Published by Imprinted at London by Iohn Daye (1570)

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From: Shapero Rare Books (London, United Kingdom)

**Item Description: **Imprinted at London by Iohn Daye, 1570. First edition in English of the first complete translation. Folio (31.5 x 20.5 cm), [28], 203, 205-464, [1] leaves, title within an allegorical woodcut border, showing Time bringing Truth and Antiquity to light [McKerrow & Ferguson 99], folding letterpress 'Groundplat' or table accompanying John Dee's preface, geometrical diagrams throughout, Book XI with 23 diagrams with one or more overslips (circa 43 in total), large woodcut portrait of John Day above colophon, woodcut historiated or decorative initials and tail-pieces, lacking final blank, short repair within table, mostly within blank area, ink smudges within text to [fist]2v and [fist]3r, occasional staining, mostly marginal, but heavier to signature D, occasional spotting, modern calf antique, a fine clean example kept in a modern solander box. The first English Euclid, with overslips, and notable for John Dee's preface, one of his most important texts. A fine clean copy. This full translation by Sir Henry Billingsley, a successful London merchant who later became Lord Mayor, relied on the achievements of two earlier editors, Campanus and Zamberti, and benefited from the involvement of the Elizabethan mathematician and magus, John Dee. As well as his preface, Dee also contributed many annotations and additional theorems to the work. "The most influential of all Dee's published works was his 'Mathematicall praeface' to Henry Billingsley's English translation of Euclid, Elements of Geometrie, printed by John Daye in 1570. The preface is firstly a long encomium of the study of 'thynges mathematicall' as partaking both of the supernatural and of the natural, and of geometry in particular. He goes on to enumerate the practical arts (proper to 'mechanicians') which derive from mathematics, and under one of the last of these, 'thaumaturgike', exculpates himself with some passion from the charge of conjuring. He also defends the use of the vernacular, as not encroaching on the rights of the universities. His concept of 'Archemastrie', which 'procedeth by Experiences', has been seen by some as foreshadowing the experimental science of the next century, but he also hints at magical interests and practices under this very heading. In general the 'Praeface' is now seen as a retrospective view of his own practice and teaching after his return to England in 1551, but the interest in magic, and possibly in skrying (seeing, or conversing with, spirits), may be a development of the late 1560s." (ODNB). Printing such a large and complex work with its folding overlays was a monumental task and the printer John Day is commemorated by his portrait at the end and possibly as the bearded figure of Mercury at the foot of the title-page. The overslips were originally printed as six bifolia bound in at the end. The number of overslips extant varies from copy to copy. STC 10560; Taylor, Mathematical Practioners, 41; Thomas-Stanford 41; cf. PMM 25. Bookseller Inventory # 91914

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Published by Joannes Tacuinus 25 October 1505, [Colophon:] Venice (1505)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Joannes Tacuinus 25 October 1505, [Colophon:] Venice, 1505. First edition of Euclid’s Elements based directly on a Greek text, and the first complete edition, including the first complete printings of Euclid’s Optics, Catoptrics, Phenomena and Data (extracts had appeared in 1501 in Giorgio Valla’s encyclopaedia De expetendis, et fugiendis rebus opus). This is the third edition overall, after the 1482 editio princeps (a Latin translation from an Arabic source), and its 1491 reprint. Euclid’s Elements is the only work of classical antiquity to have remained continuously in print, and to be used continuously as a textbook from the pre-Christian era to the 21st century. It is the foundation work not only for geometry but also for number theory. This book "has exercised an influence upon the human mind greater than that of any other work except the Bible" (DSB). "Four events seem to have been the most outstanding in determining the course of the Elements in the sixteenth and succeeding centuries: (1) the publication of the medieval version of Campanus of Novara, initially as the first printed Euclid at Venice (1482) by Erhard Ratdolt, and at many other places and dates in the ensuing 100 years; (2) a new Latin translation from the Greek by Bartolomeo Zamberti in 1505; (3) the editio princeps of the Greek text by Simon Grynaeus at Basel in 1533; (4) another Greek–Latin translation made in 1572 by Federico Commandino. The publications resulting from these four versions show their effect in almost all later translations and versions, be they Latin or vernacular" (ibid.). This edition is much rarer than the first: only four copies have appeared at auction in the last 50 years."The first publication of a Greek-based Latin Elements as an integral whole was that at Venice in 1505 prepared by Bartolomeo Zamberti (b. ca. 1473). His translation derived from a strictly Theonine Greek text, a factor which has Zamberti attributing the proofs to this Alexandrian redactor (cum expositione Theonis insignis mathematici). The work also contains translations of the minor Euclidean works (which were also, in part, in Valla’s encyclopedia). Zamberti was most conscious of the advantages he believed to accrue from his working from a Greek text. This enabled him, he claimed, to add things hitherto missing and properly to arrange and prove again much found in the version of Campanus" (ibid.). Euclid’s Elements of Geometry (ff. 11-179) is a compilation of early Greek mathematical knowledge, synthesized and systematically presented by Euclid in ca. 300 BC. Books I-IV are devoted to plane geometry, Book V deals with the theory of proportions, and Book VI with the similarity of plane figures. Books VII-IX are on number theory, Book X on commensurability and incommensurability, Books XI-XII explore three dimensional geometric objects, and Book XIII deals with the construction of the five regular solids. Book XIV is a later non-Euclidean addition, thought to have been contributed by Hypsciles (ca. 200 BC) on the basis of a treatise by Apollonius; Book XV may have been added by John of Damascus, or by a 6th-century pupil of Isadoros of Miletos. Both of these last two books continue the study of the regular solids. Euclid’s Phaenomena (ff. 180-191) is a textbook of what the Greeks called sphaeric, intended for use by students of astronomy. It was included in the collection of astronomical works which Pappus calls The Treasury of Astronomy, alternatively known as The Little Astronomy, in contrast with Ptolemy’s Syniaxis, or Great Astronomy. It consists of a preface and sixteen propositions. The preface gives reasons for believing that the universe is a sphere and includes some definitions of technical terms. Euclid in this work is the first writer to use "horizon" absolutely—Autolycus had written of the "horizon (i.e., bounding) circle"—and he introduces the term "meridian circle." The propositions set out the geometry of the rotation of the celestial sphere and prove that stars situated in certain positions will rise or se. Bookseller Inventory # 3947

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**First Edition**

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From: Lynge & Søn ILAB-LILA (Copenhagen, Denmark)

**Item Description: **Basel, Johannes Herwegen, 1533. Folio. (323x220 cm). Cont. full blind-tooled calf with a broad border of ornamental rolls with corner-pieces, inside which an oblique blind-tooled parallelogram and a rectangular tooled decoration, also with corner-pieces. Professionally rebacked in old style, w. seven raised bands blindstamped ornamentations to all compartments. Corners professionally and neatly restored. (12), 268; 115, (1) pp. incl. last page with large woodcut printer's device. Numerous woodcut diagrams in the text. The last page of Grynaeus' foreword with a half-page note on Euclid, Proclus and Grynaeus in 18th century hand. One contemporary marginal note. First 3 leaves with faint finger-soiling to lower right corner. The text framed throughout by a decorative but faint ink-border. Verso of title-page with 2 small stamps. Title with woodcut printer's device. The first text-page framed with a broad woodcut border, many smaller and larger woodcut initials throughout. Internally a very fine and clean copy w. wide margins. The monumental editio princeps of the "Elements" of Euclid, "the greatest mathematical textbook of all times", being the first printing of the original Greek text, including the first printing of Proclus' seminal commentary to the first book (the so-called "Herwagiana"). The present editio princeps constitutes one of the most important publications in the history of scientific (and philosophical) thought, and it profoundly influenced Renaissance, and in turn all modern, thought. The first printing of the original Greek text of the "Elements", which is edited by the famous Basel-professor of Greek Simon Gryneaus the elder, served as the basis for all later texts and translations of the "Elements" until the nineteenth century. Proclus's seminal commentary to the first book, which had never been printed before, is considered the earliest contribution to the philosophy of mathematics and "one of the most valuable documents in ancient philosophy" (Morrow, p. XXXII). It profoundly influenced Renaissance and modern readings of Euclid's Elements and is responsible for the role that this magnum opus came to play during the Renaissance. It is not until Proclus (ca. 410-485), the great Neoplatonist, applies Plato's manner of thinking to Greek geometry that it achieves completion as a real system. His view of mathematics as part of a larger system of thought was perfectly in tune with the currents of Renaissance thought, and with the commentary of Proclus, the Renaissance student of Euclid was carried beyond the ostensible boundaries of mathematics into the paths of cosmological and metaphysical speculation, paving the way for these fields in modern thought. But Proclus' commentary is not only of seminal importance to the antique and Renaissance interpretation of the work, it also provides us with invaluable information regarding geometers and the history of geometry prior to Euclid. "Its numerous references to the views of Euclid's predecessors, many of them otherwise unknown to us, render it an invaluable source for the history of science." (DSB, pp. 160-61). "These numerous and sometimes very extended references to opinions and accomplishments of his predecessors, taken together with the material rescued from Eudemus's early history of geometry, make Proclus' "Commentary" a priceless source of information regarding the geometry of the previous nine or ten centuries." (Morrow. p. XXVIII). -"Yet the value of the matter it contains regarding the foundations of mathematics and geometry in particular is even greater, though less widely recognized." (Morrow, p. XXXII). Proclus here explains the meaning of "Element" in geometry, he states the theoretical and pedagogical purposes of an elementary treatise, and offers a striking evaluation of the excellence of Euclid's own work. Futhermore, he famously defends pure mathematics, and geometry in particular, against its critics, and includes an important interpretation of the at. Bookseller Inventory # 39822

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Published by J. Herwagen, Basel (1533)

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From: Sokol Books Ltd. ABA ILAB (London, United Kingdom)

**Item Description: **J. Herwagen, Basel, 1533. Hardcover. Book Condition: Very good. EXTENSIVE EARLY ANNOTATIONS AND DIAGRAMS EDITIO PRINCEPS. Folio pp. (vi) 268, 115 (i). Greek letter, title page with printer's device repeated on verso of final leaf. First leaf of text within woodcut ornamental border (early manuscript Greek index in outer margin), woodcut headpieces and initials, printed mathematical diagrams throughout. Very extensive early Greek manuscript annotations and corrections to the whole of the first 61 pages (Book I) and the last 115 (Proclus' commentary in Greek and Latin) with numerous manuscript diagrammatic worked examples, very clear and legible. A very good, crisp, clean, widemargined copy, stamp erased from the verso of title page, in polished North European calf, c. 1700. An important copy of the editio princeps of Euclid's Elements together with the first edition of Proclus' commentary. The systematic and close annotations to Book I and the Proclus commentary, where the text has actually been illustrated by way of precise geometric illustrations, make this an extremely valuable copy in determining how both texts were received and used (and the relationship between them) in the first generations after their publication. It is highly unusual to find either of them consistently annotated in the same (or any) hand from beginning to end and even more so where, as here, the annotations constitute a critical commentary and do not just emphasise or note repetition of the text. Book I is the single most important book, in which Euclid outlines all of the fundamental ideas he will expand on in the rest of the work. The volume provides a rare window into the mathematical thought processes of its day. This is the first edition to have printed illustrations incorporated in the text, rather than in the margins, so it is the first in which extensive marginal worked examples were in fact possible. A work of international, cooperative scholarship, the Greek text was edited by the German Simon Grynaeus, Professor of Greek at Basle, with the assistance of the first Latin translation made directly from the Greek by the Italian Bartolomeo Zamberti, and two Greek manuscripts provided by the Frenchmen Lazare Baif and Jean Ruel. To this Grynaeus added Proclus' commentary on Book I from a manuscript provided by John Claymond, first President of Corpus Christi, Oxford. The work opens with a long dedication to Cuthbert Tunstall, Bishop of Durham, author of the first printed English arithmetic whom Grynaeus had met through Tunstall's good friend Thomas More and to whom Grynaeus presented a copy of the present work in thanks for More's favour during Grynaeus' visit to England. In fact this was the only comprehensive edition of the Greek text until David Gregory's in the early 18th century and it formed the basis of all later editions and translations until the 19th century. "Euclid's 'Elements of Geometry' is the oldest mathematical textbook in the world still in common use today. (.) [It] is a compilations of all earlier Greek mathematical knowledge since Pythagoras, organized into a consistent system so that each theorem follows logically from its predecessor, and in this lies the secret of its success. (.) The 'Elements' remained the common school textbook of geometry for hundreds of years and almost one thousand editions and translations have been published." Printing and the Mind of Man p. 14 on the first Latin edition. Proclus' commentary on Book I, here printed for the first time, is of great value in its own right. First, it is a unique source of information on the geometrical knowledge of the thousand years prior to Euclid, otherwise almost certainly lost to us. Second, it is perhaps the earliest significant contribution to the philosophy of mathematics linking it to all sorts of intellectual speculation; Morrow p. xxxii describes it as "one of the most valuable documents in ancient philosophy." It had not been reprinted up to modern times. The quintessential Renaissance volume and one of the corner stones. Bookseller Inventory # L1541

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Published by Simon Bevilaqua 30 September 1498., [Colophon:] Venice (1498)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Simon Bevilaqua 30 September 1498., [Colophon:] Venice, 1498. First edition, very rare, of this remarkable collection of twenty-two Greek texts translated by Giorgio Valla (and one translated by his adopted son Johannes Petrus Valla), some from the Byzantine period, and others earlier, most on scientific subjects from mathematics and music to medicine, but also including rhetoric, theology, and ethics, with the majority of the texts appearing here in print for the first time. Among the most notable such ‘firsts’ in this volume are: De pestilential, the most important work of the great Persian physician Rhazes, the first medical description of smallpox and the most important early work on epidemiology – Rhazes’ explanation for why the disease does not strike the same individual twice is the first theory of acquired immunity; five works by Galen (listed below); the only extant work by Aristarchus of Samos, who proposed a heliocentric cosmology almost two millenia before Copernicus; book XIV of Euclid’s Elements, generally ascribed to Hypsicles, the first 13 books having been printed by Ratdolt at Venice in 1482; De astrolabio, by the Byzantine scholar Nicephorus Gregoras, on which were based several later texts on the astrolabe, notably those of Apianus and Stöffler; and Aristotle’s Poetics, the most comprehensive work on literary theory and criticism surviving from the classical period, which came to play a foundational role in the history of scholarship. These translations are accompanied by one work of Valla himself (‘Ratio argumentandi’) and each is preceded by a dedicatory epistle. Edward Rosen (Copernicus and his Successors, p. 142) has shown that Copernicus read Valla’s collection, using in his Commentariolus (the preliminary version of his heliocentric theory prepared before 1514) the data on the orbital period of Mars given in Valla’s translation of Cleomedes’ De mundo. Valla’s companion work, De expetendis et fugiendis rebus (Venice, 1501), published shortly after his death, was also used extensively by Copernicus, as well as by Leonardo da Vinci. ABPC/RBH list only one other copy (disbound). OCLC lists copies in US at Harvard, Michigan, NLM, Newberry Library, New York Academy of Medicine, Philadelphia College of Physicians, and Yale Medical Library.Provenance: The Earls of Macclesfield, with their bookplate on front paste-down and embossed stamp on first three leaves. Giorgio Valla (1447-1500) was famous in his own time not only for his mathematical and scientific achievements, but as the owner of a remarkable collection of Greek manuscripts upon which most of his translations are based (these are now held by the Estense Library at Modena). But Valla was also an accomplished physician, evidenced by the presence of several medical works in the present volume. The most important of these (fol. 150r-156v) is the De pestilential of "Abû Bakr Muhammad ibn Zakaria, called Rhazes (865-925), a Persian like most of the great physicians of the Arabian period. He was properly regarded as chief of the practical physicians of his time. After having studied medicine at the school of Bagdad, he became physician to the hospital of Raj (Ray) in Tabaristan, near Teheran, the part of Persia in which he was born. Later he moved to Bagdad, where he quickly acquired the reputation of a great physician and a worthy teacher [Rhazes] left more than two hundred books on medicine, philosophy, religion, mathematics, and astronomy The most important book of Rhazes, from the point of view of the medical historian, is the work on smallpox, which was called Liber de Pestilentia, and was first published in Valla’s Nicephori Logica collection (Venice, 1498). "This book can be regarded as certainly and completely original; it is founded on the experiences and personal observations of a physician who knows how to examine the patient completely and to draw from his observations the conclusions of a great intellect. This is the first accurate study that we possess of the infectious diseases. Rhazes distinguished. Bookseller Inventory # 3994

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Published by Johann Herwagen,, Basle: (1533)

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From: B & L Rootenberg Rare Books, ABAA (Sherman Oaks, CA, U.S.A.)

**Item Description: **Johann Herwagen,, Basle:, 1533. EDITIO PRINCEPS. Folio. [vi], 268, 115 pp. With woodcut device on title and colophon, decorated woodcut border to first page of text and numerous woodcut diagrams. Contemporary English calf, neatly rebacked, remains of ties, later endpapers. A very good copy. Editio princeps of Euclid's Elements and of the important commentary by Proclus on the first book. The first printing of Euclid in 1482 was a Latin translation from an Arabic manuscript, but the original Greek text did not appear for a further half-century. The Greek text was edited by Simon Grynaeus, a German Protestant theologian and philologist. This edition is also important for the innovation of geometrical diagrams within the text, rather than in the margins as had been the case with the earlier printed editions.The commentary by the Neoplatonist mathematician and philosopher Proclus on the first book of the Elements is the earliest extant criticism of Euclid's fifth postulate on the existence of parallel lines, the study of which led, after a further fifteen hundred years of effort, to the discovery of non-Euclidean geometry by Gauss, Bolyai and Lobachevsky. It is also the first printing of the earliest work on the philosophy of mathematics. "Because of his interest in the principles underlying mathematical thought and their relation to ultimate philosophical principles, Proclus' commentary is a notable - and also the earliest - contribution to the philosophy 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). Bookseller Inventory # 10141

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Published by Joannes Tacuinus de Tridino, Venice (1510)

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From: Sokol Books Ltd. ABA ILAB (London, United Kingdom)

**Item Description: **Joannes Tacuinus de Tridino, Venice, 1510. Softcover. Book Condition: Very good. THE MOST FAMOUS MATHEMATICAL TEXTBOOK Folio, 240 unnumbered leaves. (10) A-Z8, AA-EE8, FF6, lacking last blank. Theorems in gothic letter, demonstrations in Roman, first two lines of title woodcut with rich gothic decoration, large woodcut device of St. John the Baptist signed BM beneath. First leaf of text printed in red and black with large white on black woodcut border on three sides of putti, mermen, vines vases (taken from the 1504, Legendario delli sancti), printer’s white on black device on verso of last, fine large white on black historiated and floriated initials, outer margins with printed geometrical diagrams on most pages, "nulla virtus sine labore" in contemporary hand in shield on woodcut border, some contemporary marginalia, including a manuscript diagram on B6. Lower outer corner of title a little thumbed, small worm trail in upper blank margin of first few leaves, occasional minor marginal water staining, the odd spot or ink splash. A very good copy, crisp and clean, on thick paper, in contemporary limp vellum, remains of ties, title manuscript on spine, vellum a little creased and stained. A lovely example of a beautiful and important book. "It was a translation into Latin from a Greek text by Bartolomeo Zamberti who claims that he has restored and excluded from the exposition of Theon many things that were ‘subversa et prepostere voluta’ in the version of Campanus. For example, the Pythagorean proposition becomes the 47th of the first book as we know it. Zamberti contributes a long preface on the life of Euclid. The thirteen books of the Elements are followed by the Phaenomena, Specularia etc. The volume itself is a first rate example of the Venetian book of the time. There is an elaborate title-page with the printer’s well known cut of John the Baptist at the foot. The first page of the text has a fine border, and the larger initial letters are a charming set depicting children playing. In 1510, some of the same sheets were reissued with a freshly printed last page. Both issues seem to be among the rarest of early Euclids" Thomas-Stanford pp. 5-6. In fact this issue is entirely reset after gathering O. Zamberti’s was a very significant edition. It was the first publication of a Greek based Latin ‘Elements’ as an integral whole, the Greek text he employed was essentially uncorrupted and it is the first to contain translations of a number of the minor Euclidian works. It may not be as superior to Campani’s recension (the first edition) as Zamberti claims but at least it is free of the errors of the mediaeval copyists. "Euclid's Elements of Geometry is the oldest mathematical textbook in the world still in common use today." Printing and the Mind of Man 25 on first edition. This is a lovely, fresh copy, with wonderfully clear impression of the type and woodcuts of this important work, rare in its original binding. BM STC It. p.238. Thomas-Stanford 5. Essling 284. Sander 2609. Latin. Bookseller Inventory # L1425

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Published by Basle, Johannes Herwagen, 1533 (1533)

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From: WP Watson Antiquarian Books (London, United Kingdom)

**Item Description: **Basle, Johannes Herwagen, 1533, 1533. Folio (296 x 197 mm), pp [xii] 268; 115 [1] with printer's device on title and last leaf, numerous woodcut diagrams in the text, woodcut border around opening page of the text; title a trifle dust-soiled, small portion of blank corner of first three leaves repaired, a very attractive copy in eighteenth-century French mottled sheep, inscription on title 'Collegii Lemovicensis Societ. Jesu Catal. inscriptus, 1672'. £28,500Editio princeps of Euclid's Elements, and of Proclus' commentary on the first book of the Elements. The first printing of Euclid was a Latin translation in 1482, but the original Greek text had to wait a further fifty-one years before its appearance. The Greek text was edited by Simon Grynaeus, a German Protestant theologian and philologist. The printer Johann Herwagen introduced the innovation in this edition of printing Euclid's diagrams within the text.The commentary by Proclus on the first book of Euclid's Elements is the first printing of the earliest work on the philosophy of mathematics. It was written in the fifth century by the Neoplatonist mathematician and philosopher Proclus who as 'the last great systematiser of the Greek philosophical inheritance . exerted a powerful influence on medieval and Renaissance thought' (Oxford classical dictionary).'Because of his interest in the principles underlying mathematical thought and their relation to ultimate philosophical principles, Proclus' commentary is a notable - and also the earliest - contribution to the philosophy 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 the science' (DSB).Adams E980; Thomas-Sandford 7; Norman 730; Stillwell 210. Bookseller Inventory # 1853

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Published by Johannes Herwagen, Basel (1533)

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**Hardcover**
**First Edition**

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From: Milestones of Science Books (Ritterhude, Germany)

**Item Description: **Johannes Herwagen, Basel, 1533. Hardcover. Book Condition: Near Fine. 1st Edition. Folio - over 12 - 15" tall. 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 manuscript. 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. ---- 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). Bookseller Inventory # 001965

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Published by I. Heinrich Petri; II. A. Brinckmann; III. Rihel I. September 1556; II. 1560; III. 1566, I. Basel; II. Köln; III. Strasbourg (1556)

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From: MEDA RIQUIER RARE BOOKS (london, United Kingdom)

**Item Description: **I. Heinrich Petri; II. A. Brinckmann; III. Rihel I. September 1556; II. 1560; III. 1566, I. Basel; II. Köln; III. Strasbourg, 1556. Three works bound in one volume, folio (316 x 199 mm.), I: [8] leaves, 416 pages, 4 folding tables bound at the end and 9 tables inserted in the text; diagrams and woodcut illustration. II: [3] leaves, 245 pages, one blank leaf. III: [4], XCVIII, [1] leaves. Contemporary German blinstampad pigskin over woodden boards, two metal clasps. A superb copy. A very fine collection of three rare scientifc works, all first editions. I Erasmus Oswald Schreckenfuchs (1511-1579) was an austrian astronomer and humanist; he studied in Vienna, Ingolstad and Tubingen where he was a scholar of Sebastian Münster. He translated into latin the Form of the Earth of the Jewish astronomer Abraham bar Hiyya and published, in 1551, a commentary to the Almagestum of Ptolemy. Schreckenfuchs major work is the Commentaria, in novas theoricas planetarum G. Purbachi. This massive commentary contained, for the first time in the Theoricae novae printed tradition, a series of three-dimensional diagrams intended to complement the ordinary diagrams of the orbs, circles, axes and poles of the planets and the eighth sphere. "Peurbach’s Theoricae novae contains very careful and detailed descriptions of solid sphere representaitios of Ptolemaic planetary models that Peurbach based either upon Ibn al-Haytham’s description of identical models in his On the Configuration of the World (transalated into Latin in the late thirteenth century) or upon some later intermediary work. Peurbach’s book was of great importance because his models remained the canonical physical description of the structure of the heavens until Tycho disproved the existence of solid spheres. Even Copernicus was to a large extent still under their influence, and the original motivation for his planetary theory was apparently to correct a number of physical impossibilities in Peurbach’s models relating to nonuniform rotation of solid spheres".(DSB,15 p.475). II Johannes Stadius (1527-1579) was a Flemish astrologer and mathematician; his real name was Jan Van Ostaeyen. Gemma Frisius had trained him. He supported the model by Copernicus that said that the Earth orbits the Sun. In 1554 published in Koln the Ephemerides novae at auctae and in 1560 the Tabvlae Bergenses aequabilis et adparentis motus orbivm coelestivm dedicated to Robert de Bergis bishop of Lieges. ‘This book promised a compendium of Copernicus’ De revolutionibus and the Prutenic Tables, provided an erudite history of astronomy, practical astronomical know-how (easy ways to calculate planetary positions), and astrological foreknowledge related to fixed stars and planets.’ (Gábor Almási (2013). Tycho Brahe and the Separation of Astronomy from Astrology: The Making of a New Scientific Discourse. Science in Context, 26, pp 330). III This edition of Euclid’s Analyseis geometricae was edited by the Swiss mathematician and astronomer Konrad Dasypodius (1530-1600) the son of the humanist Petrus Dasypodius. Dasypodius studied in Strasbourg at the famous academy of Johannes Sturm and became professor there in 1558. ‘The grater part of Dasypodius’ work was destined to be schoolbooks for his students: his editions of Euclid, his Volumen primum and Volumen secundum and his Protheoria with the Institutiorum mathematicarum erotemata (in the form of questions and answers) demonstrate his pedagogical interest. These books shows that in Strasbourg, under the influence of Sturm, mathematics was studied far more extensively than in many of the universities of the time. Worthy of special mention is his Analyseis geometricae (1566). This book, written with his teacher Christian Herlinus, contains the prof of the first six books of Euclid’s Elements analyzed as their syllogisms; it was intended to facilitate the study of mathematics for students trained in dialectics’. (DSB ad vocem) I: Zinner 2161; II: Zinner 2244; III: BMC 288. Bookseller Inventory # 009

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Published by Seville, en Casa de Alonso de la Barrera, 1576. (1576)

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**First Edition**
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Quantity Available: 1

From: Richard C. Ramer Old and Rare Books (New York, NY, U.S.A.)

**Item Description: **Seville, en Casa de Alonso de la Barrera, 1576., 1576. 4°, contemporary limp vellum (ties missing, light stains), vertical manuscript short author and title on spine, in a recent quarter brick-red morocco over reddish-orange cloth folding box. Large woodcut arms of dedicatee on title-page. Numerous woodcut geometric designs in text. Large (13-line) woodcut initial on first page of text; a few 4- and 5-line initials. Woodcut vignette tailpiece. Light dampstain in lower blank margin of final 20 leaves. Crisp; overall in fine condition. Bookplate from the Landau library, number 64704. 121, (1) ll., signed A4, B-P8, Q4, R2. A4 missigned "4", M2 missigned "M3". Leaf 11 unnumbered, 51 misnumbered 42, 78 misnumbered 70, 84 misnumbered 76, 103 misnumbered 102, 105 misnumbered 108, and 116 misnumbered 108. *** First Edition in Spanish, and the only edition of this translation prior to a Salamanca 1999 reprint. It is also the first printing of any text by Euclid in Spain, in any language. Zamorano (b. 1542) was professor of cosmography at the Casa de la Contratación de las Indias, as well as an astrologer and mathematician. He later became piloto mayor to King Philip II and wrote the official navigation manual of the Spanish Navy at the time of the Armada. In the present book, he emphasizes the sciences of mechanics, astronomy, and cosmography.Thomas-Stanford comments that this volume has the appearance of a schoolbook, which would account for its rarity, and notes that the few copies he had been able to examine were rather worn (pp. 16-17).Euclid?s Elements, a collection of definitions, axioms, theorems, and proofs in 13 books (of which 6 are included in this translation), is the oldest extant deductive treatment of mathematics, and played an important role in the development of logic and modern science. One of the world?s most successful and influential textbooks, it was first published in Venice, 1482, and has appeared in over a thousand editions.*** Thomas-Stanford 43. Adams E1018. BL, Pre-1601 Spanish STC p. 74 (British Library copy with title-page mutilated). Palau 84721. Beardsley 95 (listing copies at the Biblioteca Nacional de España and University of Michigan). Catálogo colectivo E903. Salvá 2570. Heredia 4494. Steck III, 88. Duarte, Euclides, Arquimedes, Newton pp. 46, 48. Honeyman 1011. Riccardi, Bib. euclidea, 1576 (1). Not in HSA. CCPBE locates sixteen copies. Not located in Rebiun (which cites Salamanca 1999 and Mairena del Aljarafe 2006 editions). Copac repeats the two copies at Cambridge University. Not in Orbis (which lists the Salamanca 1999 edition at SML). NUC: MiU, MB. Bookseller Inventory # 25012

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Published by Padua, Grazioso Percacino, 1560. (1560)

**Used**
**First Edition**

Quantity Available: 1

From: Antiquariat INLIBRIS Gilhofer Nfg. GmbH (Vienna, Austria)

**Item Description: **Padua, Grazioso Percacino, 1560., 1560. Folio (215 x 300 mm). (16), 272, (24) pp. With woodcut device on t. p. (Minerva and Mercury holding the wing tips of a rising phoenix), woodcut portrait on reverse, and printer's device on final leaf, as well as numerous mathematical diagrams in the text. Contemp. Italian limp vellum with ms. spine title. First Latin edition of one of the major works by Proclus Lycaeus (412-485), founder and head of the neo-Platonic school of Athens: a commentary on the first book of Euclid's "Elements of Geometry", the "oldest mathematical textbook in the world still in common use today" (PMM). Includes the text of the theorems, set within ornamental woodcut framings, and the geometrical diagrams. The editor and translator Francesco Barozzi (1537-1604) taught at the University of Padua. He was later charged with sorcery (in particular, he was said to have caused a torrential rainstorm over his native Crete) and condemned by the Inquisition in 1587. "Barocius' edition of Proclus' commentary on the first book of Euclid's 'Elements' was the first important translation of this work, for it was based on better manuscripts than previous efforts had been. The translation, published in 1560, was completed by Barocius at the age of twenty-two" (DSB). His portrait on the reverse of the title page is cut within a magnificent border. - Old ms. ownership on flyleaf obliterated (probably in the early 19th century); old ownership stamp over title woodcut erased, replaced by a different coat of arms in ink, very likely that of the Italian comital family Antico (insignificant bleeding to reverse). Occasional slight waterstaining, still an exceptionally appealing, clean copy. Edit 16, CNCE 33726. Adams P 2138. BM-STC Italian 540. Mortimer 403. Honeyman 2543. DSB I, 468. Brunet IV, 895. Riccardi I/1, 82, 1 ("Bella e rara edizione"). Cf. PMM 25. Bookseller Inventory # 34116

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Published by Russell Maret, New York (2014)

**Used**
**Hardcover**

Quantity Available: 1

From: Lux Mentis, Booksellers, ABAA/ILAB (Portland, ME, U.S.A.)

**Item Description: **Russell Maret, New York, 2014. Hardcover. Book Condition: Fine in Fine Archival Box. Limited Edition. Tight, bright, and unmarred. Full leather binding, inlayed leather decorative elements, housed in an archival drop-spine case. fo. np. Illus (color prints). Numbered limited edition. "The typefaces are Gremolata, Cancellaresca Milanese, Saturn, Saturn Shadow, and Texto Portuguez, all of which were designed by the printer. The text and the images were printed from photopolymer plates on a Vandercook Universal III proof press. Nancy Loeber assisted in the studio and prepared the sheets for binding. Daniel Kelm bound and boxed the book at the Wide Awake Garage in Easthampton, Massachusetts." There are three editions: Seventy- ve copies, numbered 1-71 and AP 1-AP 4 (printed on mouldmade Zerkall Litho 270gm paper and bound in goatskin & UICB handmade paper. Housed in a cloth covered clamshell box). Sixteen copies, numbered I-XIII and AP I-AP III (printed on a specially devised cotton and abaca Twinrocker Handmade Paper made by Travis Becker and bound in full leather with seven color leather inlays, and accompanied by a second volume of state and progressive proofs of the proposition matching the book’s number. Both volumes are housed in a leather and cloth covered clamshell box). One copy, lettered E, is printed, bound, and boxed in the manner of the above-mentioned sixteen, but, rather than the second volume, it is accompanied by a complete, unbound set of state and progressive proofs which are housed in three cloth covered clamshell boxes. 13 propositions of Euclid explored in a manner like no other. Without question the most important printing of Euclid since the 1847 Byrne edition. This is the only remaining available copy of the Deluxe edition. Bookseller Inventory # 8634

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**Used**
**Softcover**

Quantity Available: 1

From: John Windle Antiquarian Bookseller, ABAA (San Francisco, CA, U.S.A.)

**Item Description: **London: William Pickering, 1847. Small 4to, xxix, 268 pp., color diagrams throughout printed in red, blue, yellow and black; wood-engraved initials. Original half brown morocco, gilt-lettered backstrip, a very bright and clean copy without the usual heavy foxing and staining. First edition of Byrne's presentation of Euclidean geometry, in which colours are substituted for the usual letters to designate the angles and lines of geometric figures. Tufte's copy ($15,000, 2010) was described thus: "BYRNE'S SPECTACULAR RENDERING OF EUCLIDEAN GEOMETRY USING FOUR-COLOR PRINTING. The stark use of primary colors was envisaged by Byrne as a teaching aid. "Each proposition is set in Caslon italic, with a four line initial engraved on wood by Mary Byfield: the rest of the page is a unique riot of red, yellow and blue . attaining a verve not seen again on book pages till the days of Dufy, Matisse and Derain" (McLean). "Color serves as a label most notably of all in Oliver Byrne's 1847 edition of Euclid's Geometry. This truly visual Euclid discards the letter-coding native to geometry texts. In a proof, each element names itself by consistent shape, color, and orientation; instead of talking about angle DEF, the angle is shown--appropriately enough for geometry" (Tufte, Envisioning Information, p.84). Byrne's depiction of Pythagoras is a classic, with the squares being visually interpreted so in vivid blocks of colour. In a technical tour-de-force, Whittingham skillfully aligned the different color blocks for printing to produce "One of the oddest and most beautiful books of the whole century" (McLean). Against McLean's conclusion that it is a "decided complication of Euclid", Edward Tufte finds that "A close look, however, indicates that Byrne's design clarifies the overly indirect and compicated Euclid, at least for certain readers" (ibid.) "THE MOST ATTRACTIVE EDITION OF EUCLID THE WORLD HAS EVER SEEN" (Werner Oechslin, in an essay to the Taschen reprint, Cologne: 2010). Ing, Charles Whittingham Printer 46; Keynes, Pickering pp. 37, 65; McLean, Victorian Book Design p.51. Bookseller Inventory # 107051

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Published by Russell Maret, New York (2014)

**Used**
**Hardcover**

Quantity Available: 1

From: Lux Mentis, Booksellers, ABAA/ILAB (Portland, ME, U.S.A.)

**Item Description: **Russell Maret, New York, 2014. Hardcover. Book Condition: Fine in Fine Archival Box. Limited Edition. Tight, bright, and unmarred. Full leather binding, inlayed leather decorative elements, housed in an archival drop-spine case. fo. np. Illus (color prints). Numbered limited edition. "The typefaces are Gremolata, Cancellaresca Milanese, Saturn, Saturn Shadow, and Texto Portuguez, all of which were designed by the printer. The text and the images were printed from photopolymer plates on a Vandercook Universal III proof press. Nancy Loeber assisted in the studio and prepared the sheets for binding. Daniel Kelm bound and boxed the book at the Wide Awake Garage in Easthampton, Massachusetts." There are three editions: Seventy- ve copies, numbered 1-71 and AP 1-AP 4 (printed on mouldmade Zerkall Litho 270gm paper and bound in goatskin & UICB handmade paper. Housed in a cloth covered clamshell box). Sixteen copies, numbered I-XIII and AP I-AP III (printed on a specially devised cotton and abaca Twinrocker Handmade Paper made by Travis Becker and bound in full leather with seven color leather inlays, and accompanied by a second volume of state and progressive proofs of the proposition matching the book’s number. Both volumes are housed in a leather and cloth covered clamshell box). One copy, lettered E, is printed, bound, and boxed in the manner of the above-mentioned sixteen, but, rather than the second volume, it is accompanied by a complete, unbound set of state and progressive proofs which are housed in three cloth covered clamshell boxes. 13 propositions of Euclid explored in a manner like no other. Without question the most important printing of Euclid since the 1847 Byrne edition. This is the only remaining available copy of the Deluxe edition. Bookseller Inventory # 8133

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Published by Pisa Comillo Franceschini 1572 (1572)

**Used**
**First Edition**

Quantity Available: 1

From: Buddenbrooks, Inc. ABAA (Newburyport, MA, U.S.A.)

**Item Description: **Pisa Comillo Franceschini 1572, 1572. First Edition of the translation by Federico, Commandino Urbinate. With a beautifully engraved titlepage by Jacob Criegher and with hundreds of geometric diagrams within the text. 4to, full contemporary limp vellum with evidence of older printed parchment used for backing, spine handsomely labeled in antique holograph. [12], 256. A wonderful example in full contemporary state, binding unsophisticated and sturdy, very crisp and well preserved. With very old damp staining to the outer margins of the last 20 or so leaves, some expected aging to the vellum. SCARCE AND HIGHLY IMPORTANT. The First Edition of this translation into Latin and with the commentary of the Commandino. Of great historical importance and in fact still today recognized as the best of the numerous sixteenth century translations. It represents the high point of the scientific production of the great mathematician Urbinate (1509-1575). Commandino had, like his main supporter Cardinal Farnese, became passionate of the classical sciences. It is one of the few translations of Euclid solidly based on a Greek original and it served as the base for almost all later translations prior to Peyrard’s discovery of a "pristine" Greek Euclid in the early nineteenth century. Euclid’s ‘ELEMENTS’ is the "oldest mathematical textbook still in common use today" (PMM) and one of the most important scientific text in human history. Euclid was the foremost mathematician of the illustrious "Alexandrian Academy". He had studied at Athens, probably with students of Plato. His ‘Elements’ remains the most important treatise of Geometry and has determined all subsequent teaching. Perhaps no book save the Bible has been more extensively studied, and for the past 22 centuries it has held its place of importance. Although elementary works had been written by other authors prior to Euclid, his works completely displaced everything which had come before and set a standard which would remain through time right up to the 21st Century. Bookseller Inventory # 15699

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Published by Jacobus Chriegher German, Pesaro (1572)

**Used**
**Hardcover**

Quantity Available: 1

From: Rulon-Miller Books (ABAA / ILAB) (St. Paul, MN, U.S.A.)

**Item Description: **Jacobus Chriegher German, Pesaro, 1572. Folio in sixes, pp. [24] plus 255 leaves; title within an architectural woodcut border, historiated woodcut initials, numerous woodcut geometric diagrams and illustrations in the text; a clean, crisp copy in 19th century quarter vellum over marbled boards, smooth gilt-decorated spine with 2 black calf lettering pieces, edges stained yellow; nice copy. "A new translation into Latin of the fifteen books of the Elements appeared at Pesaro, a seaport on the Adriatic near Urbino, in 1572. The printer was Camillo Francischini. The translation, which was made use of by subsequent editors for centuries, was the work of Federigo Comandino, certainly an outstanding figure in the history of Euclid's Elements" (Thomas-Stanford). Adams E-984; Thomas-Stanford, Early Editions of Euclid's Elements, no. 18. Bookseller Inventory # 38312

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Published by Madrid, en casa de la viuda de Alonso Gomez, 1585. (1585)

**Used**
**Hardcover**
**First Edition**

Quantity Available: 1

From: Richard C. Ramer Old and Rare Books (New York, NY, U.S.A.)

**Item Description: **Madrid, en casa de la viuda de Alonso Gomez, 1585., 1585. 4°, nineteenth-century quarter tan calf (light wear), spine with raised, gilt-tooled bands in five compartments black leather lettering piece with author in gilt, text block edges marbled. Woodcut royal arms on title-page. Woodcut initials (6 to 8 lines high). Numerous woodcut diagrams in text (usually 10 to 11 lines high). Short tear in lower margin of title, without loss; some very slight scattered browning and spotting. Overall in very good to fine condition. Faint contemporary ink inscription at foot of title-page. Small (4 x 3.2 cm.) bookplate of Joaquin Garcia Icazbalceta in upper outer corner of front pastedown. (6), 60 ll. *** Rare first edition in Spanish of the @Optica et catoptrica, the earliest surviving Greek work on perspective and one of the most important written before Newton's works on optics. The colophon bears the date 1584.The @Perspectiva was translated by Pedro Ambrosio Onderiz, who in 1582 had been appointed by King Philip II to a chair in the newly established Academia de Matemáticas. Although Onderiz was expressly charged with the translation of scientific works into Spanish, he published no other works. By 1595, Onderiz had been appointed @cosmógrafo mayor, in which capacity he intended to correct various cartographical errors which were said to have unduly favored Portuguese territorial claims, but his death in 1596 prevented this.It is likely that Spanish painters of the Golden Age consulted this work. The only earlier work by Euclid that had been translated into Spanish was @Los seis libros primeros de la geometria, Seville 1576; prior to that, the only printing of Euclid in Spain was a truncated @Mathematicae quaedam selectae, Alcalá 1566.The @Especularia has separate title-page, @licencia, aprobacion, prologue and colophon, all dated 1584, but the quire signatures and pagination continue from the @Perspectiva.@Provenance: Joaquin Garcia Icazbalceta (1825-1894), born in Mexico City of a family of Spanish landed gentry, was a philologist and an important historian of the Spanish colonial period, as well as one of the leading Mexican bibliophiles and bibliographers of the nineteenth century. He published @Apuntes para un catálogo de escritores en lenguas indígenas de América (1866); the masterly biography @Don Fray Juan de Zumárraga, primer Obispo y Arzobispo de México (1881, various later editions); @La bibliografía mexicana del siglo XVI (1886), a model of bibliographical erudition; @Colección de documentos para la historia de México (2 volumes 1858 1866); followed by @Nueva colección de documentos para la historia de México (5 volumes 1886-1892); an edition of the @Arte de la lengua maya, of Fray Gabriel de San Buenaventura (1888); the @Opúsculos Inéditos, latinos y castellanos, of Francisco Javier Alegre (1889), as well as other translations, critical editions and documentary collections. He was one of the founders and the first secretary of the Academia Mexicana de la Lengua (1875-1883), and was that institution's third director (1883-1894), being responsible for the publication of the first volumes of the Academia's @Memorias.*** Palau 84722. Perez Pastor 219. Beardsley 103: locating one copy, at the University of Pennsylvania. Picatoste y Rodríguez 571. @Catálogo colectivo E904: locating seven copies in Spain. Antonio II, 169-70. Salvá 2569. Heredia 508. Not in @Hispanic Society of America Catalogue. Not in @Ticknor Catalogue. Not in Academia das Ciências de Lisboa, @Livros quinhentistas espanhóis. CCPBE locates 24 copies, a significant number of which are incomplete and / or in poor condition. Rebiun locates five copies: Universidad Politécnica de Madrid, Universidad de Oviedo, UCM Universidad Complutense de Madrid, and Universidad de Salamanca. Copac locates copies at the University of London and British Library. NUC: CU (lacking title page), WU. Bookseller Inventory # 21312

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Published by Pesaro: [Camillo Franceschini,] 1572 (1572)

**Used**
**First Edition**

Quantity Available: 1

From: Peter Harrington. ABA member (London, United Kingdom)

**Item Description: **Pesaro: [Camillo Franceschini,] 1572, 1572. Folio (299 × 209 mm). Eighteenth-century Italian sprinkled calf, spine with double gilt rules either side of raised bands, red and black morocco lettering-pieces, blue hand-coloured endpapers and edges. A little skilful repair to spine ends, a few minor marks internally, but an excellent copy. Woodcut geometric diagrams in the text. First edition of the famous Latin translation of Euclid by the Italian humanist and mathematician, Federico Commandino (1509–1579). Born in Urbino, Commandino studied at Padua and at Ferrara, where he received his doctorate in medicine. He was hugely influential in providing Latin translations, making newly accessible the works of the ancient Greek mathematicians, notably Archimedes, Aristarchus of Samos, Pappus of Alexandria, and Hero of Alexandria. Euclid's Elements is the father of them all, being "the oldest science textbook, 2,000 years old and still in use" (Dibner); which "has exercised an influence upon the human mind greater than that of any other work except the Bible" (DSB). Adams E984; Riccardi I 362; Thomas-Stanford 18. Bookseller Inventory # 52092

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Published by Melchior Mondiere, Paris (1625)

**Used**

Quantity Available: 1

From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Melchior Mondiere, Paris, 1625. Very rare editio princeps of this important text by Euclid, his only work in pure geometry, other than the Elements, to have survived in Greek. It is here accompanied by a commentary, or rather an introduction, by Marinus of Naples (5th century AD), the pupil and biographer of Proclus. Although the importance of the first printing of any Euclidean text goes without saying, the work is of particular interest given contemporary developments in French geometry — Descartes, Mersenne, Fermat, etc., to whose circle the translator Claude Hardy belonged."The Data is closely connected with books I-VI of the Elements. It is concerned with the different senses in which things are said to be given. Thus areas, straight lines, angles, and ratios are said to be "given in magnitude" when we can make others equal to them. Rectilineal figures are "given in species" or "given in form" when their angles and the ratio of their sides are given. Points, lines, and angles are "given in position" when they always occupy the same place, and so on. After the definitions there follow ninety-four propositions, in which the object is to prove that if certain elements of a figure are given, other elements are also given in one of the defined senses" (DSB IV.524).The most interesting propositions are a group of four which are exercises in geometrical algebra corresponding to Elements 11.28, 29. Proposition 58 reads: "If a given area be applied to a given straight line so as to be deficient by a figure given in form, the breadths of the deficiency are given;" Proposition 84, which depends upon it, reads: "If two straight lines contain a given area in a given angle, and if one of them is greater than the other by a given quantity, then each of them is given." These propositions are together equivalent to asserting the existence of the solution of a certain quadratic equation. Propositions 59 and 85 give the corresponding theorems for the excess, and are again equivalent to a quadratic equation. "A clue to the purpose of the Data is given by its inclusion in what Pappus calls the Treasury of Analysis. The concept behind the Data is that if certain things are given, other things are necessarily implied, until we are brought to something that is agreed. The Data is a collection of hints on analysis. Pappus describes the contents of the book as known to him; the number and order of the propositions differ in some respects from the text which has come down to us" (ibid.).Claude Hardy (1598?-1678) was a lawyer by profession, but took part in the weekly meetings of Roberval, Mersenne, and the other French geometricians in the Académie Mersenne, and was a friend of Claude Mydorge, who introduced him to Descartes. In his Examen of 1630, and again in his Refutation of 1638, Hardy exposed the fallacy of Paul Yvon’s solution to the problem of the duplication of the cube, a problem which attracted the attention of several seventeenth century writers, including Viéte, Descartes, Fermat, and Newton. Hardy also engaged in the dispute between Fermat and Descartes over the former’s method of maxima and minima; Hardy, together with Desargues and Mydorge, supported Descartes, while Fermat found two zealous defenders in Roberval and Pascal. "Hardy owed his greatest fame, however, to his knowledge of Arabic and other exotic languages, and in particular, to his edition of Euclid’s Data (1625), the editio princeps of the Greek text, together with a Latin translation" (DSB, under Hardy). OCLC lists copies at New York Public, Harvard, Stanford, Wisconsin and Hong Kong only. DSB IV.524; Brunet 11.1081; Graesse II, p. 511; Hoffmann II, p. 167; Riccardi, Bib. Euclidea 1625; Steck VIII.10. 4to (223 x 178 mm), pp 8, 181, [3:errata], text in Latin and Greek in parallel columns, printer’s device on title, woodcut initials and headpieces, woodcut diagrams in text, printed marginal notes. Contemporary limp vellum. A very fine and completely unrestored copy. Bookseller Inventory # 3427

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Published by Johannem Hervagium, Mense Augusto, Basel (1537)

**Used**
**Hardcover**

Quantity Available: 1

From: Antiquariat Botanicum, ABAA (Lynden, WA, U.S.A.)

**Item Description: **Johannem Hervagium, Mense Augusto, Basel, 1537. Loose_leaf. Book Condition: Very Good. Folio. Period vellum with title in ink. Collation: [8] 1-587 [1] p. + Ornamental capitals and diagrams in text. Latin text with Greek letters used for designating points on geometric diagrams. Preface present. Paper used for printing title and last pages with some defects resulting in tears around defects. The title page has been restored along the gutter with a stub of old paper. The bottom right corner of title page restored with backing from other paper. The original free end papers have been replaced by early 18th century paper having amoral watermark (front) common to paper from the Hague or Leiden. Some of the tears on title page and end page repaired with paste. One 4-6 inch closed tear on p. 181 repaired. Minor damp staining on head and tail of several signatures not affecting text. This is the first Latin edition of the Herwagen Euclid which contains the complete works derived from the 1505 translation of Bartolomeo Zanetti and comments by Campanus, Hypiciles, and others, the very scarce preface of Philip Melanchthon, and first appearance of the fragment with four theorems by Levi. Censors often removed the preface from many copies. It is rare to find this preface present. There are ink marginal notes in Latin in an earlier hand on the first two pages of the preface and Greek on p. 6 at the end of Euclid's definitions from Campanus. These could have been done by the Danish astronomer Longomontanus whose signature is on the title page. Provenance: Written on the title page to the left of publisher and date of publication: "Ex lib. Christian S. Longomans." This signature of Christian Severin known as Longomontanus (1562-1647) is very rare. Longomontanus was a Danish astronomer and pupil of Tycho Brahe. In 1607 Longomontanus became "was professor of mathematics and astronomy at the University of Copenhage, where he remained until his death." (DSB) Severin inherited the restoration of astronomy program of Tycho Brahe upon Brahe's death in 1601. The two remaining tacks to complete were: "selection and integration of data into accounts of the motions of the planets, and the representation of the entire program in the form of a systematic treatise." (DSB) This was fulfilled in the publication by Severin, Astronomia danica published in 1622 which was reprinted twice (1640, 1663) despite the publication of Kepler's Tabulae Rudolphinae in 1627. Severin had a good "skill at manipulating observational data, and he may have played an important role in Tycho's remarkable research on the lunar theory." (DSB)Armorial bookplate of Sir Alexander Campbell of Cesnok who was one of the "Senators of the College of Justice and one of the Lords of Her Majesties most Honorable Privy Counsell & Exchequer &C: 1707." This appears to be the book plate belonging to Alexander (Hume) Campbell who had married Margaret Campbell, middle daughter of Sir George Campbell of Cesnock and took the name Campbell. His official name was Alexander Hume Campbell (1657-1740), 2nd Earl of Marchmont, 2nd Lord Polwarth and was a Scottish nobleman, politician and judge. He was a member of the Scottish Parliament for Berwickshire, was an advocate of the union with England (and thus the inclusion of 1707 on the amoral book plate), Lord Clerk Register, envoy to Denmark (from 1716-1733), and succeeded his father to the earldom in 1724, and was a Scottish representative peer (1727-1734). It was probably during his visit to Denmark as envoy that Sir Alexander Campbell purchased or received Severin's copy of Euclid's Elements. (Thomas-Stanford, 9; Houzeau-Lancaster 832; Adams H. 974). Bookseller Inventory # 0000438

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Published by Sold by Mr. Watkins; Mr. Ayscough optical instrument-makers; Messrs. Heath and Wing; Mr. Bennet mathematical instrument-makers; and by the author London (1758)

**Used**
**First Edition**

Quantity Available: 1

From: Shapero Rare Books (London, United Kingdom)

**Item Description: **Sold by Mr. Watkins; Mr. Ayscough optical instrument-makers; Messrs. Heath and Wing; Mr. Bennet mathematical instrument-makers; and by the author London, 1758. First edition. 4to., (28.3 x 22.5 cm). 26pp., 42 engraved plates with moving parts, modern quarter calf, all plates fine, clean, with no tears or repairs, a fine copy. Fine copy of this rare first edition. ESTC online lists only 6 copies: British Library; Kings College London; Houghton Library, Harvard; Columbia University Libraries, New York; Sterling Memorial Library, Yale; Fisher Library, Sydney. John Cowley was a leading mathematician of his day. He became professor of mathematics at the Royal Military Academy, Woolwich in 1761, and produced two remarkable books dealing with Euclidean geometry. The first of these appeared in 1752 and provides a way of "treat[ing] of solids and their sections, by laying before them [young students] a more natural and familiar representation of those bodies, than can be obtained from perspective pictures or draughts delineated upon a plane or flat surface . I come now . to lay before the public a new performance, the chief scope of which is to produce mechanical representations of solids and their sections, for the use of such as would obtain just ideas of those bodies . without any occasion for that great attention which is absolutely requisite to be employed by the mind, when contemplating on the nature and description of those bodies, while expressed only by lines drawn according to the rules of perspective; which is an arduous task." (Preface). This work anticipates the work of others such as Oliver Byrne, who nearly 100 years later, sought to provide a commentary on Euclid using visual methods. Bookseller Inventory # 85501

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Published by Basel Johannes Herwagen 1546. (1546)

**Used**
**First Edition**

Quantity Available: 1

From: Martayan Lan (New York, NY, U.S.A.)

**Item Description: **Basel Johannes Herwagen 1546., 1546. A genuine and attractive copy of the Basel Euclid in a contemporary binding. This edition contains the whole of the Euclidean corpus: in addition to the Elements in the different versions of Campanus, Navara and Zamberti, the Phaenomena, Catoptrica, and Data, it contains the first printing of the Opusculum de Levi & ponderoso, a fragment of which was discovered just as the present work’s first edition was about to be printed in 1537. Bookseller Inventory # 2733

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Published by Johann Hervagium, Basel (1546)

**Used**

Quantity Available: 1

From: B & L Rootenberg Rare Books, ABAA (Sherman Oaks, CA, U.S.A.)

**Item Description: **Johann Hervagium, Basel, 1546. Folio [viii], 587, [1] pp. Possibly a contemporary vellum binding, title in ink on spine, certainly a remboitage, with new endpapers; despite some minor staining on the first few leaves, a clean, wide-margined copy, with the ownership signature of Jacques de Baissonrond on the title, and contemporary annotations on the first few leaves of text. A large, wide-margined copy of the 1546 Herwagen edition of Euclid. According to Zeitlinger, it is "the first complete edition of Euclid’s works." It contains Theon’s explanation of the first thirteen books rendered in Latin by Bartholomaeus of Venice, plus the explanation by Campanus for all of the books, and by Hypsiclis of Alexandria for the last two. To these are added the Phaenomena, Catoptrica, and Data, as well as the first printing of the Opusculum de Levi & ponderoso, a fragment of which was discovered just as the present work’s first edition was about to be printed in 1537."The Basle editions, an important series, all folios, were printed by Johann Herwagen between 1533 and 1558. Herwagen had migrated from Strasburg about 1528, when he acquired the citizenship of Basle, and married Gertrude, widow of the learned Basle printer John Froben and the daughter of the scholar and patron of letters Wolfgang Lachner. He was the first printer to inset Euclid’s diagrams in the text . . . In August, 1537, he published a Latin version of the Elements, followed by other works attributed to Euclid. It is in roman type and contains three pages of introduction by Philip Melanchthon addressed ‘stdiosis adolescentibus’. From many copies this introduction has been removed by the clerical censor who has added his stamp. As there does not appear to be anything objectionable in the introduction itself, this action of the censor must have arisen from hostility to the writer of it . . . A reprint of this edition appeared in 1546; it is quite differently set up.". Bookseller Inventory # 14487

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Published by per Iohannem Hervagium, Basel (1546)

**Used**
**Hardcover**

Quantity Available: 1

From: Sokol Books Ltd. ABA ILAB (London, United Kingdom)

**Item Description: **per Iohannem Hervagium, Basel, 1546. Hardcover. Book Condition: Very good. LATIN EDITION OF EUCLID'S WORKS Folio, pp. (viii) 587 (i). Roman letter in two sizes, commentary in italic, some Greek innumerable woodcut mathematical diagrams in text. Printer’s woodcut device on title and verso of last, fine white on black historiated Holbeinesque initials in various sizes. Blank fore edge of first gathering slightly frayed, that of the title with early repair, light marginal water-staining in last few gatherings, occasional minor dust soiling. Generally a most attractive copy in strictly contemporary London blind-stamped calf, covers triple blind ruled to a panel design, roll-tooled second panel with lozenge-shaped inner border to both covers (Oldham pl. LI: 866), spine neatly repaired, pastedowns taken from an English rubricated manuscript. c.1400 with decorative initials, eps. from Galen’s De Compositione medic., Basle 1530. C16th autograph and manuscript acquisition note of R. Skene or Shene on title. A very interesting copy of the second edition of Herlinus’ Latin edition of the collected works of Euclid first printed nine years earlier: it is quite differently set up. A reissue of the Elements edited by LeFèvre, Paris, 1516, "with few changes but with the addition of the ‘Phaenomena, Optica’ etc. For the edition of 1537 the Paris edition was collated with ‘a Greek copy’ by Christian Herlin." Heath, ‘The thirteen books of Euclid’s Elements’. The text is embellished with the commentaries of Theon of Alexandria and Campanus, in the Latin version of Bartholomaeus Zambertus. "I now come to the Basle editions, an important series, all folios printed by Johann Herwagen between 1533 and 1558. He was the first printer to inset Euclid’s diagrams in text. Earlier printers, and some later, placed them in the fore margin." Stanford. This copy is complete with the six-page dedication by Melanchthon to the ‘studiosis adolescentibus’ which is often mutilated or missing (see e.g. Thomas-Stanford copy). "From many copies this introduction has been removed by the clerical censor who has added his stamp" Stanford. A typographically handsome (see full-page reproduction by Thomas-Stanford) and textually significant edition of the "compilation of all earlier Greek mathematical knowledge since Pythagoras, organized into a consistent system ( ) the common school textbook of geometry for hundreds of years." (Printing and the Mind of Man 25 on first Latin edition). The last 100 pages comprise the minor works of Euclid such as the Phaenomena Data, Specularia and Perspectiva. A handsome and interesting copy in a charming contemporary London binding. BM. STC. Ger. p.288 (at least one imperfect). Adams E 975 (1 ditto). Thomas-Stanford 11. (Full page reproduction) Latin. Bookseller Inventory # L1822

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**Used**
**First Edition**

Quantity Available: 1

From: Lynge & Søn ILAB-LILA (Copenhagen, Denmark)

**Item Description: **(Colophon: Venice, Venturino Rossenelli, 1543). Folio. (30,5x22 cm.). Contemporary full Italian limp vellum. Remains of ties. Old handwritten title on spine. Upper part of frontcover slightly creased. A few small nicks to hinges at cords. Vellum with brownspots. 242 leaves (2-241 numb. II-CCXXXIX). Misnumbering of leaves in sign. A (10 lvs.), due to the insertion of corrections on f A5. (Collation corresponds to that given by Thomas-Stanford No. 34). Large margins profusely illustrated with diagrams. Upper right corner of title gone with loss of of 3 letters "NSE" in MEGARENSE, f A2-A6 with upper right corners and a wormtract-hole in lower margin repaired. A wormtract in lower margin on the next 11 lvs. A1-A6 mounted skillfully on thin opaque parchment-paper. A rather faint dampstain in upper right corner throughout. Last 5 leaves with a small nick in right margin, no loss. Otherwise remarkable clean and printed on good strong paper. On the title a large woodcut device with arms with G.T. (Gabriele Tadino, to whom the work is dedicated). Colophon with large woodcut device with the letters .P.Z.F. and this repeated on verso of last leaf. Scarce first edition of the first translation of Euclid in any modern language by the famous Niccolo Tartaglia. The translation and Tartaglia's commentaries, strongly accelerated the development of physics and mechanics in the 16th century, as it showed how mathematics could be applied to dynamics and mechanics as well as to architecture, construction and perspective. More than 20 years should elapse before the next language should receive the privilege of displaying Euclid among their goods, this was the French translation published by Pierre Forcadel, Paris 1564. "When Tartaglia submits that his redaction was made "secondo le due tradittioni", there is no question that Campanus - who appears to be heavely favored - and Zamberti are meant. When Campanus has added propositions or premises, Tartaglia has approriately translated them and noted their absence "nelle seconda tradittione", while things omitted by Campanus but included by Zamberti receive the reverse treatment" (John Murdoch in DSB).Niccolo Fontana Tartaglia of Brescia has a great name in the history of mathematics. A cut in the face from a French soldier caused him to stammer and as a consequence of this he was called 'Tartaglia' (the stammerer). He is famous for his solution of third-degree equations which occasioned a long polemic with Cardano about priority. He is also known for "Tartaglia's Triangle", later known as "Pascal's Triangle", and he is well-known for his Archimedes-edition of 1543 and 1551 with his commentaries."The most famous source of Greek geometry is the monumental work of Euclid of Alexandria, called the "Elements" (around 300 B.C.). No other book of science had a comparable influence on the intellectual development of mankind. It was a treatise of geometry in thirteen books which included all the fundamental results of scientific geometry up to his time. Euclid did not claim for himself any particular discovery, he was merely a compiler. Yet, in view of the systematic arrangement of the subject matter and the exact logical procedure followed, we cannot doubt that he himself provided a large body of specific formulations and specific auxiliary theorems in his deductions. It is no longer possible to pass judgement on the authorship of much of this material; his book was meant as a textbook of geometry which paid attention to the material, while questions of priority did not enter the discussion." (Cornelius Lanzos in "Space through the Ages").Max Steck III:40 - Thomas-Stanford: 34 - Riccardi Euclideana 1543, 1 - Adams E:992. - Brunet II:1090. (Premiere edition de ce travail estimé). - Graesse II:513. Bookseller Inventory # 34704

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Published by London: William Pickering, 1847 (1847)

**Used**
**First Edition**

Quantity Available: 1

From: Peter Harrington. ABA member (London, United Kingdom)

**Item Description: **London: William Pickering, 1847, 1847. Quarto (233 x 185 mm). Rebound to style in dark blue half calf, spine gilt in compartments, red morocco labels, raised bands, marbled paper sides, brown endpapers. Board edges lightly rubbed, spotting and offsetting as virtually always with this book. A very good copy. Geometric diagrams printed in red, blue and yellow; printed in Caslon old-face type with ornamental initials by C. Whittingham of Chiswick. First edition of this celebrated book, the most interesting and inventive attempt to revisualise the classic ur-text of geometry by printing the diagrams in various colours, a method which stretched the printers' skills to their utmost. Oliver Byrne (c.1810–c.1890) is described on the title page as "Surveyor of Her Majesty's Settlements in the Falkland Islands and Author of Numerous Mathematical Works". He was appointed professor of mathematics, at the College for Civil Engineering, Putney, at the age of 20. The 1871 census lists his place of birth as Leyden, Holland. McLean, Victorian Book Design, p. 70. Bookseller Inventory # 90367

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Published by Paganinus de Paganinis, Venice (1509)

**Used**
**Hardcover**
**First Edition**

Quantity Available: 1

From: Milestones of Science Books (Ritterhude, Germany)

**Item Description: **Paganinus de Paganinis, Venice, 1509. Hardcover. Book Condition: Very Good. 1st Edition. 4to - over 9¾ - 12" tall. [Venice]: Paganinus de Paganinis, [11 June 1509]. 4to (295x208 mm). [1], 2-144 (i.e. 145), [1: blank] ff. Signatures: a10 b-s8. Place and date of printing from colophon (Venetiis Impressum per probum virum Paganinum de paganinis de Brixia [.], M.D.VIIII. Klen. XI Iunii). Title printed in red and black. Numerous woodcut initials and geometrical diagrams in the outside margins. Entirely restored binding, original morocco with gilt arabesque frame and centre-piece laid down on thick wooden boards, four new clasps and catches attached to three edges. Title-page and damaged edges of all leaves expertly restored with Japanese tissue paper (affecting 4 words of title, two words of f.1 and some of the outer geometrical diagrams in the first 40 leaves). Light browning, faint spotting and staining throughout. A few contemp. annotations in ink. A handsome copy, wide-margined and complete with the final blank. ---- Riccardi II, 229-30; Adams E-981; Thomas-Stanford 4; Sander 2608; Choix, 6525; Graesse II, 511-12. FIRST EDITION BY PACIOLI. The very rare edition edited by Luca de Pacioli (1445-1517), who has contributed important corrections and explanations. Pacioli was a friend and collaborator of Piero della Francesca and Leonardo da Vinci. He published his Summa of arithmetical practices in 1494, and in 1509 both his great Divina proportione (in which he collaborated with Leonardo) and this important edition of Euclid. "In 1509 there had appeared a very notable edition of the fifteen books of the Elements from the press of Paganinus de Paganinis From the typographical point of view it is a very remarkable and attractive book. The title, in red and black, is admirably spaced. The text, which is not overloaded with commentary, fills only half the width of the page, the ample margin being occupied by the diagrams which are on unusually large scale. In the Venetian Euclids of 1482, 1505, and 1509 the art of book-production reached the meridian" (Thomas-Stanford 6). Bookseller Inventory # 002085

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Published by Johannes Herwagen, Basel (1537)

**Used**
**Hardcover**
**First Edition**

Quantity Available: 1

From: Milestones of Science Books (Ritterhude, Germany)

**Item Description: **Johannes Herwagen, Basel, 1537. Hardcover. Book Condition: Very Good. 1st Edition. Folio - over 12 - 15" tall. Folio (292 x 198 mm). [8], 587 [1] pp., including the preface by Melanchthon, ornamental capitals and hundreds of diagrams in text, printer's woodcut device on title and Cc6v. Signatures: +4, a-z6, A-Cc6. Latin text with Greek letters used for designating points on geometric diagrams. Contemporary full vellum, spine with 4 raised bands, ink-lettered in first two compartments, embossed lettering to bottom edge (boards soiled and rubbed, little wear to extremities, upper hinge partly split, spine wormed and chipped at foot, corners bumped). Internally very little browned, the name Melanchthon ink censored on preliminary leaves, worm track to lower blank margin of first and final few leaves, little soiling of title-page, contemporary ink marginalia throughout (some shaved, one folded), faint marginal dampstains to few pages, occasional small ink spots. Provenance: Libreria Loescher, Roma (sticker to front pastedown). A fine, unrestored and wide-margined copy in nice contemporary binding. ---- Thomas-Stanford 9; Steck III.33; Houzeau-Lancater 832; Honeyman 977; VD 16, E4154; BM STC, German Books p. 288; Adams E 974. FIRST LATIN EDITION by Herwagen (Hervagius) with the prefatory letter by Philip Melanchthon which is often missing because of censorship (his name in our copy just inked out). Hervagen uses Bartolomeo Zanetti's translation of 1505 for this edition after having previously printed the first edition of the Greek text in 1533. The 1537 edition became the first to contain also Euclids smaller tracts "Phaenomena"(Spherical geometry), "Catoptrica" (Mirror-reflexion), "Optica", "Data" and "De levi et ponderoso" It was reprinted in 1546 and in 1558. Bookseller Inventory # 002541

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Published by Apud Vicentium Accoltum, Rome (1574)

**Used**
**First Edition**

Quantity Available: 1

From: Meiwes (Stuttgart, Germany)

**Item Description: **Apud Vicentium Accoltum, Rome, 1574. First Edition. 8vo., (17 x 12.5 cm), [40], 331, [1] (blank), [1] (title) 298 lvs., vellum, handwritten title to spine. First editions. Two volumes bound in one. Both volumes have an engraved title page. Vol.2 has title: Euclidis posteriores libri sex a X. ad XV. Accessit XVI., De solidorum regularium comparatione . Numerous geometrical diagrams in text. Colophon of Vol. 2 missing. The first edition of The Elements of Euclid by Clavius with his comprehensive comments. Clavius (1537-1612) a German Jesuit stayed in Rome where he tought Mathematics at the Collegio Romano. 'The Elements' is his main work. "The Elements, which is not a translation, contains a vast quantity of notes collected from previous commentators and editors, as well as some good criticism and elucidations of his own. Among other things, Clavius made a new attempt of proving the Postulate of Parallels." (DSB Vol. 3.) Based on this edition Matteo Ricci (1552-1610) ( also called Li Madou), and Xu Guangqi (1562-1633) translated the first six books of Euclid' Elements from Latin into Chinese and published it in 1607 in Beijing under the title 'Jihe yuanben'. "Euclid' Elements, in the Latin version prepared in 1574 by Christophorus Clavius [.] was the first substantial part of a European text to be translated into Chinese." (See: Engelfriet, Peter: Euclid in China, Leiden 1998; also on Clavius' edition: Heath, Thomas: Euclid's Elements, 1908) STC (Italian) p. 238. A fine copy. Bookseller Inventory # 314641

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