23 books for « bernoulli johann »Edit

‎Demonstratio constructionis editae in Actis Lips. 1724 M. Jul. pro describenda Trajectoria reciproca, quae inter omnes algebraicas possibiles sit simplicissima [Johann B.] (+) Esplanatio Notationum suarum [Daniel B.].‎

‎Leipzig, Grosse & Gleditsch, 1725. 4to. In: ""Acta Eruditorum Anno MDCCXXV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. [Johann Bernoulli's paper:] Pp. 318-25"" [Daniel Bernoulli's paper:] Pp. 470-474. [Entire volume: (2), 54, (37) pp. + five engraved plates.].‎

‎First printing of two paper's by father and son: Johann and Daniel Bernoulli. Daniel Bernoulli paper is a solution to the Riccati-equation: ""Using the first of the two transformations in [The Riccati-equation], Bernoulli succeded in constructing solutions of ""an inifinite number"" of Riccati equations for those values of n for which a solution can be expressed in finite terms. Bernoulli published these solutions in Acta Eruditorum for 1725 [the present paper]. (Greenberg. The problem of the earth's shape from Newton to Clairaut. P. 573).The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians. ‎

‎De motu corporum gravium, pendulorum, et projectilium in mediis non resistentibus et resistentibus supposita gravitate uniformi et non uniformi atque ad quodvis punctum datum tendente, et de variis aliis huc spectantibus, Demonstrationes Geometricae (... - [JOHANN BERNOULLI ON TRAJECTORY DESIGN]‎

‎Leipzig, Grosse & Gleditsch, 1713. 4to. Bound in contemporary full vellum. In: ""Actorum Eruditorum Anno MDCCXIII"". The entire volume offered. Hand-written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper and a library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 77-95 + 1 engraved plate"" pp. 115-132. [Entire volume: (4),559,(22). + 6 engraved plates.].‎

‎First publication of Johann Bernoulli's long analysis of trajectory design in which he corrected Newton's wrong description of the same subject in his ""Principia"" published in 1687. The problem of orthogonal trajectory was a major mathematical topic in the late 17th and early 18th century and Johann Bernoulli was the first to raise the problem about the brachystochrone in 1697. Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume. ‎

‎Opera omnia tam antea sparsim edita, quam hactnus inedita -- EDITION ORIGINALE -- BEL EXEMPLAIRE -- 4 VOLUMES (complete set)‎

‎Lausanne & Genève, Bousquet, 1742, 4 VOLUMES in 4 reliés en plein veau marbré, dos ornés de fers dorés, tranches rouges (reliures de l'époque), (petite épidermure sans gravité à un volume), T.1 : (2), 2 PORTRAITS gravés, 24pp., 563pp., T.2 : (1), 620pp., T.3 : (1), 563pp., T.4 : (1), 588pp., 91 PLANCHES gravées dépliantes‎

‎---- EDITION ORIGNALE des oeuvres de Jean Bernoulli dans laquelle se trouvent réunis tous les articles parus dans divers journaux scientifiques ainsi que de nombreux mémoires restés inédits, notamment celui relatif à l'hydraulique ---- BEL EXEMPLAIRE ---- Ex-libris de l'ingénieur MAILLEBIAU ---- "THE FIRST EDITION OF Jean BERNOULLI's COLLECTED WORKS brings together 189 of his papers and 59 of his lectures. The first volume is primarily devoted to problems in geometry and the early calculus, but also contains papers on muscular mechanics, the resistance of solids and a geometrical demonstration of the motion of pendulums and projectiles in resisting and unresisting media. Volumes 2 and 3 are almost totally devoted to problems of mechanics, the first of these containing his theoretical essay on the maneuvering of vessels and related papers, as well as numerous contributions on the analysis of trajectories. His discourse on the laws governing the communication of movement opens volume 3, which also contains his essay on celestial mechanics. The last volume contains contributions on the curvature of elastic plates, his mechanico-dynamical propositions and problems in dynamics. Most important its appearance in this volume represents the first printing of the hydraulica which was written in competition with his son, Daniel". (Bibliotheca Mechanica pp. 36/37) ---- NORMAN N° 217 : "The younger brother of Jakob I Bernoulli, Johann I collaborated with his brother and with Leibnitz to produce almost all of the present elementary differential and integral calculus, along with the beginnings of ordinary differential equations and the calculus of variations. The integral calculus was published in Johann I's Opera omnia, which contains all of his mathematical papers" ---- DSB II p. 51/55 - Honeyman N° 293**478/i1‎

‎Meditatio de natura Centri Oscillationis, ejusque in Pendulis composites, tam quae in Liquoribus quam in Vacuo agitantur, determinandi Regula, novo et certiori quam hactenus fundamento suffulta. - [BERNOULLI ON THE COMPOUND PENDULA]‎

‎Leipzig, Grosse & Gleditsch, 1714. 4to. In: ""Acta Eruditorum Anno MDCCXIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 257-72 + one engraved plate. [Entire volume: Pp. (2), 565, (41) + four engraved plates.].‎

‎First printing of this influential Bernoulli-paper on the compound pendula. This paper is one of the earliest examples of his work collected under the title ""dynamics"". This group of works were written over a span of thirty years in which he occupied himself both with compound pendula, the study of trajectories and laws of dynamics. His early papers, including the present, are usually regarded as being ""provocative and verbose"". (Villagio. Die Weke Von Johann I Und Nicolaus II Bernoulli. P. 29).Bernoulli had earlier published studies on the compound pendula, but he had been stimulated to reconsider the problem by Leibnitz (Ibid.). The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians. ‎

‎Recueil pour les astronomes.‎

‎Berlin, l'auteur, Paris, Desaint, 1771.‎

‎ Premier volume de cet ouvrage périodique "fournissant de petits mémoires nouveaux d'astronomie, des tables subsidiaires, des observations, &c... présentant le tableau de tout ce qui paraît de nouveau en astronomie." Deux autres volumes seront publiés par la suite (1772 et 1776). Johan (ou Jean) (III) Bernoulli (Bâle,1744-1807) était le fils du mathématicien Jean (II) Bernoulli. Il a été un pionnier de la presse scientifique en particulier astronomique. "La curiosité universelle [de J. Bernoulli] et son prosélytisme scientifique incontestable font de ses écrits - périodiques ou autres - une mine de renseignements variés." (Sgard, Dict. des journalistes). Papier bruni, auréoles sur les premiers feuillets. Exemplaire dans son cartonnage de l'époque. /// In-8 de X, (2), 284 pp., 1 planche et 5 tableaux h.-t. dépliants. Cartonnage bleu de l'époque. //// First volume of this periodical work "furnishing small new memoirs of astronomy, subsidiary tables, observations, &c... presenting an overview of everything new in astronomy." Two further volumes were subsequently published (1772 and 1776). Johan (or Jean) (III) Bernoulli (Basel, 1744-1807) was the son of the mathematician Jean (II) Bernoulli. He was a pioneer of the scientific press, particularly astronomical. "J. Bernoulli's] universal curiosity and unquestionable scientific proselytism make his writings - periodical or otherwise - a mine of varied information." (Sgard, Dict. des journalistes). Paper browned, stains on first few leaves. Copy in its original boards. /// PLUS DE PHOTOS SUR WWW.LATUDE.NET‎

‎Theorema novum habens utilitatem in dividendis multiplicandisque angulis, nec non in condendis Tabulis sinuum, tangentium et secantium.‎

‎Leipzig, Grosse & Gleditsch, 1722. 4to. In: ""Acta Eruditorum Anno MDCCXXII"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. [Johann Bernoulli's paper:] Pp. 361-70. [Entire volume: (2), 571, (35) pp. + six engraved plates.].‎

‎First printing of this original contribution by the famous Swiss mathematician Johann Bernoulli.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians. ‎

‎Der Briefwechsel von Johann Bernoulli. Band 2. Die gesammelten Werke der Mathematiker und Physiker der Familie Bernoulli. ‎

‎Basel, Boston, Berlin. Birkhäuser Verlag. In-8. pleine toile avec jaq. Herausgegeben von der Naturforschenden Gesellschaft in Basel. 442 p. Très bon état. Jaq. légèrement défraichie. ‎

‎Extrait D'une Lettre de M. Bernoulli, écrite de Basle 10. Janvier 1711, touchant la maniere de trouver les forces centrales dans des milieux resistans en raisons composée de leurs densites & des puissances quelques des vitesses du mobile. (+) Addition...‎

‎(Paris, L'Imprimerie Royale, 1714). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1711"". Pp. 47-53 a. pp. 53-56 (Nicolas).‎

‎First appearance of an importent paper in mathematical physics. Bernoulli had shown that the principle of virtual velocities could be shown in analytical form. The principle can be derived from the energy principle and he applied this principle several times to mechanical systems of central forces. For these forces he applied the vis viva equation to the inverse two-body problem. For the corresponding problem of centrally accelerated motion in resisting medium he solved the differential equations and determined the central force in accordance with the Huygens formula(in the paper offered). - The Addenda by his his nephew, Nicolas Bernoulli, best known for the fundamental work ""Ars Conjectandi"" from 1713.‎

‎Méthode pour trouver les Tautochrones, dans des Milieux résistants, comme le Quarré des Vitesses.‎

‎(Paris, L'Imprimerie Royale, 1732). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1730"". Pp. 78-101.‎

‎First printing of Johann Bernoulli's importent paper in which he for the first time (Euler did it at the same time) solved the problem of finding the tautochrone in a medium that resists a body's motion directly as the square of the body's speed.After Huygens first discovered that the cylcoid was a tautochronous curve in vacuo according to the hypothesis of uniform gravity" Newton and Hermann have also given tautochrones following the hypothesis of non-uniform gravity acting, and pulling towards some fixed point as centre. Moreover, they have considered the motion to arise in a vacuum, with no resistance. Truly pertaining to resisting media, Newton has also shown that the cycloid is a tautochrone in a medium for which the resistance is proportional tothe speed moreover, as far as any other kinds resisting media are concerned, there has been no progress made either in roducing the curves themselves or in demonstrating possible tautochronism in them [The 3rd edition of the Principia that Euler refers to finally in 35 alters this view to include the type of resistance offered here. It may be of interest to the reader to observe that Johan. Bernoulli published a paper in the Memoire de l'Acad. Roy. des Sciences in 1730, also present in his Opera Omnia, T. III, p.173, with the title (in tra. from French): Method for Finding Tautochrones in Media Resisting as the Square of the Speed in which Euler does not get a mention.].‎

‎Der Briefwechsel von Johann Bernoulli. ‎

‎Birkhäuser Verlag Basel. 1955. Grand in-8. pleine toile. Pièce de titre au dos. Band 1. Herausgegeben von der naturforschenden gesellschaft in basel. 531 p. Ouvrage bilingue Allemand, Français. Très bon état. ‎

‎Methodus commoda et naturalis reducendi Quadraturas transcendentes cujusvis gradus ad Longitudines Curvarum algebraicarum.‎

‎Leipzig, Grosse & Gleditsch, 1724. 4to. In: ""Acta Eruditorum Anno MDCCXXIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 356-66. [Entire volume: (2), 543, (43) pp. + five engraved plates.].‎

‎First printing of one of the famous Swizz mathematician Johann Bernoulli's papers. He is known for his contributions to the infinitesimal calculus and educated Leonhard Euler in his youth.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

‎De centro Turbinationis inventa nova. - [BERNOULLI ON THE MOVEMENT OF A PENDULUM]‎

‎Leipzig, Grosse & Gleditsch, 1715. 4to. In: ""Acta Eruditorum Anno MDCCXV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 242-57 + one engraved plate. [Entire volume: (2), 549, (41) pp. + seven engraved plates.].‎

‎First publication of Bernoulli's important contribution the properties of a pendulum. The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

‎Section indéfinie des Arcs circulaires. En telle raison qu'on voudra, avec la maniére d'en déduire les Sinus, &c. Extraite d'une de ses Lettres écrite de Bàle le 13.Juillet 1702. (+) Solution d'un Probleme concernant le calcul intégral, avec quel...‎

‎(Paris, Jean Boudot, 1704). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1702"". Pp. 281-288 and pp. 289-297.‎

‎First printing of two importent papers on the calculus. Bernoulli shows that the substitution of some equations leads to the differential of the logarithm of an imaginary number, and since the original integral also leads to the arc tan function he had thus established a relation between the trigonometric and logarothmic functions. (Based on Kline).‎

‎Perfectio regulae suae editae in Libro Gall. Analyse des infiniment petits art. 163. pro determinando valore fractionis, cujus Numerator et Denominator certo casu evanescunt‎

‎Leipzig, Grosse & Gleditsch, 1704. 4to. In: ""Acta Eruditorum Anno MDCCIV"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. Two small stamps to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 375-80. [Entire volume: (2), 592 pp. + six engraved plates.].‎

‎First printing of Bernoulli's paper on infiniti series. Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume. ‎

‎Opera Omnia in quatuor tomos distributa.‎

‎"19. Lausanne et Genève, Sumptibus Marci-Michaelis Bousquet & Sociorum, 1742, 4 vols in-4°, 4 title pages printed in red and black with copper engraved vignette. Title + xxiv pp + 563 pp + 23 folding engraved plates numbered I - XXIII ; title + 620 pp + plates XXIII - XL ; title + 563 pp + plates XLI - LXXVI ; title + pp 5-588 + plates LXXVII - XCI. (Fourth volume starts exceptionally with page 3 as the Norman copy). Our copy is complete except for the two portraits which are lacking (portrait of Bernoulli and portrait of Frederic III king of Prussia). Uniform 19th century black cloth with smooth back and red cloth title label, sprinkled edges, ex-library K.K. Génie-Academie-Bibliothek, small oval 19th century stamps on title and on the verso side of the plates, some clear waterstains on pages 120-140 of volume II and on the first 35 pages of volume III. In all a reasonably good and acceptable copy complete but for the two portraits. This first edition of the collective works of Jean Bernoulli comprises 189 of his papers and 59 of his lectures. It was edited by Gabriel Cramer. After Newton and Leibniz Bernoulli was the leading mathematician to work on and to develop the differential and integral calculus. Most of the first volume is devoted to these texts. Volume II and III contain mainly his texts on mechanics. Volume four has the first printing of ''Hydraulica'' on which he worked in competition with his son Daniel. See e.g. Roberts & Trents; Bibliotheca Mechanica pp. 36-37, Poggendorff I 157-59. Norman 217, Honeyman sale item 293."‎

‎Supplementum defectus geometria Cartesianae circa inventionem locorum. [Joh. Bernoulli] + [Two other papers]. Notatiuncula ad acta decemb. 1695. [LEIBNIZ]. - [THE BRACHISTOCHRONE PROBLEM]‎

‎Leipzig, Grosse & Gleditsch, 1696. 4to. Entire volume present. Nice contemporary full vellum. Small yellow paper label pasted to top of spine and library-label to front free end-papers. Internally some browning and brownspotting. Overall a nice and tight copy. [Bernoulli paper:] pp. 264-69. [Leibniz-paper:] pp. 45-47. [Entire volume: (2), 603, (1) pp. + plates].‎

‎First printing of the famous 1696-edition of Acta Eruditorum in which Johann Bernoulli published a challenge to the best mathematicians:""Let two points A and B be given in a vertical plane. To find the curve that a point M, moving on a path AMB , must follow such that, starting from A, it reaches B in the shortest time under its own gravity.""Johann adds that this curve is not a straight line, but a curve well known to geometers, and that he will indicate that curve, if nobody would do so that year. Later that year Johann corresponded directly with Leibniz regarding his challenge. Leibniz solved the problem the same day he received notice of it, and almost correctly predicted a total of only five solutions: from the two Bernoullis, himself, L'Hospital, and Newton. Leibniz was convinced that the problem could only be solved by a mathematician who mastered the new field of calculus. (Galileo had formulated and given an incorrect solution to the problem in his Dialogo). But by the end of the year Johann had still not received any other solutions. However, Leibniz convinced Johann that he should extend the deadline to Easter and that he should republish the problem. Johann now had copies of the problem sent to Journal des sçavans, the Philosophical Transactions, and directly to Newton. Earlier that year Johann had accused Newton for having filched from Leibniz' papers. Manifestly, both Johann and Leibniz interpreted the silence from June to December as a demonstration that the problem had baffled Newton. They intended now to demonstrate their superiority publicly. But Newton sent a letter dated Jan. 30 1697 to Charles Montague, then president of the Royal Society, in which he gave his solution and mentioned that he had solved it the same day that he received it. Montague had Newton's solution published anonymously in the Philosophical Transactions. However, when Bernoulli saw this solution he realized from the authority which it displayed that it could only have come from Newton (Bernoulli later remarked that he 'recognized the lion by its claw'). The present volume contains the following articles of interest:Jakob Bernoulli: 1, Observatiuncula ad ea quaenupero mense novembri de Dimensionibus Curvarum leguntur.2, Constructio Generalis omnium Curvarum transcendentium ope simplicioris Tractoriae et Logarithmicae.3, Problema Beaunianum universalius conceptum.4, Complanatio Superficierum Conoidicarum et Sphaeroidicarum.Johann Bernoulli5, Demonstratio Analyticea et Syntetica fuae Constructionis Curvae Beaunianae.6, Tetragonismus universalis Figurarum Curvilinearum per Construitionem Geometricam continuo appropinquantem.Tschirnhaus7, Intimatio singularis novaeque emendationis Artis Vitriariae.8, Responsio ad Observationes Dnn. Bernoulliorum, quae in Act. Erud. Mense Junio continentur.9, Additio ad Intimationem de emendatione artis vitriariae.‎

‎Communicatio suae pariter, duarumque alienarum ad edendum sibi a Dn. Jo. Bernoulli, deinde a Dn Marchione Hospitalio communicatarum solutionum problematici curvae..descensus a Dn. Jo. Bernpulli....propositi solutione... (Leibniz). + Curvatura Radii in...‎

‎Leipzig, Grosse & Gleditsch, 1697. 4to. No wrappers. In: ""Acta Eruditorum Anno MDCXCVII"", No V, May-issue. Pp. 193-240 (entire issue offered). With titlepage to the volume 1697. Leibniz: pp. 201-205. Johann Bernoulli: pp. 206-211. Jacob Bernoulli: pp. 211-214. Newton: pp. 223-224. As usual, some leaves with browning.‎

‎First appearance of the famous issue of Acta Eruditorum in which the 4 solutions by the 4 most eminent mathematicians at the time, were printed together. There were in all 5 solutions to the posed problem, and Newton's solution was first printed in the Philosophical Transactions (January 1697) and reprinted here. The solution proposed by L'Hopital, not printed here, was not published until 1988.The brachistochrone problem was posed by Johann Bernoulli in Acta Eruditorum in June 1696. He introduced the problem as follows: ""I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."" Johann Bernoulli and Leibniz deliberately tempted Newton with this problem. It is not surprising, given the dispute over the calculus, that Johann Bernoulli had included these words in his challenge:- ....""there are fewer who are likely to solve our excellent problems, aye, fewer even among the very mathematicians who boast that [they]... have wonderfully extended its bounds by means of the golden theorems which (they thought) were known to no one, but which in fact had long previously been published by others.""According to Newton's biographer Conduitt, he solved the problem in an evening after returning home from the Royal Mint. Newton: ... ""in the midst of the hurry of the great recoinage, did not come home till four (in the afternoon) from the Tower very much tired, but did not sleep till he had solved it, which was by four in the morning.""Newton send his solution to his friend Charles Montague and Montague published anonymously in the Transactions. Newton's solution, presented here in the Acta, is also anonymous. The episode did not please Newton, as he later wrote: ""I do not love to be dunned [pestered] and teased by foreigners about mathematical things ..."" After the competition Johann Bernoulli said "".... my elder brother made up the fourth of these (after Leibniz, himself and Newton), that the three great nations, Germany, England and France, each one of their own to unite with myself in such a beautiful search, all finding the same truth.""Struik (Edt.) ""A Source Book in Mathematics, 1200-1800, pp. 391 ff.‎

‎1. De Linea in quam Flexile se pondere proprio curvat, ejeuque usu insignia adinveniendi quotcunque medias proportionales & Logarithmos. - 2. De Solutionibus Problematis Catenarii vel Funicularis in Actis A. 1691, aliisque a Dn. I.B. propositis. (1-2:...‎

‎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.‎

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‎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

‎Specimen Dynamicum (+) Notatiuncula Constructiones Lineae in qua Sacoma aequilibrium cum pondere moto faciens incedere debet. Et quaedam de Quadraturis (+) Resposio ad nonnullas Difficultates a Bern. Nieuwentüt circa Methodum differentialem motas (+) ... - [FIRST PUBLICATION OF THE ""BERNOULLI EQUATION"".]‎

‎Leipzig, Grosse & Gleditsch, 1695. 4to. Contemp. full vellum. Faint handwritten title on spine. A small stamp on titlepage and pasted library label to pasted down front free end-paper. In: ""Acta Eruditorum Anno MDCXCV"". (2), 560, (52) pp. + 10 plates. As usual with various browning to leaves and plates. The entire volume offered. Leibniz's papers: pp. 145-57" 184-185 310-316 369-372 493-495. Jacob Bernoulli's paper: pp. 537-553 + one folding table 65-66. Johann Bernoulli's: pp. 59-65" 374-376.‎

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‎First printing of a series of influential papers by Leibniz, Jacob Bernoulli and Johann Bernoulli.First publication of Jakob Bernoulli's famous and influential ""Bernoulli Equation"". In ""Notatiuncula Constructiones Lineae"" Bernoulli proposed a solution to non linear equations which today is one of the most common used solutions of the general fluid. Bernoulli equations are significant because they are nonlinear differential equations with known exact solutions. In the ""Specimen dynamicum"" Leibniz presents a conception of body and force which distinct between primitive and derivative forces and between active and passive forces. This article is regarded as being the clearest exposition of Leibniz' dynamics. (DSB VII, 151b).""The first attempt at a detailed account of the dynamics was a long dialogue, the ""Phoranomus seu de potentia et legibus naturae,"" written in July 1689 while Leibniz was in Rome. This was quickly followed be the composition of the massive Dynamica de potential et legibus naturae corporeae (1689-90) [...]. Though it was written with the intention of publication, and though Leibniz work at publishing it, he never considered it entirely finished and it remained unpublished during his lifetime.The later [...] he finally revealed some of the metaphysical foundations of the project in an essay [the present paper]."" (Garber, Daniel. Leibniz: body, substance, monad. 2009. 132 p.)""Its title suggests a summary of or a selection from the earlier work [...]. However, it actually contains something in a way rather more interesting: a careful exposition of the metaphysical foundations of the new science, something that is hard to find in the old Dynamica or any of the more Technical pieces."" (Garber, Daniel. Leibniz: Body, Substance, Monad. 2009. 133 p.)‎

‎1. Nova Calculi Differentialis. Applicatio & usus, ad multiplicem linearum constructionem, ex data tangentium conditione. 2. Constructio Propria Problematiis de Curva Isochrona Paracentrica....& de constructione linearum transcendentium, una maxima ge...‎

‎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).‎

‎Responsio ad nonneminis provocationem eiusque solutio quaestionis ipsi ad eodem proposititae de invenienda linea curva, quam describit proiectile in medio resistente (+) Problema Analyticum, quod omnibus Geometris non-Anglis proposuit. - [THE FINAL SOLUTION TO THE BALLISTIC CURVE]‎

‎Leipzig, Grosse & Gleditsch, 1719. 4to. In: ""Acta Eruditorum Anno MDCCXIX"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 256-270. [Entire volume: (4), 539, four engraved plates.].‎

‎First printing of Bernoulli's exceedingly important paper in which he presented the final (and correct) solution to the ballistic curve. Newton had also occupied himself with the problem but had only solved the law of resistance. In 1718, English mathematician Keill had given Bernoulli the following challenge: ""Find the curve which a projectile describes through the air on the simplest hypothesis of uniform gravity and density in the medium, the resistance varying as the square of the velocity"". The challenge was more an attempt to humiliate Bernoulli, since it was supposed to be unsolvable, than it was an attempt to advance mathematics. ""It was therefore natural the Bernoulli, when he published his solution of Keill's problem and an account of his conduct, should dwell at greater length upon his triumph over the English mathematician than upon his very considerable achievement in mathematics."" (Hall, Ballistics in the seventeenth century, Pp. 155).""Bernoulli's criticism of Taylor's Methodus incrementorum was simultaneously an attack upon the method of fluxions, for in 1713 Bernoulli had become involved in the priority dispute between Leibniz and Newton. Following publication of the Royal Society's Commercium epistolicum in 1712, Leibniz had no choice but to present his case in public. He released-without naming names-a letter by Bernoulli (dated 7 June 1713) in which Newton was charged with errors stemming from a misinterpretation of the higher differential. Thereupon Newton's followers raised complicated analytical problems, such as the determination of trajectories and the problem of finding the ballistic curve, which Newton had solved only for the law of resistance R = av (R = resistance, a = constant, v = velocity). Bernoulli solved this problem (AE, 1719) for the general case (R = avn), thus demonstrating the superiority of Leibniz' differential calculus."" (DSB)‎

‎Barometrum novum communi multo accuratius. - [BERNOULLI'S BAROMETER]‎

‎Leipzig, Grosse & Gleditsch, 1716. 4to. In: ""Acta Eruditorum Anno MDCCXVI"". The entire volume offered in contemporary full vellum. Hand written title on spine. A yellow label pasted on to top of spine. A small stamp to title-page and free front end-paper. Library label to pasted down front free end-paper. As usual with various browning to leaves and plates. Pp. 10-14 + one engraved plate. [Entire volume: (2), 567, (39) pp. + four engraved plates.].‎

‎First Latin printing of Bernoulli's paper on the luminous barometer created by mercurial phosphorus. The phenomenon was first observed by French astronomer Jean Picard in 1675, but the practical use of the phenomenon was popularized by Bernoulli who made the first horizontal or rectangular barometer. Bernoulli's study of the subject had profound influence on the English scientist Francis Hauksbee who became of seminal importance to the development of electricity and electrostatic repulsion.The offered volume contains many other papers by influential contemporary mathematicians, philosophers and historians.‎

‎Essai d'une nouvelle Physique celeste. Servant à expliquer les principaux Phenomenes du Ciel, & en particulier la cause physique de l'inclinaison des Orbites des Planetes par rapport au plan de l'Equateur du Soleil. Qui a partagé le Prix doub...‎

‎Paris, Imprimerie Royale, 1735. 4to. Fine recent marbled boards. Printed titlelabel on frontcover. (6),144 pp. and 1 double-page folded engraved plate. Johann B's paper: pp. (1-) 91. - Daniel B's papers: pp. (93-) 122 and pp. 123-144. A few marginal brownspots.‎

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‎First edition of these prize winning papers by father (Jean) and son (Daniel). - Both papers deals with the cause of the inclination of the planetary orbits relative to the solar equator. - In Daniel's paper he put foreward the hypothesis of the existence of an atmosphere, resempling air, and rotating around the solar axis, resulting in an increasing inclination of the planetary orbits toward the equator of the sun. Daniel was the first importent Newtonian outside Great Britain. The problems faced here (by Daniel) are treated in Newtonian manner.The publication of these papers by father and son resulted in a controversy between the two, forcing Daniel to leave his fathers house. - Poggendorff I:161.‎