Abraham

A Compleat and Intire Collection of the Lords Protests in the Last Session of Parliament; Particularly Touching the Late Horrid and Detectable Conspiracy. Bound with a Portion of Abraham Cowley's Miscellanies

1723AR20GLTBLK10London: Printed By A. Moore 1723. Hardback recent quarter leather marbled paper covered boards. New end-papers. 30cm x 18.5cm. Bound with a Portion of Abraham Cowley's Miscellanies - but lacking the title page for it. Pp. iv 30 17 41. Decorative initials and headpieces. 2nd edition 1723. A couple of small marks to final page 41. Scarce. ar20. 2nd Edition. Hard Cover. Very Good. Printed By A. Moore Hardcover

Besleys Books · Royaume-Uni80,00 £GB≈ 91,34 €

Fuller Abraham and T. HolmsABAA

A COMPENDIOUS VIEW OF THE EXTRAORDINARY SUFFERINGS OF THE PEOPLE CALLED QUAKERS BOTH IN PERSON AND SUBSTANCE IN THE KINGDOM OF IRELAND FROM THE YEAR 1655 TO THE END OF THE REIGN OF KING GEORGE THE FIRST. IN THREE PARTS .

1731WRCLIT61268Dublin: Printed by and For Samuel Fuller 1731. 1351pp. Octavo. Extracted from bound pamphlet volume. faint old stamps of a defunct mercantile library title neatly detached at gutter with old paper mends at lower blank tips and some early ink spots early ink ownership inscription on verso of title and in blank portion of A2; somewhat tanned with occasional corner creases and small marginal chips; a fair but complete copy quite amenable to conservation and binding. First edition. Not in Bradshaw. ESTC T103086. POLLARD pp. 230-1. Printed by and For Samuel Fuller unknown books

William Reese Company - Literature ABAA-ILAB · États-Unis225,00 $US≈ 190,37 €

SWAN, AbrahamBiblio.com

A Collection of Designs in Architecture Containing New Plans and Elevations of Houses for General Use. Volume II only.

175779383London:: Printed for and sold by the Author.by Mr. Meadows 1757. old full calf attractively rebacked with a new calf spine and the original gilt-lettered spine labels. Bookplate on pastedown; a little foxing/age toning to the text; plates generally clean. Folio. This volume complete with 65 numbered engraved plates. This is Volume II ONLY. Printed for and sold by the Author...by Mr. Meadows, unknown

Jeffrey H. Marks Rare Books · États-Unis250,00 $US≈ 211,52 €

SWAN, AbrahamBiblio.com

A Collection of Designs in Architecture. Together with: The British Architect Or The Builder's Treasury of Staircases . &c.

175747855London.: Printed for and sold by the author near the George in Portland Street Cavendish Square; by Mr. Brotherton over against the Royal-Exchange; Mr Buckland at the Buck in Pater-Noster Row; H. Piers and Partner at the Bible and Crown in High Holborn. 1757 - 1758. Later calf-backed marbled boards spine with compartments and black morocco label bearing titles in gilt board edges tooled in gilt. 3 vols. in 1. Folio 400 x 260 mm. Two vols with Title page Preface and a Description of the Plates each followed by 60 full page copper plate engravings all plates numbered signed and with imprints dated '1757'; final vol with Title page Introduction iii - viii Description of the plates beginning 'Of the Orders in General' pp. 1 - 16 followed by 65 numbered plates. PROVENANCE: Label of Doddington Library to front pastedown. Abraham Swan's extensive two volume study of domestic architectural designs 'A Collection of Designs' bound here with his seminal work on staircases 'The British Architect . ' .The two volume 'Collection of Designs' - the second of three pattern books published by Swan a carpenter and joiner - was his attempt to provide an inexpensive pattern book of inexpensive designs. Swan made his intentions of quantity over quality clear in his Preface: 'I hope that whatever defects may be observed in any of them will be candidly excused considering what a number of designs are contained in these two volumes and that they are all of my own contriving and drawing.' 'The first volume contains 4 engravings of the staircase at Blair Castle Perthshire which Swan designed for the Duke of Atholl 1757. Two Chinese Bridges for the grounds at Blair appear in the second volume. Swan's designs belong to the 'rococo' taste popular in the mid-18th century'. Weinreb.Swan's comprehensive work 'The British Architect' - first published 1745 here in the 3rd edition - was destined to be the first architectural book published in America. The title page of the earlier edition described the author as 'Abraham Swan Carpenter' later changed to 'Abraham Swan Architect.' The work includes the following: 'I. An easier more intelligible and expeditious Method of drawing the Five Orders than has been hitherto been published by a Scale of Twelve equal Parts free from those troublesome Divisions call'd Aliquot Parts. Shewing also how to glue up their Columns and Capitals.II. Likewise Stair-Cases those most useful ornamental and necessary Parts of a Building though never before sufficiently described in any Book Ancient or Modern; shewing their most convenient Situation and the Form of their Ascending in the most grand Manner: With a great Variety of curious Ornaments whereby any Gentleman may fix on what will suit him best there being Examples of all Kinds; and necessary Directions for such Persons as are unacquainted with the Branch.III. Designs of Arches Doors and Windows.IV. A great Variety of New and Curious Chimney-Pieces in the most elegant and modern Taste.V. Corbels Shields and other beautiful Decorations.VI. Several useful and necessary Rules of Carpentry; with the Manner of Truss'd Roofs and the Nature of a splay'd circular Soffit both in a streight and circular Wall never published before. Together with Raking Cornices Groins and Angle Brackets described.' From the title-page.Across all three volumes the title page imprint has been altered Meadows and Hitch and Hawes erased and replaced in ink manuscript with 'Mr Brotherton' and 'Buckland at the Buck'.'This is one of the books that had great influence on the builders and architects of eighteenth-century America.' Fowler.Park 80 / 79 first edition 1745 but citing other eds. including the present; RIBA Early Printed Books 3220; Fowler 341 second American edition 1794; Weinreb 1:166; Millard Architectural Collection Vol. 2 82; Berlin 2285. Printed for and sold by the author, near the George in Portland Street, Cavendish Square; by Mr. Brotherton, over against the Ro hardcover

Sims Reed Rare Books · Royaume-Uni3 500,00 £GB≈ 3 996,30 €

Rademaker, AbrahamBiblio.com

A coliseum and attached house at Albrechsberg; One plate from Twelve Engraved Views from Rhynland's Fraaiste Gezichten

17301611Amsterdam 1730. Engraving with extensive hand coloring in watercolor on laid paper with a partial heraldic watermark 6 3/4 x 7 3/4 inches 171 x 197 mm; sheet 6 3/8 x 8 1/8 inches 163 x 206 mm; margins unevenly trimmed at the top plate mark and 1/4- inch below the bottom platemark. Condition consistent with age including a repaired vertical tear extending 2- inches downward into the image area from the top right sheet edge and several tabs of non archival tape on the verso. There are some light areas of toning. Color is vibrant and fresh. unknown

Rob Zanger Rare Books LLC · États-Unis200,00 $US≈ 169,22 €

Bloemaert, AbrahamAntiquariat.de

[Venus und Amor]. -

1730910091CGAmsterdam:, Reimer & Ottens, um 1730. Kupferstich, Bildgröße 20,5 x 15,5 cm (hoch), Blattgröße 31,5 x 19,5 cm.

Antiquariat Tautenhahn · DE - Lübeck80,00 €

CHATELAIN (Henry Abraham).Livre Rare Book

[LE CAIRE] Vûë de la ville du grand Caire, et de ses environs.

1720LBW-2029Amsterdam, circa 1720. 365 x 430 mm.

Librairie Le Bail · Paris, France150,00 €

Abraham Alewijn; Jacques Basnage, sieur de Beauval; Mattheus Gargon; Hooghe, Romeyn deBiblio.com

'T Groot waerelds tafereel : verbeeldende in konst-prenten de heilige en waereldsche geschiedenissen zedert den aanvang des waerelds tot het uiteinde van de openbaring van Joannes

17211906090004Amsterdam J. Lindenbergh 1721. First Edition. Hardcover. Good. Folio 42 x 28 cm. Bound in contemporary mottled calf. Shelf worn corners bumped. Joints cracked. Additional engraved titles 2 engraved portraits 2 double-page maps map of the world map of Greece and the Mediterranean. A total of 179 engravings within text and plates after works by Romein de Hooghe. Includes engraving of the Temple of Jerusalem. Scattered foxing. 10 482 p. Pages misnumbered. Dutch. Hollstein IX 2; Van Eeghen/ Van der Kellen 404; Klaversma/ Hannema 129. Amsterdam, J. Lindenbergh hardcover

SequiturBooks · États-Unis1 323,00 $US≈ 1 119,39 €

GUNST, Pieter van [after RADEMAKER, Abraham]Biblio.com

't Gesigt Van de Portugeese en Hoogduytse Joden Kerken tot Amsterdam.

175214421Amsterdam c1752. 565 by 935mm. 21.5 by 36.75 inches. Engraving with etching on two sheets joined. View of the Plantage Muidergracht and the Jonas Daniël Meijerplein. The view shown from the present day Mr. Visserplien the busy intersecti.on in central Amsterdam depicts the Portuguese Synagogue on the left and the High German or Great Synagogue. These momumental buildings now house the Jewish Historical Museum. The first Jews to settle in Amsterdam were the Sephardim who had been expelled from Portugal and Spain in 1493. They were joined in the following decades by the Ashkenazi from Central and Eastern Europe the first of whom had come from Germany in 1600. In those years the only available land for them was at the outskirts of the eastern side of the Centrum the island of Vlooienburg surrounded by the Amstel River and the canals so they settled along the island's main street Breestraat which quickly became known as Jodenbreestraat. The Great Synagogue now the Jewish Historical Museum and the Portuguese-Israelite Synagogue were opened in 1671 and 1675 respectively. The Portuguese Synagogue was the place where Spinoza was placed under the ban by the Sephardic Jewish community in 1656. Pieter Stevensz. van Gunst 1659-1732 also known as Pieter Stevens van Gunst or Petrus Stephani was a Dutch draughtsman copperplate engraver and printmaker active in Amsterdam London 1704 and the Dutch town of Nederhorst 1730-1731. Abraham Rademaker 1677 21 January 1735 was an 18th-century painter and printmaker from the Northern Netherlands. Rademaker was born in Lisse. According to the RKD he was a versatile artist who painted Italianate landscapes but is known mostly for his many cityscapes and drawings of buildings that were made into print. R.W.P. de Vries auction 1925: 295. unknown

Daniel Crouch Rare Books Ltd · Royaume-Uni7 150,00 £GB≈ 8 163,87 €

VAN GUNST, Pieter [after RADEMAKER, Abraham]Biblio.com

't Gesigt Van de Portugeese en Hoogduyse Ioden Kerken tot Amsterdam.

173014402Amsterdam c1730. 565 by 935mm. 22.25 by 36.75 inches. Engraving with etching on two sheets joined. View of the Plantage Muidergracht and the Jonas Daniël Meijerplein. The view shown from the present day Mr. Visserplien the busy intersecti.on in central Amsterdam depicts the Portuguese Synagogue on the left and the High German or Great Synagogue. These momumental buildings now house the Jewish Historical Museum. The first Jews to settle in Amsterdam were the Sephardim who had been expelled from Portugal and Spain in 1493. They were joined in the following decades by the Ashkenazi from Central and Eastern Europe the first of whom had come from Germany in 1600. In those years the only available land for them was at the outskirts of the eastern side of the Centrum the island of Vlooienburg surrounded by the Amstel River and the canals so they settled along the island's main street Breestraat which quickly became known as Jodenbreestraat. The Great Synagogue now the Jewish Historical Museum and the Portuguese-Israelite Synagogue were opened in 1671 and 1675 respectively. The Portuguese Synagogue was the place where Spinoza was placed under the ban by the Sephardic Jewish community in 1656. Pieter Stevensz. van Gunst 1659-1732 also known as Pieter Stevens van Gunst or Petrus Stephani was a Dutch draughtsman copperplate engraver and printmaker active in Amsterdam London 1704 and the Dutch town of Nederhorst 1730-1731. Abraham Rademaker 1677 21 January 1735 was an 18th-century painter and printmaker from the Northern Netherlands. Rademaker was born in Lisse. According to the RKD he was a versatile artist who painted Italianate landscapes but is known mostly for his many cityscapes and drawings of buildings that were made into print. R.W.P. de Vries auction 1925: 295. unknown

Daniel Crouch Rare Books Ltd · Royaume-Uni7 350,00 £GB≈ 8 392,23 €

MOIVRE, Abraham deBiblio.com

'De Mensura Sortis seu de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus' pp. 213-264 in Philosophical Transactions Vol. XXVII. For the Years 1710 1711 and 1712

17126431London: Printed for H. Clements . and W. Innys . and D. Brown 1712. First edition. First edition published in the Philosophical Transactions and de Moivre's first published work on probability-the earliest original contribution to the subject to appear in Britain. This pioneering paper laid the groundwork for his later masterpiece The Doctrine of Chances 1718 the definitive English-language textbook on probability theory for over a century. As Hald notes "Nearly all of De Mensura Sortis was later incorporated into The Doctrine of Chances . the most important textbook on probability theory until the publication of Laplace's Théorie Analytique des Probabilités 1812.". THE FOUNDATION OF THE DOCTRINE OF CHANCES . First edition contained in a complete volume of the Phil. Trans. of de Moivre's first published work on probability and the first original work on the subject published in Britain a precursor to his Doctrine of Chances which appeared seven years later. "De Moivre's work on the theory of probability surpasses anything done by any other mathematician except Laplace. His principal contributions are his investigations respecting the Duration of Play his Theory of Recurring Series and his extension of the value of Daniel Bernoulli's theorem by the aid of Stirling's theorem" Cajori p. 245. "The only systematic treatises on probability printed before 1711 were Huygens' De ratiociniis in ludo aleae 1657 and Pierre Rémond de Montmort's Essay d'analyse sur les jeux de hazard 1708. Problems which had been posed in these two books prompted de Moivre's earliest work and incidentally caused a feud between Montmort and de Moivre on the subject of originality and priority" DSB. "Nearly all of De Mensura Sortis was later incorporated into de Moivre's book The Doctrine of Chances 1718 1738 1756 which was the most important textbook on probability theory until the publication of Laplace's Théorie Analytique des Probabilités 1812. In the preface de Moivre states that he began his work on probability theory at the exhortation of Francis Robartes who asked him to solve the division problem for two gamesters playing bowls and also to find the probability of getting certain given faces as the outcome of a given number of throws with a die. He also states that he had previously read the books by Huygens and Montmort 'but these distinguished gentlemen do not seem to have employed that simplicity and generality which the nature of the matter demands.' Furthermore he writes that 'while they suppose that the skill of the gamesters is always equal they confine this doctrine of games within limits too narrow.' Finally his remarks about Montmort may be read as if Montmort had used only the method of Huygens on some new examples. These rash remarks naturally provoked a dispute with Montmort" Hald 1984 pp. 230-1. "The most remarkable of de Moivre's contributions in De mensura sortis are his derivation of the ruin probability in Huygens' fifth problem; his use of the Poisson approximation to solve the binomial equation Bc n p = ½ with respect to n; his solution of the occupancy problem by means of the method of inclusion and exclusion and the algorithm for the continuation probability in the duration of play for the ruin problem. Furthermore he gives without proof the probability of getting a given number of points by throwing any given number of dice and the probability of ruin when one of the players has infinitely many counters. The only contemporary evaluation of these impressive results is the critical review given by Montmort in a letter of 5 September 1712 to Nicholas Bernoulli about a month after Montmort had received a copy of the paper from de Moivre . Montmort recognizes de Moivre's priority to the Poisson approximation to Robartes' problem and to the algorithm for finding the continuation probability in the problem of the duration of play" Hald 2003 pp. 403-4. No copies in auction records. Provenance: Toft Hall in Cheshire England seat of the Leycester family since the 14th century bookplate on front paste-down. De Moivre's interest in probability was awakened by Francis Robartes 1649-1718 Member of Parliament and scion of an aristocratic family. In 1692 Robartes wrote a manuscript on two probability problems that he presented to the Royal Society but never published and in the following year he succeeded in publishing another paper on probability. In 1710 Robartes helped John Harris with his article entitled "Play" in Harris's scientific dictionary Lexicon Technicum. Robartes devised an algorithm that Harris used to extract the appropriate terms in a binomial expansion in order to solve the problem of the division of stakes. At some point over the years 1708 to 1710 Robartes received a copy of Montmort's Essay which he showed to de Moivre. He also gave de Moivre three challenge problems of his own devising to work on. "Once de Moivre had solved the first problem within a day of Robartes posing it Robartes gave de Moivre the other two problems to work on while at the same time encouraging him to write on probability. The encouragement proved fruitful. De Moivre finished his manuscript on probability during a holiday that he spent at a country house possibly Robartes's. On June 11 1711 de Moivre submitted his manuscript to the Royal Society. The Society's Journal Book quietly marked the beginning of a new era for probability in England with the note 'Mr. De Moivre presented a Treatise Intituled de Probabilitate Eventum in Ludo Alea This Treatise was Ordered to be printed in the Transactions.' The treatise with the title De Mensura Sortis or 'Of the measurement of lots' comprises an entire issue Number 329 of Philosophical Transactions. At 52 journal pages it is more than three times longer than anything else de Moivre had written to that date" Bellhouse p. 70. De Moivre begins De Mensura Sortis with two basic definitions from which many of his results are derived. The first comes directly from Huygens's De ratiociniis. For two players A and B contending for a stake of value a A has p chances to win and B has q. The expected value for each player follows what Huygens obtained: ap/ p q for A and aq/ p q for B. The second definition may have come from Edmond Halley or Francis Robartes. If an event can happen in p ways and fail to happen in q and a second event can happen in r ways and fail to happen in s then all the chances for events happening or failing are in the product p qr s or pr qr ps qs. For example pr is the number of ways both events can happen and ps is the number of ways that the first event happens and the second fails. This is the approach that Halley used in evaluating joint life annuities in his 1693 paper on mortality data from the city of Breslau . "De Moivre finishes the introduction by saying that if the first event is repeated n times then the total number of chances in the game is given in the binomial expression p qn. When this expression is expanded it may be written as a sum containing terms of the form piqn-imultiplied by an appropriate coefficient where i represents the number of times the event happens and n - i represents the number of times it fails the sum of the first c terms of this expansion is denoted Bc n p . The binomial expansion becomes the motif for the paper . At the beginning nine of the first ten problems there are some simple variations on the use of the expansion of p qn and then at the end the last seven problems the expansion is used to solve a very complex problem the problem of the duration of play. In the middle there are several solutions to a number of challenge problems taken from various sources including the three from Robartes" Bellhouse p. 73. Problems 1 3 and 4 are relatively straightforward applications of the binomial distribution. Problem 1 is to find the chance of throwing an ace two or more times in 8 throws with a single die. Problem 3 is to determine the chances of A and B winning a single game supposing that A can give B two games out of three. Problem 4 is similar. In problems 5 to 7 de Moivre considers the problem of finding the number of trials that gives an even chance for getting at least one success but fewer than some given number of successes c say. This means he has to solve the equation Bc - 1 n p = ½ for n when c and p are given. De Moivre considers the two extreme cases p = ½ and p tends to 0 of which the first is easy by symmetry. De Moivre shows that as p tends to 0 Bc - 1 n p tends to e-mmultiplied by the sum of the first c terms in the series expansion of em in powers of m where m = np/1 - p de Moivre was not able to express the result this way because our notation for the exponential function had not yet been invented. This result the 'Poisson approximation' to the binomial distribution played a very important role in later developments. "There has been some discussion of whether it is reasonable to contend that de Moivre found the Poisson distribution" Hald 1984 p. 231 more than a century before Simeon-Denis Poisson. Problems 2 3 4 and 10 are on the division of stakes or 'problem of points'. "Consider a series of games with two players A and B where in each game A has probability p and B probability q = 1 - p of winning a point. If play stops when A lacks a points and B lacks b points in winning how should the stake be divided between them De Moivre proves that A's probability of winning equals the sum of the last b terms of the expansion of p qab-1 and B's probability of winning equals the remaining a terms. This result had already been derived by Johann Bernoulli in 1710 in a letter to Montmort but it was not published until 1713 . In Problem 8 de Moivre generalizes to k players say and gives the solution as the sum of the appropriate terms of the multinomial pl p2 . pknl-k n being the total number of points lacking. He points out that certain terms have to be divided among the players depending on the permutation of the p's. "In Problems 16 and 17 he gives the solution of Robartes's problem: the division problem for two gamesters playing bowls. In each game B say gets a number of points equal to the number of his bowls which is nearer to the jack than any of A's bowls. By combinatorial methods de Moivre finds the probability of getting i points in a single game assuming that the players have the same number of bowls and are of the same skill. The division problem is then solved by recursion" Hald 1984 pp. 231-2. Problems 11 12 and 13 are related to the first two of the five problems Huygens posed at the end of his De ratiociniis. "In these problems the players take turns in a specified order until one of them wins. De Moivre gives the solution as the sum of an infinite series" ibid. p. 232. Problem 15 is 'Waldegrave's problem' James Waldegrave 1684-1741 later the first Earl Waldegrave was a British diplomat living in Paris who himself published nothing in mathematics. "Let there be n 1 players A1 . An1 of equal skill. Players A1 and A2 play a game and the loser pays a crown to a common stock and does not enter the play again until all the other players have played; the winner plays against A3 and the loser pays a crown to the stock and so on. If the winner of the first game beats all the rest the play is finished; if not the play goes on each player coming in again in turn until one player has beaten in succession all the other players and he then receives all the money in the stock. The problem is to determine the probability of each player winning the stock; the expectation of each player; and the probability of a given duration of the play. "In a letter to Bernoulli of I0 April 1711 Montmort writes that the problem has been proposed to him and also solved by Waldegrave for three players. Independently de Moivre formulated and solved the problem for three p1ayers in De Mensura Sortis 1712" Hald 2003 p. 378. "De Moivre solves this problem by means of conditional expectations. First he supposes that A beats B in the first game. On this assumption the play may end with A as winner in the second fifth eighth . game. The probabilities of A for reaching these games and winning are ½ ½4 ½7 . Hence the expected stake plus fines may be found and subtracting A's expected fine his conditional expectation results. Under the same assumption B's expectation is obtained. The unconditional expectation is then found as the average of the two conditional expectations" Hald 1984 p. 232. Problems 18 and 19 are 'occupancy problems' the third type of problem posed to de Moivre by Robartes: Find the probability pn that f specified faces occur at least once in n throws with a die having k faces. De Moivre calculates pn by means of the method of 'inclusion and exclusion'. In Problem 19 he solves the equation pn = ½ under the assumption that f is small compared to k. Problem 9 is a generalization of the 'gambler's ruin problem' the fifth of Huygens's problems in De ratiociniis. "Consider two players A and B having a and b counters respectively. In each game A has probability p and B has probability q = 1 - p of winning and the winner gets a counter from the loser. The play continues until one of the players is ruined. What is the probability of A being ruined Huygens's fifth problem is obtained for a = b = 12" ibid. Problems 20-26 are a continuation of the discussion of the ruin problem: what is the probability that the play ends at the nth game or before Problem 25 is the case when A has infinitely many counters; de Moivre states the result without proof. "Although the publication date is given as 1711 De Mensura Sortis was not in print until 1712. Shortly after its publication de Moivre sent copies of the issue to several people in England including Edmond Halley Isaac Newton and de Moivre's fellow chess player at Slaughter's Coffeehouse the Earl of Sunderland. De Moivre's friend Pierre des Maizeaux handled several copies that were bound for the Continent. Using his connections in the Republic of Letters des Maizeaux sent copies of De Mensura Sortis to Abbé Jean-Paul Bignon at that time the French minister of state with responsibility for the Académie Royale des Sciences. Bignon wrote to des Maizeaux on September 24 1712 saying that the copies he received had been distributed. He also enclosed a letter from Montmort to de Moivre thanking him for his treatise; the letter has not survived. Whatever he thought personally about de Moivre's treatise Montmort was adhering to the code of civility in the Republic of Letters by sending the letter of thanks. Other people on the Continent receiving copies were Nicolaus Bernoulli Johann Bernoulli and Pierre Varignon. Johann Bernoulli received his copy via William Burnet a younger son of Gilbert Burnet Bishop of Salisbury; Bernoulli had asked Burnet to obtain a copy for him" Bellhouse p. 71. Abraham Moivre stemmed from a Protestant family. His father was a surgeon from Vitry-le-François in the Champagne. From the age of five to eleven he was educated by the Catholic Péres de la doctrine Chrètienne. Then he moved to the Protestant Academy at Sedan were he mainly studied Greek. After the latter was forced to close in 1681 for its profession of faith Moivre continued his studies at Saumur between 1682 and 1684 before joining his parents who had meanwhile moved to Paris. At that time he had studied some books on elementary mathematics and the first six books of Euclid's elements. He had even tried his hand at Huygens' 1657 tract without mastering it completely. In Paris he was taught mathematics by Jacques Ozanam who had made a reputation from a series of books on practical mathematics and mathematical recreations. Ozanam made his living as a private teacher of mathematics. He had extended the usual teachings of the European reckoning masters and mathematical practitioners by what was considered fashionable mathematics in Paris. Ozanam enjoyed a moderate financial success due to the many students he attracted. It seems plausible that young Moivre took him as a model he wanted to follow when he had to support himself. After the revocation of the Edict of Nantes in 1685 the Protestant faith was no longer tolerated in France and hundreds of thousands of Huguenots who had refused to convert to Catholicism emigrated to Protestant countries. Amongst them was Moivre who arrived in England in 1687. There he began his occupation as a tutor in mathematics. He also added a 'De' to his name probably because he wanted to take advantage of the prestige of a pretended noble birth in France in dealing with his clients many of whom were noblemen. An anecdote from this time which goes back to de Moivre himself tells that he cut out the pages of Newton's Principia of 1687 and read them while waiting for his students or walking from one to the other - the main function of this anecdote was to demonstrate that de Moivre was amongst the first true and loyal Newtonians and that as such he deserved help and protection in order to gain a better position than that of a humble tutor of mathematics. In 1692 de Moivre met with Edmond Halley and shortly afterwards with Newton. Halley ensured the publication of de Moivre's first paper on Newton's doctrine of fluxions in the Philosophical Transactions for 1695 and saw to his election to the Royal Society in 1697. Newton's influence concerning university positions in mathematics and natural philosophy persuaded de Moivre to engage in the solution of problems posed by the new infinitesimal calculus. In 1697 and 1698 he published the polynomial theorem a generalization of Newton's binomial theorem together with application in the theory of series. In 1704 de Moivre began a correspondence with Johann Bernoulli but Bernoulli's letters showed de Moivre that he lacked the time and perhaps the mathematical power to compete with a mathematician of this calibre in the new field of analysis. De Moivre ceased his correspondence with Bernoulli after he was made a member of the Royal Society commission to adjudicate in the priority dispute between Newton and Leibniz over the invention of calculus - continuing the correspondence may have made him appear disloyal to the Newtonian cause. When the Lucasian chair in mathematics at Cambridge was given in 1711 on Newton's recommendation to Nicholas Saunderson de Moivre realized that this only option was to continue his occupation as a tutor and consultant in mathematical affairs in the world of the coffee houses where he met his clients; additional income he could draw from the publication of books and from translations. He therefore turned to the calculus of games of chance and probability theory which was of great interest for many of his students and where he had few competitors in England. Hald 'A. de Moivre: De Mensura Sortis or On the Measurement of Chance' International Statistical Review 52 1984 pp. 229-262. Hald History of Probability and Statistics and their Applications before 1750 2003. Bellhouse Abraham de Moivre 2011. Cajori A History of Mathematics 1894. 4to 218 x 168 mm pp. vi 555 with 13 plates a little browning and foxing. Contemporary calf sides decorated in blind with corner fleurons a little rubbed joints starting spine label mostly missing. A handsome copy with no restoration. Printed for H. Clements ... and W. Innys ... and D. Brown unknown

SOPHIA RARE BOOKS · Danemark6 500,00 $US≈ 5 499,65 €

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