Catalogue 01-2014

32 New Arrivals Mathematics · Physics · Astronomy

Milestones of Science Books phone +49 (0) 421 1754235 www.milestone-books.de [email protected] Member of ILAB and VDA

The first approximate resolution of the three-body problem

1 ALEMBERT, Jean le Rond d'. Traité de dynamique, dans lequel les lois de l’equilibre & du mouvement des corps sont réduites au plus petit nombre possible. Paris: David l’Aine, 1743. 4to (213x165 mm). [4], xxvi, [2], 186, [2] pp, engraved title-vignette, 4 engraved folding plates at end. (A few minor marginal stains on title-page and preliminaries.) Contemporary calf (extremities scuffed, boards and spine worn, hinges repaired), marbled endpapers, very light toning and occasional very minor spotting of text. Provenance: Antonii Scherbrant(?), illegible signature to first flyleaf. Very good, internally crisp copy. (#002001) € 4,800

PMM 195; Poggendorf I, 28; Wellcome II, p. 28; Norman 31.

FIRST EDITION OF D’ALEMBERT’S IMPORTANT CONTRIBUTION TO THE FORMALIZING OF NEWTON’S NEW SCIENCE OF MECHANICS. The Traite de dynamique, one of d’Alembert’s most famous scientific works, demonstrates d’Alembert clearly recognized that a scientific revolution had occured and sets out to formalize the new science of mechanics—an accomplishment often mis- attributed to Newton. The first part of the treatise comprises d’Alembert’s own three laws of motion: inertia, the parallelogram of motion, and equilibrium. The second part contains the first statement of what has come to be known as "d'Alembert’s Principle:" which states that the internal forces of inertia must be equal and opposite to the forces that produce the acceleration - a theory which is applied to many mechanical and technical problems, in particular to the theory of the motion of fluids. 'The "Treatise on Dynamics’ was d’Alembert’s first major book and it is a landmark in the history of mechanics. It reduces the laws of the motion of bodies to a law of equilibrium" (PMM).

2 ALEMBERT, Jean le Rond d'. Réflexions sur la cause générale des vents. Piece qui a remporte le prix propose par l'Academie Royale des Sciences de Berlin, pour l'annee 1746. Paris: chez David l'aine, 1747. Two parts in one volume. 4to (214x162 mm), [8] xxviii 194, 138 pp., including engraved vignette on title, engraved headpiece on dedication, woodcut initials, head- and tailpieces and two engraved plates. Contemporary calf, spine gilt in compartments (boards rubbed and damaged, extremities scuffed, spine chipped), red morocco lettering-piece, red-dyed edges. Title page brown- stained at outer margins, text leaves unevenly browned throughout, occasional slight spotting, small wormhole at lower margin of a few leaves not affecting text. Good copy with ample margins. (#002024) € 1,200

Norman 34; DSB I, p.113; Sotheran 71; Honeyman 806.

First edition. "In 1747 d'Alembert published two more important works, one of which, the Réflexions sur la cause générale des Vents, won a prize from the Prussian Academy. In it appear the first general use of partial differential equations in mathematical physics. Euler later perfected the techniques of using these equations ... D'Alembert's treatise on winds was the only of his works honored by a prize and, ironically, was later shown to be based on insufficient assumptions. D'Alembert assumed that wind patterns were the result of tidal effects on the atmosphere, and he relegated the influence of heat to a minor role, one that caused only local variations from the general circulation. Still, as a work on atmospheric tides it was successful, and Lagrange continued to praise d'Alemberts's efforts many years later." (DSB I, p.113).

3 BARROW, Isaac [edited by Isaac Newton]. Lectiones opticae & geometricae: in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur. 2 parts in 1 volume. London: William Godbid for Robert Scott, 1674. 4to (202x152 mm). [12], 127 [1], [2], 147, [3] pp., 27 folding engraved plates. With the ‘Benevolo Lectori’ preliminary leaf bound before the ‘Lectiones Geometricae.' Bound in a contemporary English speckled calf with a spine devided by raised bands into 6 richly gilt compartments. The book-block is strong and the hinges hold very firmly. The leather upon the front hinge is lightly cracked, but the cords hold firmly. The boards themselves, the edges and the corners show only slightest wear. Internally, the leaves are toned, but generally clean, with ample margins and clear print throughout. There is light occasional spotting and little marginal staining, which remains quite unobtrusive. The title page show a very small burn hole not affecting text, the second F2 got a small burn-hole in the outer margin, not affecting text as well. The 27 folding engraved plates are excellent impressions, some browned a bit stronger. This is an unusually attractive example of a rare work. (#001989) € 5,500

Wing B 945; Babson 249; Wallis 358.4; Sotheran 5816 (2); DSB I, 475.

Very rare early issue of the first edition without the 'Addenda Lectionibus Geometricis' (pp. 149-151) and plate 13 of the second part found in later issues. In this issue, plate 12 is in uncorrected state with missing lines in figure 220 finished by hand. This plate was re-ingraved for the later issues. "Many problems connected with the reflexion and refraction of light are treated with ingenuity. The geometrical focus of a point seen by reflexion or refraction is defined; and it is explained that the image of an object is the locus of the geometrical foci of every point on it. Barrow also worked out a few of the easier properties of thin lenses; and considerably simplified the Cartesaian explanation of the rainbow. The geometrical lectures contain some new ways of determining the areas and tangents of curves. The most celebrated of these is the method given for the determination of tangents to curves" (Sotheran).

Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form. In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. During his tenure of this chair he published two mathematical works of great learning and elegance, the first on geometry and the second on optics. In 1669 he resigned his professorship in favour of Isaac Newton. In 1669 he issued his ‘Lectiones XVIII,’ which would come to be known as the ‘Lectiones Opticae.’ The ‘Lectiones Geometricae’ were first published in 1670, and the two volumes together, revised, corrected, edited and slightly expanded by Collins and Newton, were first published in 1674 (the edition offered here). It is said in the preface that Newton revised and corrected the ‘Lectiones Opticae.'

In this 1674 first complete edition, the title and preliminary matter for the ‘Lectiones Geometricae’ were supposed to be cancelled. Indeed, ESTC states that “no copy is recorded with the original second title page retained.” In addition to the new title-page, this copy actually contains the uncancelled preliminary material. Barrows work was edited by John Collins and Isaac Newton, and corrected and revised by Issac Newton, thus constituting one of Newton's earliest publications.

4 BERNOULLI, Johann. Discours sur les loix de la communication du mouvement, qui a merité les eloges de l'Academie Royale des Sciences aux années 1724. & 1726. & qui a concouru à l'occasion des prix distribuez dans lesdites années. Paris: Claude Jombert, 1727. 4to (253x185 mm). [2: blank],

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 3 of 24 [2], 108 pp., 5 folding engraved plates. Modern marbled paste paper boards, paper label to front cover. Internally fresh with occasional very minor spotting. A fine, clean copy. (#001940) € 690

DSB II, 54; Poggendorf I, 157.

Rare first edition of this important work on dynamics, "one of the major contributions to the vis viva controversy" (P. M. Heimann, "Geometry and Nature": Leibniz and Johann Bernoulli's Theory of Motion, in: Centaurus XXI1, März 1977, pp. 1- 26).

5 BORELLI, Giovanni Alfonso. Elementa conica Apollonii Paergei et Archimedis opera nova & breviori methodo demonstrata... Romae: apud Mascardum, 1679. 12mo (141x75 mm). [12], 283 [5] pp., including separate half title to Archimedes' Opera, final blank and 8 folding engraved plates at end. Contemporary limp vellum, a few leaves a little browned. Provenance: Bibliotheca Podolin (ink inscription to title). Good copy of a rare work printed on strong paper. (#002016) € 2,400

Bibliotheca Mechanica, p.42; Riccardi I, 44; Smith, History of Mathematics, I, 368; DSB II, p.308-9 (Florence ed.)

The Rome edition of Borelli’s treatise on conic sections, published in the year of his death. "His edition of book V, VI, and VII of Apollonius' conic sections first appeared in Florence in 1661. In 1672 Borelli was forced to fly Messina with a price on his head as the result of political upheavals there; his redaction of Maurolico's edition of Archimedes, in press at that time, was confiscated by the hostile regime. Borelli was also responsible for an edition of Euclid, Euclides restitutus, Pisa, 1658. (Roberts & Trent, Bibliotheca Mechanica, p.42).

The formulation of the dual nature of light

6 BROGLIE, Louis Victor, Prince de. Ondes et mouvements. Fascicule I. Paris: Gauthier-Villars, 1926. 4to (254x167 mm), [4], 133, [5] pp., including half title and 4 pages of publisher’s ads at end. Originial printed wrapper (spine and cover sun-tanned, little creased, some minor wear at spine ends), untrimmed. Internally evenly browned, a few occasional expert annotations, publishers ticket to front flyleaf. Provenance: W. von Berg, his signature to half title. Fine copy. (#001946) € 1,200

Norman 348; PMM 417.

FIRST EDITION of de Broglie's expanded presentation of the ideas in his thesis, in which he developed the idea that material particles, like electrons, have both a wave and a corpuscular nature similar to the dual behavior of light.

7 CARDANO, Girolamo. Opus novum de proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum ... Praeterea artis magnae, sive de regulis algebraicis liber unus ... Item, de aliza regula liber. 3 parts in 1 volume. Basel: Henricus Petri, 1570. Folio

(315x205 mm). [16], 271 [1], 163 [1], [8], 111 [1] pp. Signatures: *3, A-Y6, Z4, Aa-Tt4, Vv6, *4, AA- OO4. Separate title-page and pagination for Artis magnae and Operis perfecti sui sive algebraicae, printer's device on general title and verso of final leaf, numerous woodcut diagrams in text. Contemporary calf with gilt arabesque centre-pieces to covers (joints split but holding, rather rubbed and scuffed), spine with 5 raised bands gilt incompartments. 17th century marginal repair to foot of title, light marginal waterstains, text somewhat browned, few pages stronger, first part with a few annotations and markings in pencil. Provenance: 17th century inscription on front free endpaper: ‘sub parvo sed meo Bardin’; same signature on paper repair on foot of title where an earlier signature had been cut out; another illegible signature dated 1723. (#002017) € 18,000

Adams C689; Smith p.338-9; Riccardi I 256; DSB III, p.65-66.

FIRST EDITION. Comprising Cardano’s three most important scientific works: Opus novum, containing Cardano's work on the relation between the densities of air and water, the second edition of the Ars magna, his great work on algebra first published in 1545, in which he had published Tartaglia's method for solving third-degree equations and the De aliza regula, about the third-degree equation, here published for the first time.

"In his Opus novum de proportionibus, Cardano turned to problems of mechanics, with the principal aim of applying quantitative methods to the study of physics. His use of the concept of moment of a force in his study of the conditions of equilibrium in balance and his attempt to determine experimentally the relation between the densities of air and water are noteworthy." (DSB III, p.66).

"It was only in 1570, in a new edition of the Ars magna, that he added a section entitled 'De aliza regula' ... devoted to the 'irreducible case' of the cubic equation, in which Cardano's rule is extended to imaginary numbers. This was ... important for the algebraic transformations which it employed and for the presentation of the solutions of at least three important problems." (DSB III, p.65).

8 CLAIRAUT, Alexis-Claude. Théorie de la lune, déduite du seul principe de l'attraction réciproquement proportionnelle aux quarrés des distances. Paris: Dessaint & Saillant, 1765. 4to (252x200 mm), [1-3] 4 [5] 6-7 [8], [1] 2-161 [1] pp. and folding plate with diagrams. Contemporary French calf with 5 raised bands, gilt in compartments and with red morocco label (hinges cracked, extremities worn, boards rubbed), red-dyed edges, marbled endpapers, text only very minor spotted and age-toned. (#001995) € 2,500

DSB III, p.283; Honeyman 701; Poggendorff I 447.

SECOND EDITION (the first in France of both papers unified). First published in 1752, this discourse won the annual prize at the Russian Imperial Academy. "In 1743 Clairaut read before the French Academy a Paper entitled 'L’orbite de la

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 5 of 24 lune dans le systeme de M. Newton,' Newton was not fully aware of the movement of the moon’s apogee, and therefore the problem had to be reexamined in greater detail. However, Clairaut - and d’Alembert, and Euler, who were also working on this question - found only half of the observed movement in their calculations. It was then that Clairaut suggested completing Newton’s law of attraction by adding a term inversely proportional to the fourth power of the distance... The minimal value of the term added soon made Clairaut think that the correction - all things considered - could apply to the calculations but not to the law... Clairaut found toward the end of 1748... that in Newton’s theory the apogee of that moon moved over a time period very close to that called for by observations. This is what he declared to the French Academy on 17 May 1749. This first approximate resolution of the three-body problem in celestial mechanics culminated in the publication of the Théorie de la lune in 1752 and the Tables de la lune in 1754." (DSB III, p. 283).

Clairault (1713-1765) war seit seinem 18. Lebensjahr Mitglied der Akademie der Wissenschaften in Paris. Die vorliegende Schrift wurde 1752 von der Petersburger Akademie preisgekrönt. S. 119ff. enthalten "Tables de la lune, calculées suivant la théorie de la gravitation universelle". Er veröffentlichte neuartige Lehrbücher zur Geometrie und zur Algebra, die nicht axiomatisch, sondern heuristisch an die Themen herangingen. Nach ihm sind drei Gleichungen benannt, die in der Geodäsie eine große Rolle spielen.

The first statement of the second law of thermodynamics

9 CLAUSIUS, Rudolf. Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärme selbst ableiten lassen. In: Annalen der Physik und Chemie, vol. 79, pp. 368-397 and 500-524. Leipzig: Johann Ambrosius Barth, 1850. 8vo (215x127 mm). Whole volume, ix, [1], 580 pp., including half and general title (with ink and blind samps) and 3 engraved plates at end. Contemporary marbled paste paper boards, spine lettered in gilt (extremities rubbed, corners bumped), endpapers, general title and preliminaries spotted, otherwise clean and only little browned. Good copy (#001949) € 1,800 DSB III, p.303-5; Bibliotheca Mechanica, p.75f. THE RARE FIRST EDITION of Clausius' milestone paper on the mechanical nature of heat and the first statement of the second law of thermodynamics. Rudolph Clausius played a key role in advancing the theory of heat during the 19th century. His contributions concerned the development of the two fundamental principles of heat as well as the microscopic approach of kinetic theory where he introduced the new concept of the mean free path. When he began his studies, the idea that heat belonged to the so-called imponderables which were weightless and invisible had not yet disappeared. Carnot had still used that idea for his well-known cycle process. Clausius was able to make the Carnot-cycle compatible with the concept of heat as a kind of motion. The significant beginning of Clausius’ career dates from 1850, when Clausius established the foundations for modern thermodynamics in his first great paper on the theory of heat, which marks the beginning of the line of thought which led to his rejection, in 1850, of the caloric theory in favour of the new principle of the equivalence of work and heat (DSB III, p.303). In his paper, he formulates the second law of thermodynamics in the well-known form: "heat cannot of itself pass from a colder to a hotter body." In general, the total entropy of any system will not decrease other than by increasing the entropy of some other system. Hence, in a system isolated from its environment, the entropy of that system will tend not to decrease. It follows that heat will not flow from a colder body to a hotter body without the application of work to the colder body and that the entropy of a system that is not isolated may decrease. If the system is initially in a low-entropy (ordered) state, its condition will tend to slide toward a state of maximum entropy (disorder). Any unbalanced temperature distribution rapidly decays to a state of uniform temperature as energy flows from the hotter to the colder block. Having achieved this state, the system is in equilibrium. The approach to equilibrium is therefore an irreversible process. The tendency toward equilibrium is so fundamental to physics that the second law is probably the most universal regulator of natural activity known to science. (Britannica). His research pathed the way for thermodynamics, later chiefly advocated by Planck as well as for modern statistical physics mainly connected with the names of Maxwell and Boltzmann.

10 DIRAC, Paul. The Principles of Quantum Mechanics. Oxford: Clarendon Press, 1930. 8vo (236x156 mm), x, 257, [1] pp. Original publishers cloth, spine rubbed; front endpapers browned, contents otherwise clean. Provenance: the library of the Swiss- American physicist Martin C. Gutzwiller, who studied quantum physics under Wolfgang Pauli at the ETH Zurich and who is best known for his work on chaotic systems in classical and quantum mechanics. Good copy. (#001968) € 1,900 DSB XVII, pp.224-233. FIRST EDITION "Dirac was one of the greatest theoretical physicists in the twentieth century. He is best known for his important and elegant contributions to the formulation of quantum mechanics; for his quantum theory of the emission and absorption of radiation, which inaugurated quantum electrodynamics...Present expositions of quantum mechanics largely rely on his masterpiece The Principles of Quantum Mechanics" (DSB). Dirac received the Nobel prize for physics in 1933 together with Schrödinger.

The editio princeps in Greek of Euclid's elements

11 EUCLID. Stoicheion bibl. XV ek ton theonos synoysion. Proklou bibl. IV. (Elementa geometriae cum commento Procli. Graece ed. S. Grynaeus). 2 parts in 1 vol. Basel: Johannes Herwagen, September 1533. Folio (307x205 mm). [12], 1-268, 1-115 [1] pp. With numerous woodcut diagrams printed in text, register and colophon on K4r, woodcut printer's device on K4v and title, decorative woodcut border on p.1. 17th century full flexible vellum (soiled, little bumped), spine titled in script. Internally fresh with only very minor occasional spotting, title page with old ownership inscription (Jesuit collegium), an unobtrusive repair at top gutter not affecting text and a slight diagonal crease. A very fine, unusually wide- margined copy, free of markings or stamps. (#001965) € 27,000

Adams E 890; Norman 730; Thomas-Stanford 7

Editio princeps in Greek of Euclid's Elements, one of the great books in the history of the exact sciences. This is also the first Euclid to have the diagrams inset in the text. The Greek text was edited by Protestant theologian Simon Grynaeus, professor of Greek at Basel University. Grynaeus used two manuscripts - one sent by Lazarus Bayfius from Venice and the other supplied by John Claymond, president of Magdalen and later of Corpus Christi College, Oxford. The Elements occupy 268 pages, followed by 115 pages containing the four books of the commentary on the first book of the Elements by the brilliant fifth-century neoplatonist mathematician and astronomer Proclus. 'Because of his interest in the principles underlying mathematical thought and their relation to ultimate mathematical principles, Proclus’ commentary is a notable - and also the earliest -contribution to the history of mathematics. Its numerous references to the views of Euclid’s predecessors and successors, many of them otherwise unknown to us, render it an invaluable source for the history of science' (DSB).

12 EULER, Leonhard. Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. St. Petersburg: Acadamiae Imperialis Scientiarum [i.e. Berlin: Michaelis], 1755. 4to (250x203 mm), xxiv, 880 pp. Later half calf over marbled boards, spine with gilt-lettered morocco label, red-dyed edges. Text with even light browning, little occasional spotting and foxing. A fine, wide-margined copy. (#002020) € 7,800

Norman 733; DSB IV, 476; Smith I, 522, 1; Honeyman 1069; Sotheran 7686; Rouse Ball 396

First edition of the second of Euler's monumental trilogy on analysis. "This is the first text-book on the differential calculus which has any claim to be regarded as complete, and it may be said that until recently many modern treatises on the subject are based on it." (W. W. Rouse Ball, A Short Account of the History of Mathematics).

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 8 of 24 13 FOURIER, Jean Baptiste Joseph. Théorie Analytique de la Chaleur. Paris: Firmin-Didot, 1822. 4to (254x200 mm). [4], xxii, 639 [1] pp., including half title and two engraved plates at end. Contemporary half leather over marbled boards, spine lettered and decorated in gilt (spine very little rubbed, head of spine chipped), endpapers and cut edges marbled. Internally clean and unmarked with only very minor age-toning to few leaves and very little spotting in places, small brown spot to half title and title page. A clean, crisp and well-margined copy of a milestone work in mathematics. (#002022) on hold

Dibner 154; Sparrow 68; Norman 824; DSB V, pp. 93-99; Bibliotheca Mechanica, p.118; En Français dans le Texte 232; Honeyman 1358; Evans 37

FIRST EDITION of the first mathematical study of heat diffusion, originally presented as a paper to the Academie des Sciences in 1807. Fourier showed that heat diffusion was subject to simple observable physical constants that could be expressed mathematically. While Galileo and Newton had revolutionized the study of nature by discerning mathematical laws in the movement of solids and fluids, this approach had not been satisfactorily applied to the study of heat before Fourier. His work had major repercussions for the development of both physics and pure mathematics: first, he extended the range of rational mechanics beyond the fields defined in Newton's Principia, establishing an essential branch of modern physics. Secondly, his invention of unprecedentedly powerful mathematical tools for the solution of equations "raised problems in mathematical analysis that motivated much of the leading work in that field for the rest of the century and beyond" (DSB).

"Fourier's most celebrated work in which he succeeded in putting the science of heat on an analytical or mathematical basis" (Honeyman).

"Fourier's application of new methods of mathematical analysis to the study of heat extended rational mechanics to fields outside of those defined in Newton's Principia, enabling the systematization of a wide range of phenomena. To further his study of heat, Fourier introduced the Fourier series and Fourier integrals." (Norman).

"Fourier's methods find their widest application to problems of vibration such as in heat, sound and in fluid motion" (Dibner).

14 GALILEI, Galileo. Opere. In questa nuova editione insieme raccolte, e di varii Trattati dell'istesso Autore non piu Stampati accresciute. Bologna: heirs of Evangelist Dozza, 1655-1656. 4to (228x165 mm); [22], 29-32, [2], 1-48; [8], 1-160; [4], 1-68; [2] 3-48; [2] 3-43 [1]; [2] 3-264 pp. [2], [1] 2-48; [2] 3-60; [2], 53- 106; [2], 103-126; [3] 4-7 [1], 1-105, [3], 105-156; [4], 1-127 [1]; [8], 1-179 [1]; [8], 1-238 [i.e. 242], [6] pp. Including half- titles, divisional titles to each part,allegorical frontispiece by Stefano Della Bella, engraved portrait of Galileo by F. Villamoena, double-page engraved plate, numerous woodcut illustrations and diagrams in text. Without the first blank in second volume. Paper repairs of a few mm to upper margin of some leaves and repaired tear to inner gutter of portrait (without loss) in first volume; second volume with tear and small hole in O2 affecting one letter and with paper restoration to torn lower corners of F2, T2 and V2 not affecting text, very little occasional spotting and light age- toning. Contemporary full vellum with title in script to spine (spine browned, boards spotted and soiled, some wear to

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 9 of 24 extremities, repair to inner hinges with new endpapers laid down to inner boards, some leaves reinforced at gutter). Illegible ownership inscriptions to title of first volume and half title of second volume. A fine, clean copy with ample margins in original binding. Complete set of all 17 works as called for by Cinti.(#001999) € 13,500 Cinti 132; Riccardi I, 518; Houzeau -Lancaster I, 3386; Honeyman 1418; Roller -G. I, 433; Wellcome III, 83 First and rare edition of Galileo's collected works, edited by Carlo Manolessi and dedicated to Grand Duke Ferdinand II. According to Riccardi it contains a number of pieces here published for the first time. Most of these are letters to various friends and opponents, discussing questions raised by his published works. Both The Dialogo and Letter to Christiana are listed on the index 'librorum prohibitorum' and were thus not included in the Opere. Copies as here with all parts listed by Cinti, are very rare, because the first buyer arranged the selection of parts as he desired. Content: Vol. 1: 1. Lettera di Maffeo Barberini sequita dalla Advlatio perniciosa; Le operationi, del compasso geometrico e militare di Galileo Galilei; 2. Usus et fabrica circini cuiusdam proportionis, per quem omnia ... problemata facili negotio resoluuntur. Ppera et studio Balthasaris Capre... explicata; 3. Difesa di Galileo Galilei... Contro alle calunie & imposture di Baldessar Capra...; 4. Discorso... intorno alle cose, e s anno s l a qua, e in quella si muouono. Di Galileo Galilei...; 5. nno a oni di a a erna eri si so r ns rumen o delle proportioni del sig. Galileo Galilei; 6. Della scienza mechanic ... o[n]pera del signor Galileo Galilei ... La bilancetta del signore Galileo Galilei...; 7. is orso a olo e o di odo i o dell olombe, d in orno al is orso del alileo allei, ir a le ose, e s anno s l'acqua... Vol. 2: 8. De tribus cometis anni M. DC. XVIII, disputatio astronomica...; 9. Discorso delle comete di Mario Guiducci; 10. Sydereus nuncius magna, longeque admirabilia specula pandens...; 11. Continuatione del Nuntio sidereo di Galileo Galilei linceo...; 12. Lettera al... Tarquinio Galluzzi,... di Mario Guiducci...; 13. Lettere del sig. Galileo Galilei al padre Christoforo Grienberger,...; 14. Istoria e dimostrationi intorno alle macchie solari e loro accidenti...; 15. Risposta alle oppositioni del sig. Lodovico delle Columbe e del sig. Vincenzo di Gratia, contro al trattato del si alileo, alelei, dell ose e s anno s l'acqua...; 16. Il Saggiatore... dal signor Galileo Galilei; Discorsi e Dimostrationi matematiche...; 17. Discorsi, e dimostrationi matematiche ... del signor Galileo Galilei.

15 GALILEI, Galileo. Dialogo sopra i due massimi sistemi del mondo Tolemaico, e Copernicano. In questa seconda impressione accresciuto di una lettera e di vari trattati di piu autori. Florence [but Naples], sine nomine, 1710. 4to (247x176 mm). Two parts in one volume. [12], 458, [30] pp.; [2], 83 (i.e. 81), [1] pp. Edited by Lorenzo Ciccarelli (under pseudonym ‘Cellenio Zacclori’), and dedicated to Carlo Caraffa-Paceco, Duke of Maddaloni. Text in single column, mainly in Italic type, with printed marginalia in Roman type. The first title-page printed in red and black with a large fine engraved vignette, the second title-page with a woodcut vignette. Illustrated with numerous astronomical and geometrical diagrams in text. Several woodcut tail-pieces and initials.Contemporary (early 18th- century) full vellum over boards, sympathetically rebacked in vellum in 19th century. Boards slightly rubbed and somewhat bowed Flat spine ruled and lettered in gilt; edges mottled rather pleasingly in red and olive-green. Top fore-corner of the front board worn through and a bit defective (causing a short tear to pastedown). Interior very fresh, crisp and bright, with just a bit of toning to a few leaves, and a few leaves with very minor marginal soiling. Just a hint of very light dampstain to upper margin (near top edge) of a few leaves. Provenance: 18th-century armorial bookplate of William Murray of Touchadam (county Stirling, Scotland), a member of an old aristocratic Scottish family, which was seated for centuries in the county of Stirling, and is supposed

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 10 of 24 to derive from the noble house of Bothwel. In all an attractive, clean and wide-margined example of this scarce and important edition. (#001990) € 8,900

Carli 413; Cinti 168; Gamba 476; Riccardi I, 512; Rocco di Torrepadula, Bibl. Galileiana,168; Waller, Bib. Walleriana, 12044; cf. Printing and the Mind of Man 128 (1st edition)

The beautifully printed Second Edition of the original Italian text of GALILEO'S CELEBRATED "DIALOGUE CONCERNING THE TWO CHIEF WORLD SYSTEMS." A LANDMARK OF SCIENCE: THE SUMMATION OF GALILEO'S IDEAS, AND HIS CELEBRATED DEFENSE OF THE COPERNICAN VIEW OF THE SOLAR SYSTEM! This is the book that, "more than any other work, made the heliocentric system a commonplace." (PMM). The first edition was placed on the Index of Forbidden Books immediately after publication in 1632. No subsequent Italian edition followed until this 1710 edition, published clandestinely in Naples. The printing was unlicensed (hence the false imprint and anonymous printer). The banned Dialogo was omitted from both the first and the second collected editions of Galileo's works in Italian (Opere), which appeared in Bologna in 1655-6, and Florence in 1718, respectively. This 1710 edition of the Dialogo is particularly important as it contains a valuable collection of additional texts including the first Italian printing of Galileo’s famous Letter to the Grand Duchess of Tuscany, Christina of Lorraine (with a separate title page and separate pagination). It was written in 1615, but, due to the Inquisition's condemnation of Galileo, remained unpublished (circulating in manuscript only) until much later. Prior to this 1710 Naples printing it appeared only once: in Strasbourg in 1636 (with the Italian text parallel with a Latin translation). The letter contains Galileo's influential argument for the biblical orthodoxy of Copernicanism and his defense of the independence of science from religion. Also included in this edition is Paolo Foscarini's Lettera sopra l'opinione de' Pittagorici, e del Copernico. Della mobilita de la terra, e stabilita del sole, e del nuovo Pittagorico sistema del mondo, first printed in Naples in 1615. This was the first Italian work to openly advocate the Copernican theory. The Foscarini's Lettera was condemned by the Inquisition, the printer imprisoned, and all known copies confiscated and burned, in 1616. The 1616 Inquisition edict was invoked when Galileo published the Dialogo in 1632. The further texts included in this edition are an excerpt from Kepler's preface to his Astronomia nova (1609), as well as the Inquisition’s sentence against Galileo and his abjuration.

Galilei's epoch-making Dialogo sopra i due massimi sistemi "was designed both as an appeal to the great public and as an escape from silence. In the form of an open discussion between three friends - intellectually speaking, a radical, a conservative, and an agnostic - it is a masterly polemic for the new science. It displays all the great discoveries in the heavens which the ancients had ignored; it inveighs against the sterility, willfulness, and ignorance of those who defend their systems; it revels in the simplicity of Copernican thought and, above all, it teaches that the movement of the earth makes sense in philosophy, that is, in physics. Astronomy and the science of motion, rightly understood, says Galileo, are hand in glove. There is no need to fear that the earth's rotation will cause it to fly to pieces. So Galileo picked up one thread that led straight to Newton. The Dialogo, far more than any other work, made the heliocentric system a commonplace." (Printing and the Mind of Man, 128)

Galileo's formal use of the dialogue format allowed him to explore his Copernican theories fully within the rubric of the "equal and impartial discussion" required by Pope Urban VIII. The book is structured as a series of discussions, over a span of four days, among two philosophers and a layman: Salviati argues for the Copernican position and presents some of Galileo's views directly. He is named after Galileo's friend Filippo Salviati. Simplicio, a dedicated follower of Ptolemy and Aristotle, presents the traditional views and the arguments against the Copernican position. He is named after Simplicius of Cilicia, a sixth-century commentator on Aristotle, but modeled on two contemporary conservative philosophers, Ludovico delle Colombe, Galileo's fiercest detractor, and Cesare Cremonini, a Paduan colleague who had refused to look through the telescope. Sagredo is an intelligent layman who is initially neutral. He is named after Galileo's friend Giovanni Francesco Sagredo.

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 11 of 24 The first edition of the Dialogo was printed in 1632 in Florence with formal authorization from the Inquisition for a book which would present a "balanced" view of both Copernican's and church's theories. However, it was perceived that in the book, the Copernican theory clearly receives better treatment. Pope Urban VIII had been under attack by Spanish cardinals for being too tolerant of heretics, and although he encouraged Galileo to publish the Dialogo, he felt that his position would have been severely compromised if his enemies among the Cardinal Inquisitors had found out that he had been guilty of supporting a publication containing heretical views. And so, in 1633 Galileo was ordered to Rome to stand trial by the Inquisition on suspicion of heresy, "for holding as true the false doctrine taught by some that the sun is the center of the world." He was ordered imprisoned, although the sentence was later commuted to permanent house arrest, the Dialogo was banned and withdrawn from circulation, and the printing of any of his works was forbidden. In fact, the Dialogo remained on the Index of Forbidden Books until 1832.

The preliminaries include the editor's dedicatory preface (dated 17 October 1710), Galileo's original dedication to the Grand Duke of Tuscany, and Galileo's original short preface "Al discreto lettore". The text of the Dialogo followed by an extensive index (of [30] unnumbered pages). The second part (with a separate title-page) contains: "Lettera del signor Galileo Galilei [...] scritta alla granduchessa di Toscana " (pp. 1-35); "Lettera del R.P.M. Paolo-Antonio Foscarini [...] sopra l'opinione de' Pittagorici, e del Copernico..." (pp. 36-68); "Perioche ex introductione in Martem Joannis Kepleri" (pp.69-74); "Excerptum ex Didaci à Stunica [...] commentariis in Job..." (pp.74-76); "Sententia cardinalium in Galilaeum" (pp.76-80) and "Abjuratio Galilaei" (pp.80-81), the last two texts are in Latin.

16 KIRCHER, Athanasius. Physiologia Experimentalis, qua Summa Argumentorum Multitudine & Varietate Naturalium rerum scientia per experimenta Physica, Mathematica, Medica, Chymica, Musica, Magnetica, Mechanica comprobatur atque stabilitur. Extraxit, &... redegit... Joannes Stephanus Kestlerus. Amsteram: Jansson-Waesberge, 1680. Folio (373x247 mm). [8], 248, [8] pp., including additional engraved allegorical title, seven copper engravings and numerous woodcuts within text. 19th-c three- quarter vellum, spine with printed title (extremities and boards somewhat rubbed). Minor spotting and even light browning throughout. Provenance: Marcel Bekus (ex-libris to front pastedown and small ink stamp to title verso). A fine, unstained copy with ample margins. (#001966) on hold

Garrison-Morton 580, Caillet 5796; Honeyman 1834; Dunnhaupt III, 2348, 34; Krivatsy 6404; Waller 10869; Wellcome III, p.396

FIRST EDITION of this selection from Kircher's voluminous works "which includes the first recorded experiment in hypnotism in animals" (Garrison-M 580). The range of subjects covered encompasses the entire spectrum of his researches, such as astronomy, optics (laterna magica), magnetism, air pressure, harmonics, sundials or waterpipes. Johann Stephan Kestler, the editor, was Kircher's pupil and as Kircher died the year this book was published, it is uncertain to what degree he was involved in its production.

17 LACROIX, Charles-Casimir-Sévère. Leçons de géométrie appliquée aux arts, professées a Versailles. Manuscript, Versailles, 1840. Folio, 244 pp. Script in black ink on plain paper, numerous geometric drawings in ink at inner margin. Contemporary half green calf with spine lettered and decorated in gilt. (#002029) € 4,500

Original book manuscript in a neat hand for the second edition of the Lecons, which was published in 1841 by Dufaure. Lacroix (1795-1875) was professor of applied geometry at Versailles.

18 L'HOSPITAL, Guillaume Francois Antoine, Marquis de. Traite analytique des sections coniques et de leur usage pour la resolution des equations dans les problêmes tant déterminez qu'indéterminez. Paris: Jean Boudot et fils, 1707. 4to (245x188 mm). [6], 459, [3] pp., engraved title vignette, intials and head-pieces, 33 engraved plates of which 32 are folding and numbered. Contemporary mottled calf, spine richly gilt with later red morocco label (hinges and spine skillfully restored), marbled edges, later endpapers. Text leaves slightly browned and very little dust soiled at outer margins, small wormhole to upper corner of first few leaves not affecting text, plate 10 little frayed at outer margin, faint ink spot to plate 21, little dampstain to upper corner of plate 13. Provenance: presentation inscription of Jean Rudolphe Perronet to title verso with engraved portrait of the same tipped-in after. A fine copy in attractive binding. Collated complete. (#002018) € 2,200

DSB VIII, p.304; Poggendorff I, 1146

FIRST EDITION. L'Hospital's great analysis of conic sections, intended as a sequel to his Analyse des Infiniment Petits, and published posthumously.

Jean Rudolphe Perronet (1708-1794) was head of the Corps des Ponts et Chaussées and Premier Ingéneur du Roi. The inscription states that this copy is given as second prize in examinations at the École Royale des Ponts et Chaussées, 4 June 1785.

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 13 of 24 19 MACLAURIN, Colin. A Treatise of Fluxions. 2 volumes. Edinburgh: T.W. and T. Ruddimans, 1742. 4to (222x172 mm). Vol. I: [6], vi, 1-412 pp., including half-title and 25 folding engraved plates. Vol. II: [2], 413-763 [1] pp. and 16 folding engraved plates. Contemporary calf, red morocco labels to spines (binding a little rubbed and bumped, vol. 1 foot of spine damaged, hinges cracked but firm). Internally only very little browned, text of vol. II with faint dampstaining, contemporary ink inscription to vol. I title and p.50, library and withdrawal stamps "Bibliotheca Coll. Nov. Edinensis" to foot of titles. Provenance: John Sprat Rainier (1777-1822), Rear Admiral of the Royal Navy. (#002019) € 5,800

Norman 1408; DSB VIII, p.610; Honeyman 2084.

FIRST EDITION. Written as a staunch defence of Newton, and described as "the earliest logical and systematic publication of the Newtonian methods", this work was written in reply to Bishop George Berkeley's The Analyst. A letter addressed to an infidel mathematician of 1734. This latter work, which derided Newton's conception of "prime and ultimate ratios", was addressed to Halley who had steered the first edition of the Principia through the press. In his preface to the Treatise, MacLaurin lays out his reasons for defending Newton and his methods. This work is otherwise noteworthy for the solution of a great number of problems in geometry, statics and the theory of attractions, and elaborations of many of the principles described by Newton in the Principia. It stood as a model of rigor until the appearance of Cauchy’s Cours d’Analyse in 1821 (DSB).

20 MERSENNE, Marin. Novarum observationum physico-mathematicarum fr. Marinii Mersenni tomus III. quibus accessit Aristarchus Samius de mundi systemate. Paris: Antonii Bertier, 1647. 4to (230x171 mm). [32], 62, [2], 63-235, [3] pp. Woodcut vignette to title, several woodcut diagrams, head-pieces and initials in text. Errata on leaves 2G3v and 2G4r; [2] pp. containing an index to Aristarchus inserted following p. 62. Divisional half-title page "Aristarchii Samii De mundi systemate ... Adiectae sunt AE.P. de Roberual ... notae ... Editio secunda correctior" on leaf õ3r. 18th-c mottled calf with 5 raised bands gilt in compartments (extremities and boards rubbed, corners bumped and chipped, old shelf mark paper label to spine), red-dyed edges. Title page soiled and browned with erased stamp (paper restored) and shelf number A.142.4 in ink, text only mildly toned throughout, small dampstaining to upper corner. A fine copy. (#001986) € 8,600

Brunet III, 1662; Sotheran II, 11782; Honeyman 2217; Sotheby's Macclesfield Cat. V, 1374.

The very rare supplement in first edition to Mersenne's Cogitata physico-mathematica and Universae geometriae mixtaeque mathematicae synopsis, which form vols. 1 and 2 of the series published in 1644. This 3rd volume is a collection of essays concerning mechanics, pneumatics, hydrostatics, navigation, the techniques for establishing weights and measures and an examination of Aristarchus' heliocentric theory. As one of the most fascinating intellectual figures of the seventeenth century, Mersenne is well known for his relationships with many outstanding contemporary scholars as well as for his friendship with Descartes. Moreover, his own contributions to natural philosophy have an interest of their own. Mersenne worked on the main scientific questions debated in his time, such as the law of free fall, the principles of Galileo's mechanics, the law of refraction, the propagation of light, the vacuum problem, the hydrostatic paradox, and the Copernican hypothesis. Mersenne contributed to spread

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 14 of 24 Galileo's writings in France as well as the ideas of thinkers such as Hobbes and Roberval. He dealt with almost every one of the mixed and pure mathematical sciences and first collected a number of treatises on geometry and mixed mathematics in the two editions of his Synopsis (Synopsis Mathematica, 1626; Universae geometriae synopsis, 1644). He composed several treatises on music (Traité de l'harmonie universelle, 1627; Questions harmoniques, 1634; Les preludes de l'harmonie universelle, 1634; Harmonie universelle, 1636; Harmonicorum libri XII, 1648) and optics (De Natura lucis, 1623; Opticae, 1644; L'Optique et la catoptrique, 1651). (Malet and Cozzoli, Mersenne and Mixed Mathematics, 2010, pp.1-8). Whereas the first two volumes of this series are fairly well represented in libraries, this third volume is of considerable rarity. Only one copy of this volume has appeared at auction in the past 30 years (the Macclesfield copy).

21 NEWTON, Isaac. Analysis per Quantitatum Series, Fluxiones ac Differentias cum enumeratione Linearum tertii ordinis. [bound after] Philosophia naturalis principia mathematica. Auctore Isaaco Newtono, Equite Aurato. Editio Ultima. Cui accedit. Amstalodami: Sumptibus Societatis, 1723. 4to (248 x 193 mm); 2 parts in 1 volume, [26], 484, [8]; [12], 107, [1] pp. Title pages with vignettes (of the first part printed in red and black), 3 engraved folding plates, many tables in the text. Contemporary full leather, spined with gilt morocco label and 5 raised bands richly gilt in compartments (hinges strengthened, upper and lower spine repaired, extremities worn, corners bumped), red-dyed edges, marbled endpapers. Internally only little browned, very minor occasional spotting and soiling. Very good, internally fresh and wide margined copy of a rare edition. (#001941) € 5,800

Gray 12; Wallis 12, Sotheran, Second Supplement I, 5672

The reprint of the second Amsterdam edition and the only one containing (with a separate title and separate pagination) the Quantitatum Analysis Series. The second edition was edited by Roger Cotes and brought out with the assistance of Richard Bentley, Master of Trinity College, with a new preface by Cotes: "In his important preface, Cotes attacks the Cartesian philosophy, then still in vogue in the universities, and refutes an assertion that Newton's theory of attraction is a causa occulta." The second edition also contains a revised conclusion, "a second preface by Newton and considerable additions, the chapters on the lunar theory and the theory of comets being much enlarged" (Babson). This Amsterdam reprint corrects a few errors made in the printing of the second edition and precedes the third edition by twelve years.

Large paper copy of the important third edition

22 NEWTON, Isaac. Philosophiae naturalis principia mathematica. Editio tertia aucta & emendata. London: Apud Guil. & Joh. Innys, 1726. LARGE PAPER COPY. 4to (282x222 mm), [36], 530, [8] pp., including half-title, engraved frontispiece portrait by George Vertue facing title, dedication leaf, Halley's commendatory verse leaf, privilege leaf, ad leaf at end; numerous woodcut diagrams and the engraving on p. 506. Contemporary full calf, spine with 5 raised bands richly gilt in compartments, morocco letting piece (extremities worn, spine ends chipped, covers rubbed), sprinkled edges, illegible signatures to first two fly leaves. Very minor occasional spotting and marginal soiling, portrait frontispiece somewhat browned and foxed, paper flaw to fore-margin of Rrr1-2, pages 225 to 232 misbound after p.240, index leaf 3y4 re-attached, closed tear at gutter of leaves Yyy1-4. An outstanding, clean and bright copy. (#002023) € 32,000

PMM 161 (describing the first edition); Babson 13; Gray 9; Wallis 9; Todd E3(2); HBS 64483

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 15 of 24 The stated third edition, this one of the 200 large-paper copies on "Writing Royal Paper" with the "CC" watermark. According to W.B.Todd, Bibliography of the Principia, p.855, this is the second impression, determined by the progressive wearing of type fractures and dislocations. The Babson catalogue notes that the license leaf had no assigned signature location, and is found at various places in copies of the regular edition. This edition was the last published during the author's lifetime and is the basis for all subsequent editions. The editor was Henry Pemberton, M.D., F.R.S., and this rescension of the text contains a new preface by Newton and a large number of alterations. The most important of these is in the scholium on fluxions, in which Leibnitz had been mentioned by name in the earlier editions. His name is absent here, leading to claims that Newton was avoiding sharing credit for the development of calculus with his Continental rival.

23 NEWTON, Isaac. Arithmetica universalis; sive de compositione et resolutione arithmetica liber [edited by W.J.S. van s'Gravesande]. Leiden: Joh. and Herm. Verbeek, 1732. 4to (247x193 mm.), [8], 344 pp., including title-page with engraved device, printed in red and black and 13 folding engraved plates. Contemporary calf (board corners, hinges and spine ends restored, boards cratched and rubbed). Provenance: Ticket of S. Kearney, bookseller to front pastedown, old inscription "John Seymoure" to title page. Little occasional spotting and browning to text and plates, a few ink stains and annotations in pencil. Good copy. (#001967) € 1,700

Babson 204; Wallis 279; Honeyman 2330.

Third latin edition, published of Newton's lectures on algebraic notation, arithmetic, the relationship between geometry and algebra, and the solutions of polynominal equations delivered while Lucasian Professor of Mathematics at Cambridge University (1669-1702). The first edition was edited by Newton's successor in the Chair, William Whiston, from Newton's manuscript notes. Newton objected to Whiston's publication, principally to the running titles "Algebrae"

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 16 of 24 (versos) and "Elementa" (rectos), refused to have his name appear in association with the book, and threatened to buy up the entire edition in order to destroy it. When he published his own edition in 1722 (the second edition), he altered the running titles, omitted Halley's section on finding the roots of equations, and made greater use of italic type. The third edition was edited by s'Gravesande and also contains works by Halley, Colson, de Moivre, MacLaurin and Campbell, all previously published in the Philosophical Transactions and translated into Latin by J.P. Bernard. The Lucasian Chair of Mathematics is one of the oldest and arguably the most famous academic chair of mathematics in the world. Isaac Newton was the second incumbent, holding the post from 1669-1702, Professor Stephen Hawking is the current Lucasian Professor, having held the position since 1980.

24 PETAU, Denis. Uranologion; sive, Systema variorum authorum, qui de sphaera, ac sideribus, eorumque motibus Graecè commentati sunt. Sunt autem horum libri. Omnia vel Graece ac Latine nunc primum edita. Paris: Sébastien Cramoisy, 1630. Folio (345x221 mm), [16], 424, [16], 338, [10] pp., text in Greek and Latin, title printed in red and black with engraved vignette, numerous woodcut text diagrams and letterpress tables. Contemporary plain vellum with yapp edges (short vertical crack near center of spine, hinges cracked, joints and cords sound), blue-dyed edges. Title page lightly damp- wrinkled, with small portion of fore-margin torn and restored touching one letter, occasional browning in second half of volume, final leaf with small hole affecting a letter. Provenance: 19th-century Ricasoli- Firidolfi armorial bookplate on title verso; the library of the Swiss-American physicist Martin C. Gutzwiller. Complete. (#001969) € 2,400

Houzeau-Lancaster 786; Hoffmann III, 350-51; Roller-G. II, 295; De Backer-S. VI, 597, 28; Honeyman 2460

First edition of a collection of ancient and Byzantine Greek astronomical texts, including works by Geminus, Achilles Tatius, Hipparchus, and Claudius Ptolemaeus, and dissertations by Petau on spherical astronomy, the zodiac, calendar systems in antiquity, etc.

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 17 of 24 25 PLANCK, Max. Ueber irreversible Strahlungsvorgänge. Offprint from: Annalen der Physik, vol. 1 (1), 1900, pp. 69-122. Berlin: Johann Ambrosius Barth. 8vo (222x145 mm). Original printed wrapper (little soiling and chipping, ownership inscription to top corner), internally fresh and unmarked. Presentation copy ("Überreicht vom Verfasser"). (#001952) on hold

The rare offprint version of the first edition of a milestone paper by Planck. A summarization of Planck's five-part series on irreversible radiation processes, published between 1897 and 1899, submitted to the Annalen der Physik in November 1899, and published early in 1900.

26 PLANCK, Max. Ueber die Natur des weissen Lichtes. Offprint from: Annalen der Physik, vol. 7, 1902, pp. 390-400. Berlin: Johann Ambrosius Barth. 8vo (223x145 mm). Original printed wrapper (little soiling and chipping, ownership inscription to top corner), internally fresh and unmarked. Presentation copy ("Überreicht vom Verfasser"). (#001954) € 300

Interesting association copy, presented to Sylvestre Francois Lacroix

27 POISSON, Siméon-Denis. moire sur la ro or on des naissan es des lles e des ar ons ar oisson u l ad mie, le rier 1829. Paris: Didot, [1829]. 4to (270x207 mm). [2], [1] 2- 70 pp. 20th-c marbled paper boards, gilt morocco lettering piece to spine, text spotted (first and last pages stronger), first page folded in at lower margin. Provenance: Sylvestre Francois Lacroix (1765-1843), French mathematician. Dedication by Poisson in black ink to title page "A Monsieur Lacroix de la part de l'auteur" and a few annotations in black ink by Lacroix. (#001974) € 4,400

Exceedingly rare offprint of Poissons important tratise on population statistics which was published in vol. 9 of the moires de l ad mie oyale des ien es de l'Institut de France, 1830. Poisson here reformulates Laplace's analysis of the error dispersion for distribution of the sexes at birth. Poisson gave a reading of his paper before an assembly of the Academy. With this and two other papers by Poisson published in 1835 and 1837, the mathematician rescued the analytical theory of probabilities from the singularity of its first Laplacian expression. They led Poisson to what he called the "law of large numbers" (E.Brian & M.Jaisson, The Descent of Human Sex Ratio at Birth, 2007, pp.44-50). Only two copies of this offprint recorded in COPAC and WorldCat (Ushaw College, Durham and Berlin State Library).

28 SCHWARZSCHILD, Karl. Zur Quantenhypothese. Offprint from: Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, vol. 25, 1916, pp. 548-568. 4to (251x178 mm). Original printed wrappers (very little soiling, ex-libris "Christian Heuer" to inner cover), internally fresh and unmarked. Presentation copy ("Überreicht vom Verfasser"). (#001979) € 300

Schwarzschilds last paper during his lifetime, "an attempt to enlarge upon several recent papers on the quantum theory written by Planck and by Sommerfeld. This subject, Schwarzschild said, awaits a Kepler - but he did not live to see who it would be." (DSB, XII, 251-2).

29 SOMERVILLE, Mary. Mechanism of the Heavens. London: John Murray, 1831. 8vo (222x145 mm). lxx, 621, [3] pp., with numerous diagrams in text, index and errara leaves at the end. Original green cloth with printed label to spine (spine ends bumped, rubbed, hinges repaired), leaves untrimmed. Text with occasional light soiling, slight spotting to title and endpapers, very little age-toning, a few leaves chipped or frayed at outer margins, a few small closed tears, bookplate to upper pastedown. Good copy. (#002021) € 1,700

DSB XII, p.524; Poggendorff I, 957

Scarce first edition (limited to 750 copies) of the author's first work, which is an English version of Laplace's Mecanique Celeste (1798-1827) for which she rewrote Laplace’s text and added full mathematical explanations and diagrams.

"Mary Somerville was the first woman scientist to win an international reputation entirely in her own right rather than by working in association with a father, husband, or brother. Self-educated in mathematics and astronomy, she wrote many textbooks dealing with celestial mechanics, geography, and the sciences in general" (BEA, p.1072).

Somerville's "books were remarkably influential... [and] provided definition and shape for an impressive spread of scientific work" (DNB).

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 19 of 24 "In 1827 Henry Brougham wrote William Somerville to ask him to persuade his wife to put Laplace’s Mécanique céleste, which she had studied in Edinburgh, into English for the Library of Brougham’s Society for the Diffusion of Useful Knowledge. Unsure of her ability, she finally gave in to their urgings, provided the manuscript, if unsatisfactory, would be destroyed. A rendition rather than mere translation - since full mathematical explanations and diagrams were added to make Laplace’s work comprehensible to most of its English readers - her treatise when completed in 1830 was too long for the Library series, Somerville, however, submitted it to their great friend J. F. W. Herschel, who urged the publisher John Murray to bring it out. Dubious of the success of a book on such a subject, Murray printed 750 copies in 1831. To his and Mrs. Somerville’s amazement, The Mechanism of the Heavens sold well and won praise for her. It was put to use in advanced courses at Cambridge. Its preface - the necessary mathematical background - was reprinted in 1832 as A Preliminary Dissertation on the Mechanism of the Heavens; both it and the previous volume were immediately pirated in the United States and were used in Britain as textbooks for almost a century. The Royal Society hailed the work by voting to place a portrait bust of Mrs. Somerville in their Great Hall. Acclaim came also from the younger generation of British scientists, including Babbage, Brewster. Buckland, Faraday, Herschel. Lyell Murchison. Sedgwick, and Whewell. who gave her the same unstinting admiration, respect, and assistance their elders had bestowed, regarding her as the spokeswoman for science and offering her honors and opportunities unique for a woman." (DSB XII, p.524).

30 TAYLOR, John. Thesaurarium Mathematicae, Or The Treasury of the Mathematicks. Containing Variety of usefull Practices in Arithmetick, Geometry, Trigonometry, Astronomy, Geography, Navigation and Surveying. As also The Mensuration of Board, Glass, Tiling, Paving, Timber, Stone, and Irregular Solids. Likewise it teacheth the Art of Gauging, Dialling, Fortification, Military-orders, and Gunnery: Explains the Logarithms, Sines, Tangents and Secants: Sheweth their use in Arithmetick, &c. To which is Annexed a Table of 10000 Logarithms, Log-Sines and Log- Tangents. Illustrated with Several Mathematical Sculptures on Copper Plates. London: Printed by J.H. for W. Freeman, 1687. 3 parts in one volume. 8vo (185x115 mm). [20], 1-328, [2], [339] 340-399 [400-402] 403-416 [417] 418-507, [3] pp. including frontispiece portrait by Van Houe, 3 part titles and 8 folding engraved plates. Signatures: pi1, A-X8, Y4, Aa-Kk8, Ll7. Half leather over marbled boards with paper label to spine dated 1868 (little wear to extremities, endpapers renewed). Light age-toning of text and minor spotting in places, some fraying and soiling to fore-edges of plates not affecting image, short tears to plates 3, 6 and 8 outside plate mark, plate 6 misbound before p.217. A fine copy with ample margins. (#002006) € 3,800 Wing T534, ESTC R23734 The rare FIRST EDITION. Among the "Geographical Descriptions" is a section on America, "the fourth part of the world... When the Spanish had entred on America they found the people without Apparel, and their Bread was made from the Jucca-Root, whose juice is a strong poyson: but it being squeezed out and dried it makes bread. They worshiped Devillish Spirits..." (pp.169- 180). Other sections are included on astronomy, navigation, surveying and gunnery. The pagination is continuous throughout (although there are no pages numbered 329-336) but there are separate title-pages: "A table of logarithm numbers", "A table of proprtional parts" and "A table of artificial sines and tangents" on 2A1r, 2E1r and 2F1r, respectively. Advertisements on Ll6v and Ll7r.

31 VARIGNON, Pierre. Elemens de mathematique. Paris: Pierre-Michel Brunet fils, 1731. 4to (252x195 mm), two parts in one volume. [12], 66, 155, [9] pp., including woodcut device on title- page, woodcut initials, head- and tailpieces, 22 folding engraved plates, pages untrimmed. Near contemporary mottled calf, spine gilt in compartments. Some creasing to first pages, large woodcut devices on red-colored by hand, occasional ink stains, text little browned and spotted throughout, a few leaves with scribbling in pencil to text margins and verso of some plates, marginal soiling to text and plates, repaired tear at fore-margin of one plate, light damp-staining to text and plates in places and some paper mould at gutter of text, worm hole to lower gutter affecting a few letters. Still good, wide-margined copy. (#002015) € 750 DSB XIII pp. 584-7; Cantor II, 526-7

FIRST EDITION. "From the papers Varignon left at his death, most of which are now lost, his disciples assembled several posthumous works: Nouvelle mécanique (announced in the Project of 1687) and E lair issemens sur l’analyse des in inimen e i s, both published in 1725, and Élémens de mathématiques (1731), which was based on his courses at the Collège Mazarin." (DSB XIII, p. 585).

Catalogue 01-2014 Copyright © 2014 Milestones of Science Books. All rights reserved Page 21 of 24 32 WING, Vincent. Astronomia Britannica: in qua per novam concinnioremq[ue] methodum hi quinq[ue] tractatus traduntur. I. Logistica astronomia . . . II. Trigonometria . . . III. Doctrina sphaerica . . . IV. Theoria planetarum... V. Tabulae novae astronomicae... cui accessit Observationum astronomicarum synopsis compendiaria... additur Postscriptum de refractione. London: John Macock for George Sawbridge, 1669. Folio (315x200 mm). [20], [2] 3-244, [2]; 192, [2], 193-366, [2], 367-369 [1] pp., including engraved frontispiece portrait of the author, woodcut diagrams, engraved illustration and the blank 3A4. Contemporary panelled calf (extremities worn, spine ends damaged, joints cracked at top and bottom, boards rubbed, corners bumped), gilt morocco label to spine, red- sprinkled edges. Some faint dampstaining in upper inner corners at beginning and end, very little occasional spotting and marginal finger- and dust soiling, few scattered rust holes generally not impairing legibility. Provenance: John Reynolds, student of medicine, astronomy, and astrology (early ownership inscription); 19th-century Jesuit stamps (Acole Sainte-Genevieve, Paris, and Maison Saint- Louis, Jersey) on portrait verso and title; the library of the Swiss-American physicist Martin C. Gutzwiller. A fine, clean copy with ample margins. (#001970) € 6,900 DSB XIV, p.446; Houzeau & Lancaster 9232; Wing W2986 First edition. "Like many astronomers in the second half of the seventeenth century, Wing, following Boulliau and Seth Ward, opted for an 'empty-focus' variant of Kepler's second law, holding that a planet moving in an elliptical orbit describes equal angles in equal times about the focus not occupied by the sun. In works published in 1651 and 1656 Wing, adopting Boulliau's method, had his elliptical orbits, including that of the moon, generated in purely geometrical fashion by circles and epicycles.

In his posthumously published Astronomia Britannica, however, he discarded the epicycles in favour of a refined version of the theory proposed by Ward in the latter's Astronomia geometrica (1656), in which the elliptical orbits were assumed to be physically generated. Wing's celestial mechanics contained a mixture of Cartesian and Keplerian components, with a rotating sun and celestial vortex pushing the planets around in their orbits" (DSB XIV, p.446).

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