Bernoulli

"BERNOULLI, (JACOB). - A NEW ERA IN THE MECHANICS OF ELASTICAL BODIES.

Paris, Jean Boudot, 1706. 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1705"". Pp. 176-186 and 1 folded engraved plate.

First appearance of a founding paper in the theory of elastic curves. ""Importent also is his last work, on the resistance of elastic bodies (1705)."" (DSB II, p.49 s).""During the last quarter of the seventeenth century and the beginning of the eighteenth centuries a rapid development of the infinitesimal calculus took place. Started on the Continent by Leibnitz...it progresssed principally by the work of Jacob and John Bernoulli. In trying to expand the field of application of this new mathematical tool, they discussed several examples from mechanics and physics. One such example treated by Jacob Bernouilli..concerned the shape of the deflection curve of an elastic bar and in this way he began an importent chapter inthe mechanics of elastic bodies.""(Timoshenko ""History of Strenght of Materials"" p. 25-26).

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JACOBI (JACOB).

Leipzig, Gross & Fritsch, 1701. 4to. Contemporary full vellum. Handwritten title on spine. A small stamp to title page and page . Pasted library label to pasted down front free end-paper. In: ""Nova Actorum Eruditorum Anno MDCCI"". Pp 213-228 + 1 engraved plate. [Entire volume: (2), 581 pp. + 8 engraved plates].

First publication of Jacob Bernoulli influential dissertation in which he published the first correct solution to the isoperimetric problem both Johann Bernoulli and Leibniz had been seeking without success. The paper influenced both Leonhard Euler in writing his first research paper and British mathematician Brook Taylor to begin a dispute which has later been referred to as Taylor versus Continental mathematicians. ""It [the dissertation] was considered as a prodigy of sagacity and invention: and indeed, if the time be considered, it will not be too much to assert, that a more difficult problem never was solved."" (Bossut. A general history of mathematics. 341 p.).The isoperimetric problem is an ancient problem which dates back to antiquity and can be described as which curve, if any, maximizes or minimizes the area of its enclosed region?Euler, who had been taught by Johann Bernoulli, published his first paper in 1726 which was a note on the construction of isochronous curves in a resistant medium.DSB II, 48b.The following papers by Johann Bernoulli are also contained in the present volume:1. Disquisitio Catoptrico-Dioptrica exhibens Reflexionis et Refractionis naturam ex aequilibrii fundamento deductam. Pp 19-26.2. Novaratio construendi radios osculi seu curvanturae in Curvis quibusvis etc. Pp. 136-40.3. Multisectio Anguli vel Arcus, duplici aequatione universali exhibita. Pp. 170-75.

Herman H. J. Lynge & Son

Copenhagen, Denmark

BERNOULLI Jacques

Professeur de mathématiques. Beau portrait. Beau tirage XVIIIè sur vergé. en feuille Très bon 15 x 11 cm

Librairie Seigneur

BERNOULLI, JAKOB.

Basel, Birkhäuser Verlag, 1975. Small 4to. Orig. full cloth with dustjacket X,585 pp.

Herman H. J. Lynge & Son

Copenhagen, Denmark

BERNOULLI Jean

Professeur de mathématiques. Beau portrait. Beau tirage XVIIIè sur vergé. en feuille Très bon 15 x 11 cm

Librairie Seigneur

BERNOULLI Jean:

A Berlin, Chez G.J. Decker, 1777. In-8 de [8]-280 pages, cartonnage d’attente, titre au haut du dos. Quelques rousseurs.

Illustré d'une planche dépliante. Vol. 1 seul. Rare édition originale. HORAIRE ESTIVAL : DU LUNDI 27 JUILLET AU SAMEDI 21 AOUT NOUS SERONS OUVERTS UNIQUEMENT SUR RENDEZ-VOUS.

ILLIBRAIRIE | Bombadil SA

Genève, Switzerland

"BERNOULLI, JEAN.

(Berlin, Haude et Spener, 1768). 4to. No wrappers. Extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXII, pp. 99-107 a. 1 folded engraved plate + pp. 108-116 a. 2 folded engraved plates.

First appearance of two importent papers in the theory of elasticity of materials in which Bernoulli gives, for the first time, the solution to a main problem, and stating a formula which expresses the shape of the loaded beam without reference to the load acting or to the elastic properties of the materials.

Herman H. J. Lynge & Son

Copenhagen, Denmark

BERNOULLI, Jean / BERNOULLI, Daniel

Paris De l'Imprimerie Royale 1735 in 4 (25x19,5) 1 volume broché sous couverture muette de papier marbré ancien, page de titre avec vignette gravée fleurdelysée, [2] 144 pages. Prix double de l'année 1734: A/ Bernoulli, Jean, Essai d'une nouvelle physique céleste, Servant à expliquer les principaux Phénoménes du Ciel, & en particulier la cause physique de l'inclinaison des Orbites des planétes par rapport au plan de l'Equateur du Soleil, 91 pages, avec une planche gravée dépliante. B/Bernoulli, Daniel, Recherches physiques et astronomiques sur le probleme proposé par l'Académie des Sciences de Paris pour la seconde fois: Quelle est la cause physique de l'inclinaison des Plans des Orbites des Planétes par rapport au plan de l'Equateur de la révolution du Soleil autour de son axe; Et d'ou vient que les inclinaisons de ces Orbites sont différentes entre elles (pages 93 à 122), suivi du même: Disquisitiones Physico-Astronomicae problematis ab inclyta scientarium Academia Regia iterum propositi. Quellle est la Cause physique de l'inclinaison des plans des Orbites des Planetes par rapport au plan de l'Equateur (pages 123 à 144). Bon exemplaire ( Photographies sur demande / We can send pictures of this book on simple request )

Bon

(BERNOULLI, JEAN (JOHANN) & BERNOULLI, DANIEL. - THE MECHANICS OF THE HEAVENS.

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.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOANN.

Leipzig, Grosse & Gleditsch, 1723. 4to. In: ""Acta Eruditorum Anno MDCCXXIII"". 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. 75-9. [Entire volume: Pp. (2), 543, (55) + three engraved plates.].

First printing of this paper by the influential Swiss mathematician Johann Bernoulli, known for his contributions to infinitesimal calculus and education of Leonhard Euler.The volume contains many other papers by influential contemporary mathematicians, philosophers and historians.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOANNES.

Leipzig, Grosse & Gleditsch, 1737. 4to. In: ""Nova Acta Eruditorum Anno MDCCXXXVII"". 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. 82-88. [Entire volume: Pp. (4), 555, (33) + 7 engraved plates.].

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

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOANNES [JOHANN].

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOANNES [JOHANN].

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)

Herman H. J. Lynge & Son

Copenhagen, Denmark

BERNOULLI, Joh. Gustav.

Stuttgart, J.G. Cotta 1857, 185x115mm, XIV- 477Seiten, Verlegereinband.

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Bouquinerie du Varis

Russy, Switzerland

Bernoulli, Johann:

Berlin Selbstverlag, 1781, in-8vo, (2) II, 420 S. Mit 2 (1 mehrfach gefalteten) Kupfertafeln und 1 gefalteten Tabelle. Stellenweise gering gebräunt. gest. Ex-Libris ‘G. Mori(signiert R. Völlmy (19) 04)). Original-H.-Pergament d. Zeit (um 1900). Einband leicht berieben, sonst gut erhalten

Erste Ausgabe. Begegnungen mit sehr vielen prominenten Leuten der Zeit, Schellenberg, Lavater, Sulzer und Ziegler, auch mit einen Engländer namens Windham, der so freundlich war, meine Gepäckstücke in seiner ‘Chaise’ mitzunehmen. Im gleichen Buch noch Prof. Sanders Reise nach Constanz am Bodensee und nach Schafhausen zum Rheinfall 1781, ausserdem diverse Lustreisen in Deutschland. Die große Tafel zeigt einen Plan der Gartenanlagen des von Adrian Bernhard von Borcke in Stargordt erbauten Schlosses im Stil des norddeutschen Barocks in der polnischen Woiwodschaft Westpommern. - Wäber 40; Haller, 1, Nr 1010 ‘ist von ein Basler’. Reise Basel - Zürich - Luzern - Bern - Basel).

Harteveld Rare Books Ltd.

Fribourg, Switzerland

"BERNOULLI, JOHANN.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOHANN.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOHANN.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOHANN.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOHANN.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, JOHANN (+) DANIEL BERNOULLI.

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.

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, (JOHANN). - ESTABLISHING RELATION BETWEEN TRIGONOMETRIC AND LOGARITMIC FUNCTIONS.

(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).

Herman H. J. Lynge & Son

Copenhagen, Denmark

"BERNOULLI, (JOHANN I) - THE TAUTOCRONE CURVE IN A MEDIA.

(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.].

Herman H. J. Lynge & Son

Copenhagen, Denmark

BERNOULLI, Johann (Jean III)

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.

Hugues de Latude

"BERNOULLI, (JOHANN). (+) NICOLAS (NIKOLAUS) BERNOULLI. - VIS-VIVA CONTROVERSY

(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.

Herman H. J. Lynge & Son

Copenhagen, Denmark