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Weidle, Wladimir

Published by Electa Editrice, Milan, Italy (1956)

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From: Saucony Book Shop (Kutztown, PA, U.S.A.)

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About this Item: Electa Editrice, Milan, Italy, 1956. Hardcover. Condition: Near Fine. Dust Jacket Condition: Very Good. 1st Edition. Ivory polished paper covered boards, lettered in gilt. Covers a bit tanned, otherwise nearly as issued. Color pictorial dust jacket shows minor shelf wear, 1/2" closed tear at bottom front corner. 18 pp. + 156 color, b&w plates at rear, folding index leaves. Text in Italian. Size: 12mo - over 6¾" - 7¾" tall. Book. Seller Inventory # 045618

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Weidle

Published by Electa Editrice, Milano (1956)

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From: Ed Buryn Books (Nevada City, CA, U.S.A.)

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About this Item: Electa Editrice, Milano, 1956. Venetian Mosaics, with plates in color and b/w, text in Italian language. Nice bright clean tight copy. 5 x 6-3/4, 18 pp with 5 color plates + 152 glossy b/w plates + several fold-out indexes. Near Fine unmarked, in VeryGood bright jacket. Hardcover in ivory boards w gilt titling & logo, in color illus jacket. No edition stated, assumed 1st printing. Seller Inventory # 18802

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CARLI, Enzo

Published by Electa Editrice, Milano (1951)

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From: Between the Covers-Rare Books, Inc. ABAA (Gloucester City, NJ, U.S.A.)

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About this Item: Electa Editrice, Milano, 1951. Hardcover. Condition: Very Good. Dust Jacket Condition: Very Good. First edition. 16mo. Text in Italian. Very good in very good dustwrapper. Small nicks on dustwrapper spine ends, corners. Please Note: This book has been transferred to Between the Covers from another database and might not be described to our usual standards. Please inquire for more detailed condition information. Seller Inventory # 269369

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Matthaei, Otto

Published by Im Selbstverlag, Berlin (1912)

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From: German Book Center N.A. Inc. (Mountaindale, NY, U.S.A.)

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About this Item: Im Selbstverlag, Berlin, 1912. Trade Paperback. 1. Aufl. 111 Seiten. Umschlag bruechig mit Fehlstellen, auch nachgedunkelt. Papier maessig vergilbt. Widmung auf dem Vorsatz, ueberreicht vom Verfasser, nicht signiert. Size: 8vo - over 7.75 - 9.75" tall. Book. Seller Inventory # 022803

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Bennett, Jim & Domenico Bertoloni Meli

Published by Cambridge: Whipple Museum of the History of Science, 1994 (1994)

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From: Atticus Books (Toronto, ON, Canada)

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About this Item: Cambridge: Whipple Museum of the History of Science, 1994, 1994. Soft cover. Condition: Very Good. No Jacket. 1st Edition. (= GR ). Minor impact damage to the top edge. Digital photo upon request.Heavily illustrated, oversized." An illustrated catalogue produced to coincide with the Museum's 50th anniversary exhibition. Utilising books from the Whipple collection, it deals not only with bibliographical issues and with practical and technical aspects of the astronomy of the time, but also with such things as dedicatory letters, as a reminder of the importance of patronage in astronomical careers of the period.". Seller Inventory # HD439

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Weidle, W

Published by Electa Editrice, Milano (1955)

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From: Simply Read Books (Boat Of Garten, United Kingdom)

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About this Item: Electa Editrice, Milano, 1955. Hardback. Condition: Very Good. No Jacket. 1st Edition. 1955 Electa Editrice first edition hardback, Collection Sphaera series, small format; TEXT IN FRENCH; very good, clean and bright copy, with very good unclipped dj; UK dealer, immediate dispatch. Seller Inventory # 139at33

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Husberg, Christopher:

Published by München. Knaur. (2016)

ISBN 10: 3426519208ISBN 13: 9783426519202

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From: HENNWACK - Berlins größtes Antiquariat (Berlin, Germany)

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About this Item: München. Knaur., 2016. Deutsche Erstausgabe. 8vo. 701 S. OKt. Einband minimal berieben, sonst gut erhalten. Sprache: deutsch. Seller Inventory # 17565EB

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Quaestiones novae in libellum de sphaera Ioannis: Hartmanno Beyer

Hartmanno Beyer

Published by Ex officina Petri Brubachii, Francoforti (1549)

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About this Item: Ex officina Petri Brubachii, Francoforti, 1549. Full-Leather. Condition: Very Good. 1st Edition. An extremely rare work. Johannes Sacrobosco¿s Tractatus de Sphaera, first written around 1230 and first printed around 1472, set the framework for European understanding of astronomy for 400 years. Based on the work of Ptolemy Alfraganus, and using more recent Arabic sources, he presented a vision of the heavens as a series of enveloping spheres. The tables in his work are an almanac relating the 'rising' and 'setting' of celestial spheres with respect to the calendar. As this work presented the stars in terms of constellations, it also became of value to astrologers. In this setting the Earth is also a sphere, at the centre of the universe, around which the spheres of the heavens rotate. It was copied many times in the 15th and 16th centuries - sometimes as a whole text, and sometimes in the form of 'Quaestiones'. This version by Hartmann Beyer is in the latter form. Beyer (1516-1577) was a mathematician, theologian and reformer - much influenced by Martin Luther. This copy is in a recent plain full leather binding with raised bands. The endpapers are new with no signs of previous ownership. Internally with decorative title page (small loss to bottom edge and top corner); Note on the edition with decorative initial capital 11pp; Index 3pp; Questiones with large decorative initial capital - pp1-125 with 'finis'; 3 further pages; errata; repeat of title page motif with some scholarly notes in ink on the reverse. There are 2 diagrams in the text and numerous tables. There are two sets of scholarly annotations - one in red and one in black ink (at one stage doing calculations). The pages are browned and, towards the end, have some nibbled edges but the text is clear and complete. A rare survival. Please enquire if you would like additional images to assess content and condition. Seller Inventory # 031646

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About this Item: Ulm, Wagner [et] Bartholomé, 1679. Couverture rigide. Condition: Très bon. Edition originale. Ulm, Wagner [et] Bartholomé, 1679-1706. Deux ouvrages en 1 volume in-12 de (12) [comprenant le frontispice], 233, (7), pages et 105 planches, puis 61, (1) pages et 5 planches ; vélin de l'époque. Seconde édition, la première ayant paru en 1675, avec le rare supplément de 1706, de cet important et exhaustif traité allemand de gnomonique. Exceptées quelques rares planches avec des auréoles, bon exemplaire dans son vélin d'origine. Peu courant en l'état et avec le supplément. Seller Inventory # ABE-1588051374897

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Uranologion; sive, Systema variorum authorum, qui de: PETAU, Denis

PETAU, Denis

Published by Sébastien Cramoisy, Paris (1630)

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About this Item: Sébastien Cramoisy, Paris, 1630. Hardcover. Condition: Very Good. 1st Edition. 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. ---- 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. Seller Inventory # 001969

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About this Item: Paris, Seb. Cramoisy, 1630. Folio. [x i],424,[4].[xii],338,[9] pp. Half calf (new calf spine underlaid, edges and corners rubbed, first pages marginal waterstain, paper age-toned throughout, some margins slightly frayed, new endpapers, p copy) Parallel greek and latin editions of Geminus' Elementa astronomiae, Ptolemaeus' De apparentiis inerrantium (stellarum), Achilles Tatius' Isagoge ad Arati phaenomena, Hipparchus' Ad Arati et Eudoxi phaenomena, Eratosthenes'Ad Arati phaenomena, Arati genus et vita, Theodorus Gazae Liber de mensibus, Maximus Martyr Brevis ennaratio christiani paschatis (i.e. Computus ecclesiasticus; editio princeps), Isaac Monachus (Computus), Andreas Cretensis' Computus Paschalis (ed.princeps)., et al. Hoffmannn III,350-351 for full contents. Dénis Petau (1583-162), ami de Casaubon, jésuite. "Le roi d'Espagne Philippe IV et le pape Urbain VIIII voulurent l'attirer, l'un à Madrid, l'autre à Rome, et l'on raconte qu'en 1645 un des premiers soins des ambassadeurs polonais fut de se rendre au collège des Jésuites, ou ils entrèrent en criant "Volumus videre clarissimum Petavium". Il fut admiré de son temps , au point qu'on frappa en son honneur une médaille avec ces mots: 'Au prince des chronologistes". NBG.39/689-91. Seller Inventory # 127053

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Opera Geometrica [De sphaera et Solidis Sphaeralibus;: TORRICELLI, Evangelista

TORRICELLI, Evangelista

Published by Amadoro Massa & Lorenzo de Landis, Florence (1644)

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About this Item: Amadoro Massa & Lorenzo de Landis, Florence, 1644. Hardcover. Condition: Fine. 1st Edition. 3 parts in one, 4to. (220x158 mm), [2], [2:blank], [1-2] 3-243 [1], [1-2] 3-115 (i.e. 151) [1] pp., general half-title, part I title with imprint, section titles to parts II & III, dedication to Grand Duke Ferdinand II de' Medici, part III separately signed & paginated with separate dedication to Prince Leopold de' Medici, imprimatur leaf at end, numerous small woodcut diagrams, one full-page engraving, letterpress tables, numerous mispaginations. Internally clean and unspotted, light browning (mainly marginal), contemporary vellum with old ms. mathematical notations on covers. A fine, unsophisticated copy, collated complete. ---- Honeyman VII 2991; Norman 2086; PMM 145; Riccardi II 542; Carli-Favaro 43 (204); Cinti 226 (114). - FIRST EDITION of the only work published during Torricelli's lifetime. A brilliant mathematician, Torricelli was Galileo's assistant and companion during the last two years of the elder scientist's life, and he succeeded Galileo in the post of grand ducal mathematician. In his Opera Geometrica, published at the expense of Grand-Duke Ferdinand II, Torricelli elucidated and diffused the difficult geometry of Cavalieri (see lot 359), thereby gaining himself widespread recognition throughout Europe. The first part, compiled around 1641, 'studies figures arising through rotation of a regular polygon inscribed in or circumscribed about a circle around one of its axes of symmetry. Torricelli. classifies such rotation solids into six kinds, studies their properties, and presents some new propositions and new metrical relations for the round bodies of elementary geometry. As Torricelli acquired increasing familiarity with the method of indivisibles, he reached the point of surpassing the master - as Cavalieri himself said' (DSB). In the second section, De moto gravium, Torricelli continued Galileo's study of the parabolic motion of projectiles. The treatise includes several significant contributions to mechanics, the calculus and ballistics. It also 'refers to the movement of water in a paragraph so important that Ernst Mach proclaimed Torricelli the founder of hydrodynamics' (DSB). This states 'Torricelli's theorem' in which Torricelli determined that the efflux velocity of a jet of liquid spurting from a small hole at the bottom of a vessel is equal to that which a single drop of the liquid would have if it could fall freely in a vacuum from the level of the top of the liquid. Seller Inventory # 001794

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Sphaera Mundi compendium foeliceter inchoat. with Regiomontanus: SACROBOSCO, JOHANNES DE;

SACROBOSCO, JOHANNES DE; REGIOMONTANUS, JOHANNES & PUERBACH, GEORGE VON

Published by Erhard Ratdolt (1482)

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About this Item: Erhard Ratdolt, 1482. Hardcover. Condition: Fine. 1st Edition. Venice: Published by Erhard Ratdolt, 6 July, 1482, 4to, (220 x 160mm) Early panelled calf, 39 woodcut diagrams in the text, 8 are coloured, some minor text restoration, a very attractive copy of this important work. First printing of this assembly of the most influential pre-Copernican texts on astronomy. Sacrobosco's De sphaera mundi (editio princeps 1472) was the first printed astronomical book, and a fundamental text of medieval and post-medieval astronomy. It is a synthesis of Ptolemy and his Arabic commentators, presenting an elegant, accessible Ptolemaic cosmology, and for this reason was adopted as the most authoritative astronomical textbook of its time. From the time of its composition, ca 1220, Sacrobosco's De sphaera 'enjoyed great renown, and from the middle of the thirteenth century it was taught in all the schools of Europe. In the sixteenth century it gained the attention of mathematicians, including Clavius. As late as the seventeenth century it was used as a basic astronomy text. ' (John F. Daly in DSB). It was the most frequently printed astronomical work, some 30 incunable editions alone being published, and an even greater number of sixteenth-century editions. In the final text in this volume, Disputationes contra Cremonensia deliramenta (Arguments against the Errors of [Gerard of] Cremona), Peurbach s student Regiomontanus offers a critique of Gerard s aforementioned Theorica , and demonstrates the superiority of Peurbach s Theoricae novae. Adopting the form of a dialogue between Viennensis (the man from Vienna , representing Regiomontanus) and Cracoviensis ( The one from Krakow , representing Martin Bylica of Ilkusch), Regiomontanus used geometrical proofs, often supplemented by diagrams, to refute specific claims in the earlier Theorica. In the course of his critique, Regiomontanus -renowned for the accuracy of his own predictive tables and calendars- also makes corrections to Gerard s planetary tables.Sacrobosco s Sphere : Sacrobosco s fame rests firmly on his De Sphaera , a work based on Ptolemy and his Arabic commentators, published about 1220 and antedating the Sphaera of Grosseteste. It was quite generally adopted as the fundamental astronomy text, for often it was so clear that it needed little or no explanation. It was first used at the University of Paris. There are four chapters to the work. Chapter one defines a sphere, explains its divisions, including the four elements, and also comments on the heavens and their movements. The revolutions of the heavens are from east to west and their shape is spherical. The earth is a sphere, acting as the middle (or center) of the firmament; it is a mere point in relation to the total firmament and is immobile. Its measurements are also included. Chapter two treats the various circles and their names- the celestial circle, the equinoctial, the movement of the primum mobile with its two parts, the north and south poles, the zodiac, the ecliptic, the colures, the meridian and the horizon, and the Arctic and Antarctic circles. It closes with an explanation of the five zones. Chapter three explains the cosmic, chronic, and heliacal risings and settings of the signs and also their right and oblique ascensions. Explanations are furnished for the variations in the length of days in different global zones namely the equator, and in zones extending from the equator to the two poles. A discussion of the seven climes ends the chapter. The movement of the sun and other planets and the causes of lunar and solar eclipses form the brief fourth chapter. (Dictionary of Scientific Biography). BMC V 286; Goff J405; Hain-Copinger 14110; Klebs 874.9; Sander 6661. Seller Inventory # 318

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Sphaera mundi seu Cosmographia, demonstrativa ac facili: BIANCANI, Giuseppe [Josephus
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About this Item: Sebastiano Bonomi for Geronimo Tamburini, Bologna, 1620. Hardcover. First edition. JESUIT TEXTBOOK OF ASTRONOMY INCORPORATING THE DISCOVERIES OF GALILEO AND KEPLER. First edition of Biancani's rare Jesuit treatise on astronomy which "brought Clavius's Sphaera up to date, incorporating in it the discoveries of Galileo, Kepler, and others, and enthusiastically endorsed the advances being made in astronomy . [Biancani] defended Galileo's stand regarding mountains on the moon-which elicited a long letter from Galileo to another Jesuit astronomer, Christopher Grienberger, in which Galileo states that he is "infinitely obliged" to Biancani. Unfortunately this student of Clavius got too enthusiastic in Galileo's cause, and his remaining writings were never passed for publication by the censors of his Order" (Wallace 2003, pp. 108-9). "In 1620 there appeared an important treatise on astronomy which consistently and repeatedly used the word telescope. This was the Sphaera mundi of Josephus Blancanus, or Giuseppe Biancani . [He] was the first to employ exclusively and repeatedly the term 'telescope' in an extended treatise. More importantly, however, is the fact that his example and influence undoubtedly hastened general acceptance and use of the term" (McColley, pp. 364-5). "In present-day literature [Biancani] is sometimes depicted as an opponent of Galileo and the new science, but his exchanges in the unpublished sources with several Jesuit censors over his two main books show that quite the opposite was the case. These documents clearly reveal a split within the Jesuits at that time between the philosophers of orthodox Aristotelian persuasion and a group of mathematicians and astronomers, including Biancani, who advocated the autonomy of astronomy and mathematics and a more quantitative and descriptive approach, which resulted in some quite anti-Aristotelian views. Thus although he disputed some of Galileo's calculations, Biancani agreed that the surface of the Moon was mountainous and not a smooth sphere; he also maintained that the heavens were composed of fluid matter, not solid spheres, another anti-Aristotelian view" (Blackwell, pp. 148-9). Blackwell even sees Biancani's book as precipitating, via Grienberger's support, "the beginning of the end of classical Jesuit science" (p. 152). Biancani was perhaps the first to suggest, in this book, that comets may return (Thorndike VII, p. 51). The third appendix of the book, Echometria, is devoted to the study of acoustics. "Giuseppe Biancani can be considered as the founder of geometrical acoustics (1620), a theory that - from the time of Athanasius Kircher until at least the end of the 18th century - was traditionally used to explain how speaking- and hearing-trumpets worked" (Barbieri, p. 156). Pages 387-414 contain a very interesting bibliography of books in the mathematical sciences (in their widest sense) including astronomy, physics, perspective, music, mechanics, etc. ABPC/RBH list just one copy (and that with a defective title page). "Giuseppe Biancani, the author of the Sphaera mundi (1620), tied his book to Clavius' farewell injunction: 'in view of what Galileo diligently and accurately set forth in his Nuncius sidereus, astronomers should see how the celestial orbs are to be constituted so that these phenomena can be accounted for.' Biancani's solution, worked out partly in correspondence with Grienberger, was to adopt Tycho's system and justify it and other statements about the constitution of the world by appeal to 'the best astronomers' or 'the common opinion of astronomers.' The closer to physics, the more diffident the statements. Are the stars carried by a rigid firmament, like rivets in steel? Probably. Do the planets move through the heavens like fish in the sea or birds in the air? 'Incompertum mihi est', I do not know.' Under this cover, Biancani delivered a very good textbook, filled with information indifferent to the choice of world systems (calendars, eclipses) and descriptions of the new phenomena - the mountainous moon, spotted sun, horned Venus, companions of Jupiter, bumps of Saturn. The sun sits in the middle of the other planets, except for the moon, as if their Lord, "according to the common opinion of astronomers.' Copernicus, Tycho, and Kepler all teach that the planets circle the sun as the moon does the earth. The statement was strictly true and patently false, a perfect, even a Jesuitical equivocation, since the earth is a planet to Copernicus and a unique something else to Tycho. Biancani ended his celestial survey with comets. Again he follows Tycho in placing them in solar orbit above the moon. The arrangement agreed with observations by Jesuit astronomers in many parts of Germany and Italy of the brilliant comet first seen in late November 1618" (Heilbron, p. 232). Biancani had been censured by the Jesuits for his astronomical teachings even before the condemnation of Copernicanism in March 1616. The initial area of dispute with the censors occurred over Biancani's Aristotelis loca mathematica (1615), a systematic and highly critical analysis of the passages in Aristotle pertaining to mathematics and its use in the sciences. "In the meantime Biancani had written another book for which he is more famous and which was directly devoted to astronomy, his Sphaera mundi, seu cosmographia. This book must have been completed in penultimate draft form sometime late in 1615, and then submitted to the censors as usual. "Of the numerous reports from the censors on this book, by far the most significant was writtem by Grienberger, a close friend of Biancani, and who, judging from his comments, must have been personally in agreement with him and also anguishing over the same problems of intellectual freedom. On the second page of his long and undated censure appear the following most significant remarks. 'He [Biancani] says on page 91b, line 14, that astronomers, whom he names, and especially Copernicus, use diagrams in determining and explaining celestial motions, and they call them hypotheses. But. Seller Inventory # 4501

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Theodosii sphaericorum elementorum libri III ex traditione: MAUROLICO, Francesco

About this Item: Pietro Spira, Messina, 1558. Hardcover. First edition. 'EXCESSIVELY RARE' (SOTHERAN). First edition, 'excessively rare' (Sotheran), of this collection of works on 'spherics', the geometrical and trigonometrical techniques necessary for the description of the motion of the celestial bodies, including Maurolico's Latin translations of works by four ancient Greek writers, Autolycus, Menelaus, Euclid and Theodosius, those of the first two authors constituting the first printed editions. Maurolico, one of the most original mathematicians of the 16th century, appended his own original propositions on sphaerics, probably based on astronomical observations made from 1548 to 1550 in Sicily, contained in his Sphaericorum libri II, Sermo de Sphaera, and Compendium mathematicae. He also includes a number of trigonometrical tables, including the first printed tables of secants, the Tabula Benefica, "in frank imitation of Regiomontanus's Tabula Feconda for tangents. It therefore seems that Maurolico had, independently of Rheticus, discovered the use of secants" (Rose, p. 173). Spherics, the geometry of the sphere, was regarded by the ancient Greeks as a branch of astronomy rather than of geometry. "The year 1558 was a turning point in the spherics tradition because in that year the printed versions of the text ended their dependence on the medieval heritage and participated in the Renaissance of mathematics . In Messina, in the same year, 1558, Francesco Maurolico . published the Sphaericorum elementorum libri tres ex traditione Maurolyci. Persuaded of the dignity of mathematical knowledge, Maurolico regretted the silence that had fallen on the ancient works of Euclid, Archimedes, Theodosius, Menelaus, Apollonius, and Serenus, as well as the corruption of their texts. Hence, he carried out a program of restoring the ancient works so that the knowledge they contained-set free of errors, gaps and imperfections-should shine again. Far from pursuing a philological and faithful reconstruction made by strictly adhering to the manuscript sources, Maurolico was guided by an interest in the enrichment of scientific knowledge. Hence, he integrated the original works with various contributions made throughout the centuries and presented the works' content following a rigour that he regarded as proper to mathematics" (Malpangotti, pp. 78-79). OCLC lists copies in the US at Burndy (although the work is not listed in the Huntington Library catalogue), Columbia, Michigan State and Oklahoma. No copies listed on ABPC/RBH. The volume's original dedication of 1555 was to no less a personage than Charles V, whom Maurolico had met in Sicily in 1535. After the emperor's death, however, Maurolico rededicated the printed book of 1558 to the viceroy La Cerda with a request that the book be transmitted to Philip II. No doubt Maurolico expected several advantages from this high patronage. In the first place, there would be continued sponsorship of his printing programme, and indeed Maurolico prefaces the collection with a new draft of his Index lucubrationum of 1540 [see below] . There seems to have been a hope on Maurolico's part that the patronage of the court might commend his book to the schools whose use of Sacrobosco he keenly criticised. Thus, the dedication in noting that spherics is essential to both astronomers and geometers, laments that this science lies neglected in the schools, a defect of the schools no longer to be tolerated. For this reason, he has tried to restore the spherics of Theodosius and Menelaus working from the most corrupt of texts. (This explains why Maurolico often gives only a note in place of the proofs.)" (Rose, p. 173). The order in which the works are presented by Maurolico is pedagogical rather than historical. He begins with his own De sphaera sermo, which is a non-technical introduction to astronomy on the sphere ('inter Sicut planas circulum, ita inter solidas figuras Sphaeram maximae excellentiae them multis plane rationibus constat''). This is followed by his translation of the Sphaerica of Theodosius of Bithynia (ca. 160 BC - ca. 100 BC), a mathematician and astronomer who lived in Tripoli on the Fenicia coast who is thought to be a younger contemporary of Hipparchus, the inventor of trigonometry (although no work by Hipparchus on this subject has survived). Arranged in three books, the Sphaerica discusses the properties of circular arcs lying on the surface of a sphere, notably great circles. Maurolico's version is based on a Latin manuscript of Plato of Tivoli (in turn prepared on the basis of an Arabic translation). The Sphaerica first appeared in the compendium Sphaera published at Venice in 1518; the first separate Latin edition at Vienna in 1529; and the editio princeps of the Greek text at Paris in the same year as the present work. Maurolico "retained all the propositions [from Plato of Tivoli's version], adopting the enunciations verbatim. Nevertheless, he introduced substantial changes to the work, adding further propositions, whose number increased from 79 to 84, reworking the demonstrations according to the requirements of modernity and renewal, which also involved the iconographic apparatus" (Malpangotto, p. 93). Maurolico's commentary contained short tables of sines, tangents and secants, probably inspired by Rheticus' tables in his Canon doctrinæ triangulorum (1551), but in part recomputed directly using Regiomontanus' original tables of sines. Maurolico next presents his translation of the Sphaericorum of Menelaus of Alexandria (fl. 100 AD). "Menelaus' major contribution to the rising science of trigonometry was contained in his Sphaerica, in three books. It is this work which entitles him to be regarded as the founder of spherical trigonometry and the first to have disengaged trigonometry from spherics and astronomy and made it a separate science" (DSB). The book introduces the concept of spherical triangle (a figure formed by three great circle arcs, which he named "trilaterals") and proves Menelaus's theorem on the ratios. Seller Inventory # 2881

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Sphaerae mundi compendium foeliciter inchoat. [Sphaera mundi;: SACROBOSCO, Johannes; REGIOMONTANUS,

SACROBOSCO, Johannes; REGIOMONTANUS, Johannes; PEURBACH, Georg

Published by Erhard Ratdolt, Venice (1482)

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First Edition
Hardcover

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

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About this Item: Erhard Ratdolt, Venice, 1482. Hardcover. First edition. THE FIRST PRINTED ASTRONOMICAL BOOK. First printing, rare, of this assembly of basic texts of pre-Copernican astronomy, an exceptional copy in an untouched contemporary binding (this book, and its several fifteenth-century reprints, are almost always found in 19th or 20th century bindings). Sacrobosco's De sphaera mundi (editio princeps 1472) was the first printed astronomical book, a synthesis of Ptolemy and his Arabic commentators, presenting an elegant, accessible Ptolemaic cosmology, and accepted as the most authoritative astronomical textbook of its time. From the time of its composition (ca. 1220), it "enjoyed great renown, and from the middle of the thirteenth century it was taught in all the schools of Europe. In the sixteenth century it gained the attention of mathematicians, including Clavius. As late as the seventeenth century it was used as a basic astronomy text" (DSB). Sacrobosco's text is accompanied in this edition by two treatises by Regiomontanus (1436-1476) and his teacher Georg Peurbach (1423-1461), who were the outstanding astronomers of their time and their early deaths were "a serious loss to the progress of astronomy, [which] left the technical development of mathematical astronomy deprived of substantial improvement until the generation of Tycho Brahe" (ibid.). The tract by Regiomontanus is a critique of the Theoricae planetarum communis, the anonymous thirteenth-century university textbook usually attributed to Gerard of Cremona. It is followed by Peurbach's Theoricae novae planetarum, composed around 1454 and first published at Nuremberg in ca. 1473), which became the standard astronomical text for over a century and a half. Following Arab astronomers, Peurbach "added trepidation to Ptolemy's six motions of the celestial spheres and substituted solid crystal spheres for the hypothetical circles employed in Ptolemy's Almagest" (Stillwell). The full-page woodcut on the verso of a1 (the recto is blank so it forms a frontispiece) features a hand holding an armillary sphere. ABPC/RBH list only four complete copies in the past 50 years: Bonham's 2015 (modern binding); Dominic Winter 2004 (old vellum, a1 supplied from a shorter copy); Sotheby's 1989 (modern binding); Sotheby's 1985 (modern binding). Johannes de Sacrobosco, or John of Holywood, or Halifax, was probably an Englishman, although even his nationality is uncertain. He lived at the end of the twelfth century and the beginning of the thirteenth century, and apparently spent most of his life in Paris, where he was a student and teacher of mathematics and astronomy at the university. "Sacrobosco's fame rests firmly on his 'De Sphaera', a work based on Ptolemy and his Arabic commentators, published about 1220 and antedating the 'Sphaera' of Grosseteste. It was quite generally adopted as the fundamental astronomy text, for often it was so clear that it needed little or no explanation. It was first used at the University of Paris. There are four chapters to the work. Chapter one defines a sphere, explains its divisions, including the four elements, and also comments on the heavens and their movements. The revolutions of the heavens are from east to west and their shape is spherical. The earth is a sphere, acting as the middle (or center) of the firmament; it is a mere point in relation to the total firmament and is immobile. Its measurements are also included. Chapter two treats the various circles and their names ? the celestial circle, the equinoctial, the movement of the 'primum mobile' with its two parts, the north and south poles, the zodiac, the ecliptic, the colures, the meridian and the horizon, and the Arctic and Antarctic circles. It closes with an explanation of the five zones. Chapter three explains the cosmic, chronic, and heliacal risings and settings of the signs and also their right and oblique ascensions. Explanations are furnished for the variations in the length of days in different global zones namely the equator, and in zones extending from the equator to the two poles. A discussion of the seven climes ends the chapter. The movement of the sun and other planets and the causes of lunar and solar eclipses form the brief fourth chapter" (DSB). Georg Peurbach received his Bachelor of Arts at Vienna in 1448 and, after spending several years traveling in Italy and elsewhere, his Master's degree in 1453. Apparently self-taught in the subject, Peurbach lectured on astronomy at Vienna, where one of his students was Johannes Regiomontanus (1436-1476). A notebook that Regiomontanus kept at Vienna during 1454-1462 begins with Peurbach's Theoricae novae planetarum, completed 30 August 1454. "Theoricae novae Planetarum is an elementary but thorough textbook of planetary theory written by Peurbach to replace the old, and exceedingly careless, so-called Theorica planetarum Gerardi, a standard text written probably in the second half of the thirteenth century. The original version of the Theoricae novae, completed in 1454, contained sections on the sun, moon, superior planets, Venus, Mercury, characteristic phenomena and eclipses, theory of latitude, and the motion of the eighth sphere according to the Alphonsine Tables. Peurbach later enlarged the work by adding a section on Th?bit ibn Qurra's theory of trepidation. Regiomontanus brought out the first printed edition (Nuremberg, ca, 1474) . A number of printings from the 1480s and 1490s in small quartos (e.g. 1482, 1485, 1488, 1490, 1491), also containing Sacrobosco's De sphaera and Regiomontanus' Disputationes contra Cremonensia in planetarum theoricas deliramenta, seem to represent the standard school edition and common text, which is generally sound. The colored figures in these editions are copied from Regiomontanus' printing . The diagrams are of considerable importance since parts of Peurbach's text would be unintelligible without them. The Theoricae novae contains very careful and detailed descriptions of solid sphere representations of Ptolemaic plane. Seller Inventory # 3949

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