Bernoulli

BERNOULLI, JOHN. - THE CENTER OF OSCILLATION.

(Paris, L'Imprimerie Royale, 1717). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1714"". Pp. 208-229, 7 textfigs.

First appearance of this importent paper in which John Bernoulli gives his famous solution to the question of the center of oscillation. The solutions of Bernoulli and Brook Taylor were in principle identical and became an occasion of a grat dispute between these two eminent mathematicians.

Herman H. J. Lynge & Son

Copenhagen, Danemark

"BERNOULLI, NICLAUS.

Leipzig, Grosse & Gleditsch, 1718. 4to. In: ""Acta Eruditorum Anno MDCCXVIII"". 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. 248-262. [Entire volume: Pp. (4), 564, (40) + five engraved plates.].

First printing of Bernoulli's paper on trajectories. The volume contains many other papers by influential contemporary mathematicians, philosophers and historians.

Herman H. J. Lynge & Son

Copenhagen, Danemark

BORELLI (Giovanni Alfonso) et BERNOULLI (Daniel)

Hagae comitum, Petrum Gosse, 1743, , 3 parties en 1 vol. in-4, front, [10]-228-[18] et [4]-270-[14] pp. ; 45 pp, 19 pl. dépl, Basane de l'époque, dos à nerfs fleuroné, pièce de titre grenat, tranches rouges, Frontispice gravé sur cuivre. Ouvrage publié pour la première fois en 1680. C'est un monument consacré à l'étude du mouvement des muscles et de leurs fonctions. L'édition présentée ici contient des nouvelles figures et, à la fin, un important traité du mathématicien et physicien Daniel Bernoulli sur le même sujet. Élève de Galilée et disciple de Harvey, Giovanni Alfonso Borelli (1608-1679) applique les lois de la mécanique aux mouvements du corps; il démontre que les os des membres agissent comme des leviers et que les muscles qui les meuvent doivent être considérés comme des sortes de moteurs. Pour lui, d'autres fonctions comme la digestion, la respiration et la circulation du sang obéissent aussi à des lois purement mécaniques et mathématiques dont il démontre le rythme par des diagrammes chiffrés, parfois très complexes. Plats frottés, coiffes arasées, coins émoussés. Exemplaire provenant de la bibliothèque du mathématicien Michel Chasles. Couverture rigide

Bon 3 parties en 1 vol. in-4,

Christoph Bernoulli.

, Singer Museum, 1977 Original publishers paper-covered boards, 22 pages 21x21cm Deutsch.

Austellungcatalog des Basler Malers Alber Kohler 600 numerierten exemplaren NR. 183

ERIK TONEN BOOKS

Antwerpen, Belgique

Claude Roy - colonel Bernouilli (Paul Bergeron)

1945 Montrouge, Impr. de Draeger frères - 1945 - In-4° , 270 x 215 mm - Broché - Couverture remplié, illustrée, texturée aux armes de Paris -108 pages., fig., portr., fac-sim. - Riche documentation photographique sur les journées de la libération - Ouvrage imprimé pour le colonel Bernouilli (Paul Bergeron) - Bel exemplaire - Réf. 47881

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A l's.p.rance

Brest, France

COLLECTIF - BERNOUILLI, IMBART DE LA TOUR EHRHARDT etc.

1 volume in-8° broché, pagination de 530 à 956. Léger état d'usage en couverture bordures rousses sinon très bon état d'occasion.

Comptoir du Livre Ancien et Moderne - Librairie MESNARD

Collectif. Boulduc - De la Hire - Cassini - Varignon - Lemery - Tournefort - Geoffroy - Couplet - Bernoulli - Homberg - Littre - Rolle - Amontons - Carré - Maraldi - Lagny - Newton - Chomel.

A Paris, Chez Gabriel Martin, Jean-Baptiste Coignard Fils, Hippolyte Guerin, rue S. Jacques, 1730, 1 volume in-4 de 260x200 mm environ, 1 f. blanc, 4 ff. (titre avec large vignette, table pour l'Histoire, table pour les Mémoires), 154-395 pages, 1 f.blanc, plein veau moucheté brun, dos à 5 nerfs portant titres et date dorés sur pièces en maroquin bordeaux, orné de caissons à motifs dorés, coupes dorées, gardes marbrées, tranches mouchetées de rouge. Avec 8 planches dépliantes, et des figures dans le texte. Quelques frottements et épidermures sur le cuir, ex-libris manuscrit sur la page de titre, des pages légèrement brunies, sinon bon état.

Table pour l'Histoire : Physique Générale : Sur un nouveau Baromètre à l'usage de la mer - Sur la dilatation des Vaisseaux par la chaleur - Sur l'Aiman & sur l'aiguille aimantée - Sur la rarefaction & la condensation de l'air - Sur une irrégularité de quelques Baromètres - Sur les Tuyaux capillaires - Sur un nouvel Instrument appelé Manomètre - Sur les différentes hauteurs de la Seine en différens Tems - Diverses observations de Physique generale - Mémoire sur l'Ambre jaune. - Anatomie : Sur les structures des Reins - Sur une matrice double - Diverses observations anatomiques. - Chimie : Sur le Camphre - Sur la Gratiole - Sur la generation du Fer - Diverses observations chimiques. - Botanique : Observation Botanique. - Arithmétique : Sur les Carrés magiques. - Algèbre : Sur une méthode générale pour la résolution des Equations. - Géométrie : Sur les Tangentes & les Sécantes des Arcs circulaires - Sur les forces centrales des Planètes. - Astronomie : Sur les Satellites de Saturne - Sur une nouvelle methode pour les Longitudes - Sur les taches du Soleil. - Géographie - Méchanique : Sur la résistance d. s solides, & sur la courbure des Ressorts pliés - Sur les proportions nécessaires au diamètres des Tuyaux, pour donner précisément certaines quantités d'eau déterminées - Machines ou Inventions approuvées par l'Académie en 1705 - Eloge de M. Bernoulli - Eloge de M. Amontons. Merci de nous contacter à l'avance si vous souhaitez consulter une référence au sein de notre librairie.

Librairie Diogène

Lyon, France

Daniel BERNOULLI

S.n. | Paris s. d. [1753] | 19.5 x 25.2 cm | Broché

Rare édition originale orné d'une planche hors-texte (cf Polak 666.) Exemplaire dérelié. Une des applications à la navigation des recherches sur la motricité du physicien Daniel Bernoulli (1700-1782). - Photographies et détails sur www.Edition-Originale.com -

Librairie Le Feu Follet – Edition-Originale.com

Paris, France

Daniel BERNOULLI - Abbé BRAGELONGNE

Chez Pierre Mortier | A Amsterdam 1733 | 10 x 17 cm | 2 volumes reliés

Edition illustrée de 22 planches pour le tome 1, 21 pour le tome 2, la plupart dépliantes, soit 41 planches. Pages de titre en rouge et noir. Reliure en plein veau brun marbré d'époque. Dos à nerfs orné. Pièces de titre en maroquin rouge, et de tomaison à la cire noire. Mors supérieur du tome 2 étroitement fendu. 2 trous de vers en queue. Frottements. Bon exemplaire. On retiendra dans chacune des sections mentionnées les articles remarquables suivants : Solution fort simple d'un problème astronomique d'où l'on tire une méthode nouvelle de déterminer les noeuds des planètes, par M. Godin. Methode pour trouver les Tautochrones, dans des milieux résistants, comme la quarré des vitesses, par M. Bernouilli. Examen des ligne du quatrième ordre, ou courbes du troisième genre, par l'abbé de Bragelongne. La courbe Descensus aequabilis dans un milieu résistant comme une puissance quelconque de la vitesse, par M. de Maupertuis. Méthode pour déterminer le sort de tant de joueurs que l'on voudra, par M. Nicole. Nouvelles propriétés de l'hyperbole, par M. Mahieu. Réflexions sur le mouvement des eaux, par M. Pitot. - Photographies et détails sur www.Edition-Originale.com -

Librairie Le Feu Follet – Edition-Originale.com

Paris, France

DOHM , Christian Wilhem von

Dessau, Librairie des auteurs et des artistes, 1782, XII-255pp.-2ff, relié demi basane postérieure, dos à nerfs avec auteur, titre et date en pied.

Bon exemplaire de ce livre qui joue un rôle majeur dans l'accession des Juifs européens à la citoyenneté. Cette traduction en français, ici en première édition, comporte des changements par rapport à la parution originale en allemand (Berlin, 1781).Elle est due à Jean Bernoulli (1744-1807, auteur de la préface) et son texte fut supervisé par Moses Mendelssohn et par Cerf Berr. On y trouve, à partir de la page 214, un Mémoire sur l'état des juifs en Alsace, qui a été certainement pris en compte par Malesherbes dans l'élaboration de l'édit de 1784. Elle est d'autant plus rare que la plupart des volumes, entrées en France sans déclaration, ont été confisqués et mis au pilon, l'autorisation obtenue par Mirabeau et Lalande étant arrivée trop tard (voir la préface de l'édition donnée par Dominique Bourel , Paris, Stock, 1984, p. 16). Szajkowski, Franco-judaïque, 1633. Christian Wilhelm von Dohm (1751-1820) est un haut fonctionnaire prussien, libéral et éclairé, proche de la philosophie des Lumières. The Alsacians Jews ask Moses Mendelssohn to help to write a report for the french state council, Mendelssohn send them to Christian Wilhelm von Dohm, who first write it under the title "Über die bürgerliche Verbesserung der Juden".P1-2N

Librairie Voyage et Exploration

"LEIBNITII, GODOFREDI GUILIELMI. (GOTTFRIED WILHELM LEIBNIZ) & BERNOULLII (IACOBI). (JACOB BERNOULLI) & BERNOULLII (IOHANNIS). (JOHANN BERNOULLI).

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.

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.)

Herman H. J. Lynge & Son

Copenhagen, Danemark

"LEIBNITZ, GOTTFRIED WILHELM., JOHANN BERNOULLI, JACOB BERNOULLI & ISAAC NEWTON - SOLVING THE BRACHISTOCHRONE PROBLEM.

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.

Herman H. J. Lynge & Son

Copenhagen, Danemark

"LEIBNIZ, GOTTFRIED & JOHANN BERNOULLI & JAKOB BERNOULLI & EHRENFRIED WALTHER VON TSCHIRNHAUS.

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.

Herman H. J. Lynge & Son

Copenhagen, Danemark

"LEIBNIZ (LEIBNITZ), G.F. - CHRISTIAAN HUYGENS - JOHANN BERNOULLI - JACOB BERNOULLI ET AL. - THE DISCOVERY OF THE ""CATENARY CURVE"" , THE ""LOGARITHMIC CURVE"" AND THE ""POLAR COORDINATES"".

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

Herman H. J. Lynge & Son

Copenhagen, Danemark

LEIBNIZ (LEIBNITZ), G.F. - DENYS PAPIN - JAKOB BERNOULLI.

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.

Herman H. J. Lynge & Son

Copenhagen, Danemark

"LEIBNIZ (LEIBNITZ), G.F. - JOHANN BERNOULLI - JAKOB BERNOUILLI. - CHRISTIAAN HUYGENS ET AL. - INTRODUCING THE LEMNISCATE CURVE.

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).

Herman H. J. Lynge & Son

Copenhagen, Danemark

OVERBECK Franz (& BERNOULLI Carl Albrecht, hrsg.)

Basel, Benno Schwabe 1917 xii + 315pp., original 1917-edition, 24cm., softcover, good condition, R102688

QUENEAU (Raymond). PREVERT (Jacques). FERRY (Jean). BERNOULLI (Jacques). DUCHATEAU (Jacques). GAYOT (Paul). FRANCUEIL (Bernard). BASSARD (Pierre).

Paris : Collège de Pataphysique, 1965. Un volume 12x21cm agrafé, de 105 pages illustrées. Exemplaire en bon état.

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Le Livre à Venir

Chantelle, France

[REVUE]. [ARCHITECTURE].

Jahrgang XII. Heft 6. Juni 1913. Alfred Grenander, Hans Jessen, Hans Bernoulli, Ernst Dobler Très bon état.

Stuttgart. Verlag Julius Hoffmann. Directeur : Dr. C. H. Baer. In-4° broché. Chaque numéro est abondamment illustré de planches en couleurs, de photographies, de croquis, de plans. Cette importante revue d'architecture allemande a paru mensuellement de 1902 à 1944.

"RICCATO, JACOBO. (JACOPO FRANCESCO RICCATI) - DANIELIS BERNOULLI (DANIEL BERNOULLI).

Leipzig, Gross & Fritsch, 1724. 4to. Entire volume present. Nice contemporary full vellum. Small yellow paper label pasted to top of spine and library-label to inside of front board. Two smaller library stamps to title-page. Internally some browning and brownspotting, due to the paper quality. Overall a nice and tight copy. [Riccati-paper:] pp. 66-73. [Bernouilli-paper:] pp. 73-75. [Entire volume: (2), 532, (34) pp.].

The important first printing of Riccati's main work, his influential ""Animadversiones in aequationes differentiales secundi gradus"", in which the famous Riccati-equation is presented + Bernouilli's famous note on it.""In his ""Animadversiones in aequationes differentiales secundi gradus,"" published in Acta Eruditorum in 1724, Riccati suggested the study of cases of integrability [...] which is now known by his name. In response to this suggestion Nikolaus II Bernoulli wrote an important treatise on the equation and Daniel Bernoulli presented, in his Exercitationes quaedam mathematicae, the conditions under which it may be integrated by the method of separation of the variables. Euler also integrated it."" (DSB, XI).""In the supplement volume to Acta Eruditorum, Riccati's paper is immediately followed by Daniel Bernoulli' Notata (St. 5.). As the latter admitted in the Exercitationes, he had Riccati's paper in his hands for two days before it was sent to Leipzig. In this short paper Daniel Bernoulli first claims that equation (D) is not an appropriate example because by substituting dy=q it can easily (""Haud magno negotio"") be reduced to a first order differential equation."" (Die Werke von Daniel Bernoulli, 1996, Birkhäuser, Volker Zimmermann (edt). ""Riccati ( 1676 - 1754) was the son of a noble family who held land near Venice. His renown was such that Peter the Great invited him to come to Russia as president of the St. Petersburg Academy of Sciences. [...]. Riccati carried on an extensive correspondence with mathematicians all over Europe. His work were collected and published, four years after his death, by his sons, of whom two, Vincenzo and Giordano were themselves eminent mathematicians. (DSB, XI).

Herman H. J. Lynge & Son

Copenhagen, Danemark

SCHIESS, / ROTH, Moritz / BERNOULLI, G. u.a.:

Bern, Dalp, 1864, gr. in-8°, VIII + 200 S., illustriert, Bibl.-Stempel, Original-Broschüre. Umschlag lose, Rücken gespalten.

Enthält: Moritz Roth: Untersuchungen über die Drüsensubstanz der Niere / Dr. Schiess: Beitrag zur pathologischen Anatomie des Hornhautstaphyloms 2 Tafeln./ Dr. G. Bernoulli: Bemerkungen über Tropenkrankheiten / Kleinere Mittheilungen / Spitalbericht (Jenner Kinderspital Bern, 1862-1863) / Recensionen und Referate.

Harteveld Rare Books Ltd.

Fribourg, Suisse

TITS / THIEBAULT / PERES / THIRY

Paris Gauthiers Villars 1923 In8 Pagination continue - ( environ 40 pages ) - broché - Bon etat - Au Sommaire : Identités Nouvelles Pour le Calcul Des nombres De Bernoulli par Tits - Sur Un Théorème classique De Dandelin par Thiébault - A Propos de La Formule D'euler Savary par Pérès - Etude D'un Probleme Particulier ou intervient Le Frottement De Glissement par Thiry

Bon

L'Encrivore

Vendôme, France

Vischer, Wilhelm. - Stern, Alfred. - Boos, Heinrich. - Bernoulli, August (hrsg).

Basel - Leipzig, S. Hirzel 1872-1915, 230x150mm, broschiert. Tomes 3 et 7, dos cassé, tome 5 manque la couverture remplassée par une couverture neutre.

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Bouquinerie du Varis

Russy, Suisse