jacob bernoulli (29 Ergebnisse)

HRD. Zustand: New. New Book. Shipped from UK. Established seller since 2000.

HRD. Zustand: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000.

Zustand: New. In.

Zustand: New. In.

Zustand: New. In.

Zustand: New. In.

Hardcover. Zustand: Very Good. With dust jacket. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting.

Verlag Georg Olms, Hildesheim, 1969. 438 S., mit 35 Tafeln im Anhang, goldgeprägter Leinen---- neuwertig / ungelesen / Reprografischer Nachdruck der Ausgabe Berlin und Stuttgart 1886 - 844 Gramm.

2 Bände, 215+241 S., OLwd. m. Goldpräg., Reprint, Einbände fleckig, sonst gut erhalten Aufgrund der EPR-Regelung kann in folgende Länder KEIN Versand mehr erfolgen: Bulgarien, Finnland, Frankreich, Griechenland, Luxemburg, Österreich, Polen, Rumänien, Schweden, Slowakei, Spanien.

Taschenbuch. Zustand: Neu. Die erhaltenen Darstellungen Alexanders des Großen | Ein Nachtrag zur griechischen Ikonographie | Johann Jacob Bernoulli | Taschenbuch | 172 S. | Deutsch | 2013 | EHV-History | EAN 9783955643027 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu.

4 Bände, 305+438+266+275 S., OLwd. m. Goldpräg., Reprint, Einbände fleckig, sonst sehr gut erhalten Die Bildnisse berühmter Römer mit Ausschluß der Kaiser und ihrer Angehörigen/ Die Bildnisse der römischen Kaiser und ihrer Angehörigen, Das julisch-claudische Kaiserhaus/ Von Galba bis Commodus/ Von Pertinax bis Theodosius Aufgrund der EPR-Regelung kann in folgende Länder KEIN Versand mehr erfolgen: Bulgarien, Finnland, Frankreich, Griechenland, Luxemburg, Österreich, Polen, Rumänien, Schweden, Slowakei, Spanien.

Taschenbuch. Zustand: Neu. Die erhaltenen Darstellungen Alexanders des Großen | Ein Nachtrag zur griechischen Ikonographie | Johann Jacob Bernoulli | Taschenbuch | 172 S. | Deutsch | 2019 | Vero Verlag | EAN 9783956108891 | Verantwortliche Person für die EU: Vero Verlag GmbH & Co. KG, Trakehner Weg 52, 22844 Norderstedt, info[at]vero-verlag[dot]de | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Die erhaltenen Darstellungen Alexanders des Großen | Ein Nachtrag zur griechischen Ikonographie | Johann Jacob Bernoulli | Taschenbuch | 172 S. | Deutsch | 2019 | Vero Verlag | EAN 9783957000927 | Verantwortliche Person für die EU: Vero Verlag GmbH & Co. KG, Trakehner Weg 52, 22844 Norderstedt, info[at]vero-verlag[dot]de | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Aphrodite - Ein Baustein zur griechischen Kunstmythologie | Johann Jacob Bernoulli | Taschenbuch | 444 S. | Deutsch | 2016 | hansebooks | EAN 9783742874825 | Verantwortliche Person für die EU: Hansebooks GmbH, Trakehner Weg 52, 22844 Norderstedt, gb[at]hansebooks[dot]com | Anbieter: preigu.

Hardcover. First edition. EVANS 8 - ESTABLISHED THE FUNDAMENTAL PRINCIPLES OF THE CALCULUS OF PROBABILITIES. First edition, an exceptionally fine copy, rare in this condition. "Jakob 1 Bernoulli's posthumous treatise, edited by his nephew [Nicholas I Bernoulli], (the title literally means "the art of [dice] throwing") was the first significant book on probability theory: it set forth the fundamental principles of the calculus of probabilities and contained the first suggestion that the theory could extend beyond the boundaries of mathematics to apply to civic, moral and economic affairs. The work is divided into four parts, the first a commentary on Huygens's De ratiociniis in ludo aleae (1657), the second a treatise on permutations (a term Bernoulli invented) and combinations, containing the Bernoulli numbers, and the third an application of the theory of combinations to various games of chance. The fourth and most important part contains Bernoulli's philosophical thoughts on probability: probability as a measurable degree of certainty, necessity and chance, moral versus mathematical expectation, a priori and a posteriori probability, etc. It also contains his attempt to prove what is still called Bernoulli's Theorem: that if the number of trials is made large enough, then the probability that the result will lie between certain limits will be as great as desired" (Norman). This was the first statement of the law of large numbers. "In the first Part (pp. 2-71) Jakob Bernoulli complemented his reprint of Huygens's tract by extensive annotations which contained important modifications and generalisations. Bernoulli's additions to Huygens's tract are about four times as long as the original text. The central concept in Huygens's tract is expectation. The expectation of a player A engaged in a game of chance in a certain situation is identified by Huygens with his share of the stakes if the game is not played or not continued in a 'just' game. For the determination of expectation Huygens had given three propositions which constitute the 'theory' of his calculus of games of chance. Huygens's central proposition III maintains: "If the number of cases I have for gaining a is p, and if the number of cases I have for gaining b is q, then assuming that all cases can happen equally easily, my expectation is worth (pa + qb)/(p + q)." "Bernoulli not only gives a new proof for this proposition but also generalizes it in several ways . "Huygens's propositions IV to VII treat the problem of points, also called the problem of the division of stakes, for two players; propositions VIII and IX treat three and more players. Bernoulli returns to these problems in Part II of the Ars Conjectandi. In his annotations to Huygens's proposition IV he generalised Huygens's concept of expectation . This is the only instance in the annotations and commentaries to Huygens's tract where Bernoulli uses the word 'probabilitas', or probability as understood in everyday life. Later in Part IV of the Ars Conjectandi Bernoulli replaced Huygens's main concept, expectation, by the concept of probability for which he introduced the classical measure of favourable to all possible cases. The remaining propositions X to XIV of Huygens's tract deal with dicing problems of the kind: What are the odds to throw a given number of points with two or three dice? or: With how many throws of a die can one undertake it to throw a six or a double six? . The meaning of Huygens's result of proposition X, that the expectation of a player who contends to throw a six with four throws of a die is greater than that of his adversary, is explained by Bernoulli in a way which relates to the law of large numbers proved in Part IV of the Ars Conjectandi . "In the second Part (pp. 72-137) Bernoulli deals with combinatorial analysis, based on contributions of van Schooten, Leibniz, Wallis, and Jean Prestet . [It] consists of nine chapters dealing with permutations, the number of combinations of all classes, the number of combinations of a particular class, figurate numbers and their properties (especially the multiplicative property), sums of powers of integers, the hypergeometric distribution, the problem of points for two players with equal chances to win a single game, combinations with repetitions and with restricted repetitions, and variations with repetitions and with restricted repetitions. "Evidently Bernoulli did not know Blaise Pascal's Triangle arithmétique, published posthumously in 1665, though Leibniz had alluded to it in his last letter to him in 1705. Not only does Bernoulli not mention Pascal in the list of authors that he had consulted concerning combinatorial analysis, except for Pascal's letter to Fermat of 24 July 1654; it would also be difficult to explain why he repeated results already published by Pascal in the Triangle arithmétique, such as the multiplicative property for binomial coefficients for which Bernoulli claims the first proof for himself. His arrangement differs completely from that of Pascal, whose proof for the multiplicative property of the binomial coefficients has been judged to be clearer than Bernoulli's. It is fair to add that in the Ars Conjectandi, which Bernoulli left as an unpublished manuscript, he was much more honest concerning the achievements of his predecessors than Pascal in the Triangle arithmétique. It is also true that Bernoulli was concerned with combinatorial analysis in the Ars Conjectandi first of all because it constituted for him a most useful and indispensable universal instrument for dealing numerically with conjectures, since 'every conjecture is founded upon combinations of the effective causes' (p. 73) . "In the third Part (pp. 138-209) Bernoulli gives 24 problems concerning the determination of the modified Huygenian concept of expectation in various games. Here he uses extensively conditional expectations without, however, distinguishing them from unconditional expectations. All the games are games of chance wit.

Originalleinen. Zustand: Gut. 1. Teil: X, 305 S.: Abb., 2. Teil, Band 1: XIV, 438 S.: Abb., 2. Teil, Band 2: XII, 266 S.: Abb., 2. Teil, Band 3: XII, 275 S.: Abb. Aus der Bibliothek von Prof. Wolfgang Haase, langjährigem Herausgeber der ANRW und des International Journal of the Classical Tradition (IJCT) / From the library of Prof. Wolfgang Haase, long-time editor of ANRW and the International Journal of the Classical Tradition (IJCT). - 1. Teil: Einband leicht berieben und verfärbt, sonst guter Zustand, 2. Teil, Band 1: Einband leicht berieben und verfärbt, leichte Randläsuren, Fußschnitt minimal angegraut, sonst guter Zustand, 2. Teil, Band 2: Einband leicht berieben und verfärbt, sonst guter Zustand, 2. Teil, Band 3: Einband leicht berieben und verfärbt, sonst guter Zustand. - INHALT. Anfänge der Porträtbildnerei bei den Römern Königszeit Romulus Titus Tatius Numa Pompilius Ancus Marcius Die drei letzten Könige Republik L. Brutus Postumius Regillensis L. Domitius Ahenobarbus P. Valerius Poplicola Servilius Ahala Ser. Sulpicius Rufus M. Atilius Regulus M. Claudius Marcellus Scipio Africanus Die erhaltenen sog. Scipioköpfe Kritik ihrer Bezeichnung Titus Flamininus Cato Censorius P. Terentius (L. Accius) Der Praetor L. Cornelius Cornelia, die Mutter der Gracchen Ti. und C. Gracchus C. Marius Coelius Caldus L. Cornelius Sulla Q. Pompejus Rufus Antius Restio Arrius Secundus Numonius Vaala Livinejus Regulus Hortensius L. Licinus Lucullus Pompejus Erhaltene Bildnisse Cicero Caesar Erhaltene Bildnisse Beurteilung der Bildnisse Atius Balbus Cn. Lentulus Marcellinus Cato Uticensis Marcus Brutus C. Cassius Q. Labienus Parthicus Cn. Domitius Ahenobarbus Sallust M. Antonius Fulvia, Gem. des Antonius Kleopatra M. Antonius d. jüngere L. Antonius, Bruder des Marcus Der Triumvir Lepidus Die Söhne des Pompejus Cn. Pompejus Sextus Pompejus Statue des sog. Germanicus Apokryphe Republikanerbildnisse Kaiserzeit Maecenas Vergil Horaz M. Agrippa Römische Proconsuln Veidius Pollio M. Tullius Cicero P. Corn. Scipio Quinctilius Varus Volus. Saturninus Paullus Fab. Maximus Africanus Fab. Maximus Asinius Gallus Nonius Balbus und seine Familie Domitius Corbulo Seneca Ursus Servianus L. Junius Rusticus Apulejus Apokryphe Römerbildnisse der Kaiserzeit Nachträge und Berichtigungen Beschreibung der abgebildeten Münzen Ortsregister / 2. Teil, Band 1: I. Das julisch-claudische Kaiserhaus: INHALT. Einleitung Stammtafel des augusteischen Hauses Augustus Ikonographische Quellen (Münzen) Historisch überlieferte Bildnisse Erhaltene Bildnisse 1. Büsten und Statuen 2. Reliefs 3. Geschnittene Steine Vergleichung und Klassificierung der Bildnisse Livia Direkt beglaubigte Bildnisse Bildnisse, die auf blosse Aehnlichkeit basiert sind Weibliche Bildnisse der augusteischen Zeit Octavia Marcellus Julia, die Tochter des Augustus Cajus und Lucius Caesar. Agrippa Postumus Tiberius Erhaltene Denkmäler 1. Statuarisches 2. Reliefs 3. Geschnittene Steine Vergleichung und Klassitication der Bildnisse Unbekannte oder noch nicht sicher bestimmte Claudier 1. Statuen und Büsten 2. Reliefs 3. Geschnittene Steine Frauenbildnisse des claudischen Zeitalters 1. Statuen und Büsten 2. Geschnittene Steine Drusus, der Sohn des Tiberius (der jüngere Drusus) Die Familie des jüngeren Drusus Nero Drusus (der ältere Drusus) Geschnittene Steine Antonia Statuarische Denkmäler Verification der Antoniabildnisse Geschnittene Steine Germaniens Numismatische und glyptische Hilfsmittel Erhaltene Denkmäler Die ältere Agrippina Ikonographische Hilfsmittel Erhaltene Denkmäler Nero und Drusus, die Söhne des Germanicus Heber ein paar auf die Familie des Augustus bezügliche Relief- und Cameen-Darstellungen 1. Das Relief von Ravenna 2. Pompa mit angeblich julischen Figuren in Florenz 3. Die Gemma Augustea in Wien 4. Der grosse Pariser Cameo 5. Das Berliner Onyxgefäss Gajus Caesar (Caligula) Erhaltene Denkmäler 1. Statuen und Büsten 2. Geschnittene Steine Verification der Bildnisse Die Gemahlinnen und Schwestern des Caligula Claudius Erhaltene Denkmäler 1. Statuen und Büsten 2. Reliefs J 3. Geschnittene Steine Vergleichung und Klassification der Bildnisse Messalina Britannicus Heber zwei auf Claudius und seine Familie bezogene Cameen 1. Der sogenannte Triumph des Claudius im Haag 2. Der Cameo mit den Fruchthornbüsten in Wien Die Kaiserin Agrippina Nero Erhaltene Denkmäler 1. Statuen und Büsten 2. Reliefs 3. Geschnittene Steine Verification der Bildnisse Die Gemahlinnen des Nero 1. Octavia 2. Poppaea 3. Statilia Messalina Nachträge und Berichtigungen Register 1. Sachregister 2. Ortsregister 3. Verweisungen für die Gemmen- und Münztafeln / 2. Teil, Band 2: II. Von Galba bis Commodus: INHALT. Galba Geschnittene Steine Clodius Macer Otho Geschnittene Steine Vitellins Die Familie des Vitellius Vespasianus Erhaltene Denkmäler 1. Statuen und Büsten 2. Reliefs 3. Geschnittene Steine Domitilla und Vespasia Titus Erhaltene Denkmäler 1. Statuen und Büsten 2. Reliefs und Gemälde 3. Geschnittene Steine Weibliche Bildnisse des flavischen Zeitalters Julia, die Tochter des Titus Geschnittene Steine Domitianus Erhaltene Denkmäler 1. Statuen und Büsten 2. Reliefs 3. Geschnittene Steine Domitia Geschnittene Steine Vespasianus der jüngere Nerva Erhaltene Denkmäler (Statuen und Büsten) Geschnittene Steine Trajanus Erhaltene Denkmäler 1. Statuen 2. Büsten und Köpfe 3. Reliefs 4. Geschnittene Steine Der Vater des Trajan Plotina Geschnittene Steine Marciana Erhaltene Denkmäler 1. Marmorbildnisse 2. Reliefs 3. Geschnittene Steine Matidia 1. Marmorbildnisse 2. Geschnittene Steine Hadrianus Erhaltene Bildnisse 1. Statuen und Torsi 2. Büsten und Köpfe 3. Reliefs und Gemälde 4. Geschnittene Steine Ergebnisse Sabina Geschnittene Steine Aelius Verus Erhaltene Denkmäler Antoninus Pius Erhaltene Denkmäler 1. Statuen 2. Büsten und Köpfe 3. Reliefs und Gemälde 4. Geschnittene Steine Ergebnisse Faustina, die Gemahlin des Antoninus Erhaltene Denkmäler 1. Statuen 2. Büsten und Köpfe 3. Reliefs 4. Geschnittene Steine Ergebnisse Galerius Anton.

Nachdr.d. Ausg. Stgt./Bln. 1882. 4 Bde. X,305/XIV,438/XII,266/XII,275 S., zahlr. Abb., Ln. 2, Goldpräg., N.

2 Bde. XIX,215/XI,241 S., zahrl. Tafeln i. Anhang, Hpgt. 2, marmoriert, Rücken m. Goldpräg., N, ee. leichte Bleistiftanstr. bzw. Anmerk. (Griechische Ikonographie mit Ausschluss Alexanders und der Diadochen / Johann J. Bernoulli, Teil 1 u. 2).

8°., Original-Leinen, zus. XXX/612 Seiten und 68 Tafeln, sehr gutes und sauberes Exemplar, Sprache: Deutsch Gewicht in Gramm: 1400.

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).

First edition of the first systematic treatment of probability theory, the source of the law of large numbers, binomial distribution, and Bernoulli numbers. The Ars Conjectandi was the first work to suggest that probability could be applied in civil, moral, and economic matters, and it remains the foundation of much modern practice in such fields as insurance and statistics. Jacob Bernoulli (1655-1705) was the first of the famed Bernoulli family to study mathematics: Johann (1667-1748) was his brother while Nicolaus (1687-1759) and Daniel (1700-1782) were his nephews. Nicolaus revised his uncle's manuscripts for this publication and provided his own two-page preface. The Bernoulli numbers in the Ars Conjectandi inspired the first published computer programme, as devised by Ada Lovelace in 1843. Looking to demonstrate the potential of Babbage's analytical engine, Lovelace wrote an algorithm with which the machine could calculate the Bernoulli sequence, each generated recursively from previous values. The algorithm was published in Taylor's Scientific Memoirs in August 1843. Amusingly, the final section includes several comments on jeu de paume - a ball game having much in common with modern tennis and very little in common with the rest of the work. Dibner 110; Horblit 12; Norman 216; Printing and the Mind of Man 179; Tomash & Williams B143. Quarto (215 x 170 mm), pp. [iv], 35, [1]; 306. Folding engraved plate, 2 folding engraved tables, woodcut vignette to title page, head- and tailpieces and initials, tables in the text. Nineteenth-century marbled boards, outer and lower edges uncut. Front free endpaper and initial two leaves remounted on stub. Late 19th-century "Wirtz" signature. Recent pencil annotation to N3. Light rubbing, faint sunning to spine, minor browning and foxing to content extremities, closed tear to outer margin of D1, professionally repaired, plates crisp: a very good copy.

First edition. EXCEPTIONALLY RARE DISSERTATION BY JACOB BERNOULLI. First edition, exceptionally rare, of this dissertation which Bernoulli (1655-1705) submitted in order to secure the chair of mathematics at the University of Basel. This was the beginning of a remarkable career in mathematics, in which he "greatly advanced algebra, the infinitesimal calculus, the calculus of variations, mechanics, the theory of series, and the theory of probability [and] was one of the most significant promoters of the formal methods of higher analysis" (DSB). The dissertation, 'The solution of a triplet of problems, arithmetical, geometrical, and astronomical, together with corollaries from general mathematics,' treats three elementary problems in number theory, one arising from arithmetic, one from geometry, and one from astronomy/navigation. "Jacob Bernoulli's research on elementary mathematics, taken as a whole, constitutes a work of no mean importance, very diverse in content, lacking organic unity to be sure, but also of exceptional historic interest. Indeed, only from very few of the mathematicians who have left a lasting mark do we have the documentation which allows us to examine carefully the process of their scientific education . However, in contrast, from Jacob Bernoulli we actually possess some 'exercises' that he wrote, beginning during the early years of his education. This is how we might characterize some of his Meditationes which he worked on with great diligence and singular ability. The interest of these exercises lies not only in their relationship to the general state of mathematics of the time, but also (and perhaps more) in the way in which they represent an almost complete psychological picture of the formation of a great mathematician - which he certainly was - toward the end of the XVIIth century" (Werke 2, p. 15). These Meditationes remained unpublished until the twentieth century, except for the three published, with much additional detail, in the present pamphlet. On the last page of the dissertation is a list of 'Corollaries', one of which concerns the values of expectations in a lottery, and is of particular interest in view of Bernoulli's posthumously-published Ars conjectandi (1713), the founding work of mathematical probability. "The academic dissertation Solutionem tergemini problematis arithmetici, geometrici et astronomici, which was presented at the University of Basel (4.2.1687), secured him the desired teaching post. Therefore this paper has particular biographical interest" (ibid., p. 18). OCLC lists only 5 copies worldwide (Yale only in US); not on COPAC. "Let us recall briefly what we know of Jacob Bernoulli's education before he obtained, at the age of34, the chair in mathematics in his hometown Basel. Jacob was born in this city on December27th, 1654 (according to the old calendar) in a protestant family of spice traders who had fled theSpanish low lands after the fall of the Duke of Alba. Complying with the wish of his father NicolasBernoulli, a state adviser and magistrate, Jacob studied philosophy and then theology until 1676. Aswas common at the time, he chose a motto. His came from Phaeton who drew the solar carriageInvito patre sidera verso, which may be translated by 'Despite my father, I am among thestars'. Rather than exaggerated modesty, this motto was a proud affirmation of superiority. "The young Jacob fully benefited from what Daniel Roche calls 'culture de la mobilité', promoted in the second half of the XVII century by new institutions which facilitated the movement of individuals and the spread of knowledge. Starting in August 1676, he traveled by horse to Geneva where he remained for twenty months preaching, instructing a blind young girl, Elisabeth von Waldkirch, and serving as an opponent during the theological disputations. He relates his experience teaching mathematics to the blind in an article published in the Journal des Savants in 1685. This article is probably a reaction to an account by Spon published in the same journal in 1680, in which the author attributes to the father of the blind girl the writing system that was in fact developed by Jacob. It is here that Jacob meets Nicolas Fatio de Duillier, a life long friend who recalled, in a letter dating from July 22nd, 1700, that he had seen Jacob play court tennis in Geneva, a game on which Jacob later wrote a famous letter . "In June 1678, Jacob continues his extensive traveling in France, residing in the Limousin (in Nède with the marquis de Lostanges, where he constructs two sundials in the castle courtyard), then in Bordeaux and a few weeks in Paris. During this journey, he begins, in 1677, to write his mathematical journal, Meditationes, annotationes, animadversiones theologicae et philosophicae, which contains 236 articles . The journal is a precious testimony from this early phase of Jacob's scientific training which only really began when he encountered the Cartesian environment, initially in France, later mainly in the Netherlands (Amsterdam and Leiden) and in England during a second journey (April 1681- October 1682). In August 1682, Jacob attended a meeting of the Royal Society in London. Jacob started out by acquainting himself with the Cartesian philosophy of nature after which he turned to geometry . "After his return to Basel in 1682, Jacob gave up the idea of a career in the clergy and decided to devote himself to mathematics. At the University of Basel he gave courses in experimental physics, as can be gathered by a pamphlet printed in Basel in 1686. From 1682 on, he also submitted short articles to the Journal des Savants - reactions to the works of others that he presented or criticized - initially in the area of natural philosophy (machines for breathing under water, to elevate water, to weigh air, oscillation center), then from 1685, in mathematics . "[Jacob] slowly acquired a knowledge of mathematics, at first through his readings of the second Latin edition of Descartes' Géo.

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.

8°., Original-Leinen, XLVII/1284 S. mit 118 Abbildungen und 194 Tafeln, Einbände etwas fleckig, ansonsten gut erhaltenes Exemplar, (Inhalt der Einzelbände: I: Die Bildnisse berühmter Römer mit Ausschluß der Kaiser und ihrer Angehörigen. Band II,1: Die Bildnisse der römischen Kaiser und ihrer Angehörigen, 1.Teil: Das julisch-claudische Kaiserhaus. Band II,2: Die Bildnisse der römischen Kaiser und ihrer Angehörigen, 2. Teil: Von Galba bis Commodus. Band II,3: Die Bildnisse der römischen Kaiser und ihrer Angehörigen, 3. Teil: Von Pertinax bis Theodosius.). Sprache: Deutsch Gewicht in Gramm: 2900.

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.

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.).

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.