S. OHprgtbde. m. Rsch. Einbde. leicht bestoßen. Bd. 2 m. Exlibris a. Innendeckel. Unbeschn. Exemplar. 1: Getreuer Abdruck d. Textes; 2. Übertragung, Rhythmik u. Melodik. Sprache: Deutsch.

Leipzig, Grosse & Gleditsch 1697. Acta Eruditorum Anno MDCXCVII. 4to. 594 . mit 4 (von 8) Tafeln (vorhanden Tafeln 1,4,6,8). Text komplett (S.135/136 in der Paginierung übersprungen ? so komplett!). Die wichtigestn Schriften und Beiträge von Leibniz, Bernoulli und Newton sind vorhanden: Leibniz, G.W.: Communicatio suae pariter, duarumque alienarum ad edendum sibi a Dn. Jo. Bernoulli, ? Solutio problematum a Jo. Bernoullio geometris publice propositorum. S. 201-205 mit 1 gefalt. Tafel; Leibniz, G.W.: Epistola ad Actorum horum Collectores. S.254-256. Bernoulli, Johann: Problemapure gemometricum Eruditis propositum. S.95-96. Bernoulli, Johann: De Conoidibus et Sphaeroidibus Quedam et c. S.113-118. Bernoulli, Johann: Principia Calculi exponentialium seu percurrentium. S. 125-132. Bernoulli, Johann: Curvatura radii in Diaphanis non uniformibus, solutioque Problematis a se in Actis 1696 ? S. 206-211. Bernoulli, Jacob: Solutio Problematum fraternorum, pecultiari Programmate Cal.Jan. 1697 ? S. 211-214. Bernoulli, Jacob: Solutio Difficultatis cujusdam circa naturam Flexus contrarii . S.410-412. Bernoulli, Jacob: Addenda ad constructionem Problematis Beauniani. S.412-413. Newton, Isaack: Excerpta eTransactionibus Philos.Anglig. Jan.1697: Epistola missa ad praenobilem virum d. Carolum Montague Armigerum, ? Solutio duorum problematum Mathematicorum a Jo. Bernoullio prpositorum. S. 223-224. Weitere Beiträge von Marchio, Hospitalius. S.217-218. Erstes Erscheinen der berühmten Ausgabe von Acta Eruditorum, in der die vier Lösungen der vier damals bedeutendsten Mathematiker zusammen gedruckt wurden. Es gab insgesamt fünf Lösungen für das gestellte Problem, und Newtons Lösung wurde erstmals in den Philosophical Transactions (Januar 1697) abgedruckt und hier nachgedruckt. Die von L'Hopital vorgeschlagene, hier nicht abgedruckte Lösung wurde erst 1988 veröffentlicht. Das Brachistochrone-Problem wurde von Johann Bernoulli in Acta Eruditorum im Juni 1696 gestellt. Er führte das Problem wie folgt ein: ?Ich, Johann Bernoulli, spreche den brillantesten an.? Nichts ist für intelligente Menschen attraktiver als ein ehrliches, herausforderndes Problem, dessen mögliche Lösung Ruhm verleihen und als bleibendes Denkmal bleiben wird. Ich hoffe, die Dankbarkeit zu gewinnen der gesamten wissenschaftlichen Gemeinschaft, indem ich den besten Mathematikern unserer Zeit ein Problem vorlege, das ihre Methoden und die Stärke ihres Intellekts auf die Probe stellt. Wenn mir jemand die Lösung des vorgeschlagenen Problems mitteilt, werde ich ihn öffentlich für lobenswert erklären. Johann Bernoulli und Leibniz haben Newton mit diesem Problem bewusst in Versuchung geführt. Angesichts des Streits um die Infinitesimalrechnung ist es nicht verwunderlich, dass Johann Bernoulli diese Worte in seine Herausforderung aufgenommen hat: ?Es gibt weniger, die unsere hervorragenden Probleme lösen können, ja, weniger selbst unter den Mathematikern, die sich rühmen, dass [ Sie] haben ihre Grenzen wunderbar erweitert, und zwar mithilfe der goldenen Theoreme, die (ihrer Meinung nach) niemandem bekannt waren, die aber tatsächlich schon lange zuvor von anderen veröffentlicht worden waren. ?Laut Newtons Biograph Conduitt löste er das Problem auf einem Abend nach der Heimkehr von der Royal Mint. Newton: . ?Inmitten der Hektik der großen Neuprägung kam er erst um vier Uhr nachmittags sehr müde vom Turm nach Hause, schlief aber nicht, bis er das Problem gelöswas um vier Uhr morgens geschah.? Newton. Seine Lösung schickte er an seinen Freund Charles Montague und Montague veröffentlichte ihn anonym in den Transaktionen. Auch Newtons Lösung, die hier in der Acta vorgestellt wird, ist anonym. Die Episode gefiel Newton nicht, wie er später schrieb: ?Ich mag es nicht, von Ausländern über mathematische Dinge belästigt und gehänselt zu werden.? Nach dem Wettbewerb sagte Johann Bernoulli: ?Mein älterer Bruder stellte den vierten von ihnen zusammen (nach Leibniz, ihm selbst und Newton), dass die drei großen Nationen, Deutschland, England und Frankreich, jede für sich, sich mit mir in einer solchen vereinigen.? schöne Suche, alle finden die gleiche Wahrheit.?Struik (Hrsg.) ?A Source Book in Mathematics, 1200-1800, S. 391 ff.

Leipzig, Grosse & Gleditsch, 1689. 4to. Contemporary full vellum. Faint hand-written title to spine. A small stamp on title-page. In: "Acta Eruditorum Anno MDCLXXXIX". (8), 653, (7) pp. and 15 engraved plates. As usual with various browning to leaves and plates. The entire volume offered. Leibniz's papers: pp. 36-38 a. 1 engraved plate" pp. 38-46 pp. 82-89 a. 1 engraved plate" pp. 195-198. First printing of these extremely important papers, in which Leibniz 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. 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, (see D.B. Meli: Equivalence and Priority. Newton versus Leibniz. pp. 90-91):- 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.Denys Papin's papers:1. Descriptio Torcularis, cujus in Actis Anni 1688 pag. 646 mentio facta a suit. and 1 plate. Pp. 96-101.2. De Gravitatis Causa et proprietatibus Observationes. Pp. 183-188.3. Examen Machinæ Dn. Perrault. Pp. 189-195 a. 1 plate.4. Rotatilis Suctor et Pressor Hasciacus, in Serenissima Aula Cassellana demonstratus & detectus. Pp. 317-322 a. 1 plate.5. In J.B. Appendicem Illam Ad Perpetuum Mobile, Actis Novemb.A. 1688 p. 592.Pp. 322-324 a. 1 plate.6. Excerpta et Litteris Dn. Dion Papini ad --- de Instrumentis ad flammam sub aqua conservandam. Pp. 485-489 a. 1 plate.With the paper describing and depicting Papin's famous invention of the CENTRIFUGAL PUMP. ( Rotatilis Suctor et Pressor Hasciacus, in Serenissima Aula Cassellana demonstratus & detectus. - The paper offered (no.4).Jakob Bernoulli's papers:1. De Invenienda Cujusque Plani Declinatione, ex unica observatione projectæ a flylo umbræ. Pp. 311-316 a. 1 plate.2. Vera Constructio geometrica Problematum Solidorum & Hypersolidorum, per rectas lineas & circulos. Pp. 586-588 a. 1 plate.3. Novum Theorema Pro Doctrina Sectionum Conicarum. Pp. 586-588 a. 1 engraved plate.

Leipzig, Grosse & Gleditsch, 1694. 4to. Contemp. full vellum. Faint handwritten title on spine. a small stamp on titlepage. In: "Acta Eruditorum Anno MDCXCIV". (2),518 pp. and 11 folded engraved plates. As usual with various browning to leaves and plates. The entire volume offered. Leibniz's papers: pp. 311-316, pp. 364-375. - Johann Bernoulli's papers: pp. 200-206, pp. 394-99, pp. 435-437, pp. 437-441. - Huygen's papers: pp. 338, pp. 339-41. - Jakob Bernoulli's papers: pp. 262-276, pp. 276-280, pp. 336-338, pp. 391-400. Some mispaginations. All papers first appearance, dealing with, and clarifying the problems and the new applications of Leibniz' inventions of the differential- and integral calculus.In the papers Leibniz shows how to reduce linear first order ordinary differential equations to quadratures. I the other paper he gives a general method of finding the envelope of a family of curves, which helped to spread the theory of plane curves.In the groundbreaking paper offered here, Jakob Bernoulli introduces THE LEMNISCATE, a symmetric self-intersecting curve resembling a figure eight and defined by the condition that the product of the distance of anay point on the curve from two fixed points is (d/2)2, where d is the distance between the fixed points."Jacob Bernoulli was fascinated by curves and the calculus, and one curve bears his name - the "lemniscate of Bernoulli", given by the polar equation r2=a cos 2"0". The curve was described in the Acta Eruditorum of 1694 as resembling a figure eight or a knotted ribbon (lemniscus). However the curve that most caught his fancy was the logarithmic spiral.he swowed that it had several strioking properties not noted before.it is easy to appreciate the feeling that led Bernoulli to request that the "spira mirabils" be engraved on his tombstone together with the inscription "Eadem mutata resurgo" (Though changed, I arise again the same)." (Boyer in his History of Mathematics).

Leipzig, Grosse & Gleditsch, 1691. 4to. Contemp. full vellum. Faint handwritten title on spine. a small stamp on titlepage. In: "Acta Eruditorum Anno MDCLXXXXI". (8),590,(6) pp. and 13 (of 15) folded engraved plates. The 2 first plates lacks, but they do not belong to the papers listed.Leibniz' papers: pp.277-281 a. 1 plate, pp. 435-439. Johann Bernoulli: pp. 274-276 a. 1 plate. Huygens: pp. 281-282. - Jacob Bernoulli: pp. 282-290 a. 1 plate. All papers first apperance. All 5 of extreme importence in the development of the Calculus. Leibniz' 2 papers on the catenary curve (paper 1-2 offered here) was written at the instigation of Jacques Bernoulli. Following the example of Blaise Pascal, who had initiated, in 1658, a contest for the construction of the cycloid, Leibniz also provoked the geometers of his time, by challenging them to submit, at the fixed date of mid-1691, their geometric method for the construction of the catenary curve. Leibniz later provided the answer, followed by Johann Bernoulli and Huygens.'These two papers are a historical account of the origin of the study of this transcendental curve, and, at the same time, the first physical-geometric construction showing the species-relationship between the catenary and the logarithmic curves, as two companion curves" one arithmetic, the other geometric. All of the differentials of the catenary curve, are arithmetic means of corresponding differentials of the logarithmic curve" and, all of the differentials of the logarithmic curve, are geometric means of the catenary.'"The Catenary is the form of a hanging fully flexible rope or chain (the name comes from "catena", which means 'chain'), suspended on two points. The interest in this curve originated with Galileo, who thought that is was a parabola. Young Christiaan Huygens proved in 1646 that this cannot be the case. What the actual form was remained an open question till 1691, when Leibniz, Johann Bernoulli and the then much older Huygens sent solutions to the problem to the "Acta" (Jakob Bernoulli, 1690, Johann Bernoulli 1691, Huygens 1691 and Leibniz 1691), - these 4 1691-papers offered here - in which the previous year Jakob Bernoulli had challenged mathematicians to solve it. As published, the solutions did not reveal the methods, but through later publications of manuscripts these methods have been known. Huygens applied with great ( paper 4) virtuosity the by then classical methods of 17th century infinitesimal mathematics, and he needed all his ingenuity to reach a satisfactory solution. Leibniz ( the papers 1-2) and Bernoulli (paper 3), applying the new Calculus, found the solutions in a much direct way. In fact, the catenary was a test-case between the old and the new style in the study of curves, and only because the champion of the old style was a giant like Huygens, the test-case can formally be considered as ending in a draw." (Grattan-Guiness in "From the Calculus to Set Theory, 1630-1910.").The paper by JACOB BERNOULLI ( no. 5 offered here) is a milestone papers as it marks the invention of the "SYSTEM OF POLAR COORDINATES" with points located by reference to a fixed point and a line through that point. Although newton had earlier also devised such a coordinate system (in 1671), his work was not known, so that the credit for the discovery generally goes to Bernoulli. (Parkinson, Breakthroughs (1691).Further papers contained in this volume of Acta Eruditorum:DENYS PAPIN: Mecanicorum de Viribus Motricibus sententia, asserta a D. Papino adversius C.G.G. L. (Leibniz) objectiones. pp. 6-13. The plate lacks. - and Dion. Papini Observationes quaedam circa materias ad Hydraulicam spectantes. Pp. 208-213 a. 1 plate. This importent paper is part of the LEIBNIZ-PAPIN-CONTROVERSY.JACOB BERNOULLI: Specimen Calculi Differentialis in dimensione Parabolæ helicoidis, ubi de flexuris curvarum in genere, carundem evolutionibus. Pp. 13-22. The plate lacks. - and J.B. Demonstratio Centri Oscillationis ex Natura Vectis, reperta occassione eorum, quæ super hac materia in Historia Literaria Roterodamensi recensentur, articulo.Pp.317-321.LEIBNIZ: O.V.E. Additio ad Schediasma de Medii Resistentia publicatum in Actis mensis Febr. 1889. Pp. 177-178. and O.V.E. Quadratura Arithmetica Communis Sectionum Conicarum quæ centrum babent,.Pp. 178-182 a. 1 plate.TSCHIRNHAUS: Singularia Effecta Vitri Caustici bipedalis, quod omnia magno sumtu hactenus constructa specula ustoria virtute superat, per D.T. Pp. 517-520.