Published by Imprinted at London by Iohn Daye (1570)

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** First Edition **

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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 Basle, J. Herwagen (1533)

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**Hardcover**

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

**Item Description: **Basle, J. Herwagen, 1533. Hardcover. Book Condition: Very Good. EDITIO PRINCEPS. Folio pp (vi) 268, 115 (i). Greek letter, t.p. with printer's device repeated on verso of final leaf. First leaf of text within woodcut ornamental border (early ms Greek index in outer margin), woodcut headpieces and initials, printed mathematical diagrams throughout. Very extensive early Greek ms. annotations and corrections to the whole of the first 61 pp. (Book I) and the last 115 (Proclus' commentary in Greek and Latin) with numerous ms diagrammatic worked examples, very clear and legible. A very good, crisp, clean, wide-margined copy, stamp erased from the verso of t.p., in polished N. 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 1 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 ed. **** BM STC Ger. p. 288. Thomas-Stanford no. 7. Norman 730. Adams E 980. Stillwell II 210. Graesse II "édition encore aujourdhi indispensable. Bookseller Inventory # 1541

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**Used**
**
Softcover
**
** 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 Venice, Joannes Tacuinus de Tridino (1510)

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**Hardcover**

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

**Item Description: **Venice, Joannes Tacuinus de Tridino, 1510. Hardcover. Book Condition: Very Good. Folio, 240 unnumbered ll. [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 etc. (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 waterstaining, the odd spot or ink splash. A very good copy, crisp and clean, on thick paper, in contemporary limp vellum, remains of ties, title ms. 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 the first book as we know it. Zamberti contributes a long preface and a 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 1st edn.) as Zamberti claims but at least it is free of the errors of the mediaeval copyists. “Euclids Elements of Geometry is the oldest mathematical textbook in the world still in common use today.” Printing and the Mind of Man 25 on 1st edn. This is a lovely, fresh, totally unsophisticated 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. Bookseller Inventory # 1425

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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 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 Valentin Ottmar, Augsburg (1555)

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**Hardcover**

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

**Item Description: **Valentin Ottmar, Augsburg, 1555. Hardcover. Book Condition: Near Fine. (6) ff, CCXXXIIII, (2) ff. Bound in splendid contemporary calf, covers ruled in blind, with floriate gilt border, cherubs gilt on each side, with florettes at corners. Central panel boldly gilt: ARITHMETICA EUCLIDIS MEGARENSIS Teutsch Jac(ob) F(ugger). All edges gilt and gauffered. Head and foot of spine chipped and extremities rubbed, joints starting and one or two small wormholes on front board; inconsequential foxing in margin of title and scattered leaves; former ownership stamp on title. Withal an impressive example of a noble binding for the most important German family of its era, internally clean and fresh, an excellent copy. Exceptionally rare first appearance of any part of Euclid¿s work in German, edited and translated by one of the first German algebraists, Johann Scheubel (1494-1570). This is his only work addressed to advanced mathematicians rather than students, but appears to be little-known in studies of Scheubel¿s work, presumably owing to its rarity. An unusually fine copy with a distinguished provenance, bearing the contemporary binding of Jakob Fugger (1542-95) of the famous family of German merchant princes. It is unusual to find 16th century science books in such luxurious bespoke bindings, surely a sign of its owner¿s fabulous wealth. Scheubel¿s translation treats only Books VII-IX, containing all of Euclid¿s work on arithmetic and number theory, deliberately forming a coherent collection in itself. Book 7 deals strictly with number theory: divisibility, prime numbers, and the Euclidean algorithm for finding the greatest common divisor and least common multiple. Here Euclid also establishes the fundamental theorem of arithmetic, that every positive integer can be written as a product of primes in an essentially unique way. Book 8 deals with proportions in number theory and geometric sequences, including discussion of cubic and quadratic roots. Book 9 applies the results of the preceding two books. Here is Euclid¿s great proof that there are infinitely many prime numbers. He also gives the sum of a geometric series, and the construction of even perfect numbers (i.e. numbers that are equal to the sum of their divisors). Euclid¿s theorems are often illustrated in Scheubel¿s work with basic numerical or dot diagrams, and practical demonstrations are often added by Scheubel to illustrate the theorem at work. . The present copy belonged to Jakob Fugger (1542-95), whose name is gilt-stamped on the cover, son of the family patriarch Anton (1493-1560), whose commercial interests stretched from the mines of Eastern Europe to trade in the West Indies, Buenos Aires and Mexico. At the time the richest family in Europe, the Fuggers were generous patrons of the arts, notably at Augsburg, their principal residence. While the Fugger systems of patronage and mercantile empire-building have become the subject of much modern study, the practical aspects of their day-to-day financial success is usually neglected (see Häberlein¿s The Fuggers of Augsburg 2012). The first Fugger balance sheet had been drawn up only in the 1520s, and by 1560 there were deep concerns about the future of the company following Anton¿s death (Häberlein, p. 94). Scheubel¿s explicit focus on improving accounting methods may well have reflected the concerns of his patrons ¿ a topic for further research. More recently, the present copy was owned by Constantin Caratheodory (1873-1950), a distinguished mathematician who made significant contributions to the theory of functions, the calculus of variations and measure theory. He held a number of academic posts, eventually succeeding Felix Klein at Göttingen. Very rare: no copies in the major collections of Macclesfield, Honeyman, Horblit, or De Vitry (of nearly 200 editions of Euclid). OCLC: Brown, Columbia, British Library, National Library of Wales. Bookseller Inventory # 5153

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Published by Johann Herwagen, Basel (1546)

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**Hardcover**

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

**Item Description: **Johann Herwagen, Basel, 1546. Hardcover. Book Condition: Very Good. Folio, (1) f., 587 (1) pp.[printer¿s mark]. Note: with 3 ff. preface by Melancthon censored, as often (see Thomas-Stanford #9, first edition of 1537). Bound in contemporary reverse calf. Contemporary stenciling of title on lower fore-edge. Ownership inscription of Aldrovandi on title and several hundred lines of marginalia on 87 pages of text in his hand, ranging from a few lines to completely covering the margins. Highly interesting copy of the second edition of the Basel Euclid, the first complete collection of the Euclidean texts. The present copy bears extensive manuscript annotations by the celebrated Renaissance polymath Ulisse Aldrovandi (1522-1607), of great interest for charting the intellectual biography of this important Italian scientist. While undated, it seems likely that the annotations were made when Aldrovandi studied mathematics under the guidance of Pietro Catena in Padua between 1546-49. The Herwagen edition includes the most important modern commentaries on Euclid (Campanus and Zamberti), as well as printing for the first time a Euclidean tract translated from the Arabic, the ¿Opusculum de Levi & Ponderoso¿. As a man of considerable means, Aldrovandi assuredly owned a substantial library (given upon his death to the University of Bologna), but this is the first volume annotated by him that we have encountered on the market. The annotations have been briefly examined by Professor Robin Hartshorne at Berkeley, the world¿s leading authority on Euclid. According to Hartshorne, Aldrovandi¿s annotations are characteristic of a Renaissance student, often diligently working through concrete examples of theoretical problems. Occasionally his notes show evidence of additional knowledge drawn from other texts, whether from other editions of Euclid such as Tartaglia¿s or other mathematical discussions which were au courant. The annotations concentrate on Books VII-IX. This is no accident: these three books on number theory enjoyed a particular vogue around the middle of the sixteenth century all across Europe (witness the first German translation of Euclid (1555), which contained only these three books). The particular interest evinced by Aldrovandi in Euclid¿s work on number theory may also reflect the growing influence of his countryman Girolamo Cardano, whose famous work on probability was intimately tied to that field. Although he would become famous as a natural historian and physician, Aldrovandi¿s first line of study was mathematics. As a young man he studied the subject under Annibale della Nave; around 1547 he re-commenced his mathematical studies in Padua under Pietro Catena, the teacher of Bernardino Baldi and Guidobaldo del Monte. Catena is recorded as having lectured on Euclid, allowing us to hypothetically date the present annotations with some precision to between 1546 and 1549 (the year Aldrovandi returned to Bologna and faced arrest for heresy). Aldrovandi himself, in his manuscript autobiography, recounts having taught Euclid to ¿many students¿ (Lind, p xx). Catena would have passed onto the young Aldrovandi his own particular appraisal of Euclidean mathematics: that it cannot treat things which contain matter, but is instead a wholly abstract ¿ yet entirely valid ¿ method of scientific inquiry. This shift in the fundamental understanding of mathematical entities, according to Giulio Cesare Giacobbe, in turn fostered the spirit of empirical enquiry exemplified in the next generation by minds such as Galileo ¿ and, one might add, Aldrovandi? Ulisse Aldrovandi (1522-1605) was one of the most prolific and ¿multifaceted¿ (DSB) minds of the Renaissance. Aldrovandi applied himself to the natural sciences, principally medicine and natural history. He pioneered the study of embryology as well as being one of the first to elevate the studies of botany and pharmacology to a scientific plane. Bookseller Inventory # 5178

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

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

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. 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. 121, (1) ll., signed A@4, B-P@8, Q@4, R@2. 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. 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. Light dampstain in lower blank margin of final 20 leaves. Crisp; overall in fine condition. Bookplate from the Landau library, number 64704. ---- 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. NUC: MiU, MB. OCLC: 23621006 (Burndy Library, Indiana University, Houghton Library, University of Michigan, Brown University, Cambridge University, National Library of Wales), 560851127 (British Library); 266086700 (Cambridge University); 57317460 (microfilm copy: Center for Research Libraries, ProQuest). 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). 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 Paris: Henri Estienne 7 January /1517 (1516)

**Used**

Quantity Available: 1

From: Blackwell's Rare Books ABA ILAB BA (Oxford, United Kingdom)

**Item Description: **Paris: Henri Estienne 7 January /1517, 1516. Roman types, with numerous woodcut geometrical diagrams in the margins, fine criblé initials in a variety of styles and sizes, title-page soiled and cut down and mounted on old paper, one diagram just cropped at its extreme outer corner, ff. 261 (of 262, without the final blank), folio (296 x 210 mm), nineteenth-century half brown calf, by Hatton of Manchester, marbled edges, original order for the binder loosely inserted (in fact calling for half Russia), the Macclesfield copy with bookplate but no blind stamps, and annotated by John Collins, preserved in a cloth folding box, good. The sixth edition of Euclid, the first to be printed north of the Alps, the translation from the Greek of Bartolommeo Zamberti newly revised by Lefèvre d'Etaples, who added the "commentaries" of Campano, Theon, and Hypiscles. Thomas-Stanford is slightly dismissive: 'The Diagrams are well executed, but the tradition of the book beautiful is not maintained.' We are more inclined to agree with Schreiber who described it as 'a typographical masterpiece.' Ours moreover is a good size, 2 cm taller than Schreiber's and more than 1 cm wider (his in modern half calf). Thus all the diagrams are safe within generous margins, all except one, and that barely touched. The binder was not quite so kind to John Collins's notes however, which are in some instances cropped. This volume was Lot 699 in the Macclesfield sale, but failed to sell. The annotations were not mentioned in the catalogue, and were apparently overlooked by viewers since they certainly add interest to what is, apart from the title-page, a very good copy. Without a formal education, John Collins (1625-83) became a pivotal figure in the early years of the Royal Society where 'he had the opportunity to render the services for which he is remembered. For about ten years he served the society as a kind of unofficial secretary for all kinds of mathematical business. (The official secretary, until his death in 1677, was Henry Oldenburg who, in mathematical questions, relied heavily upon Collins's advice and assistance.) Collins conducted an extensive correspondence with some of the leading mathematicians in Britain and abroad, and he also drafted the mathematical details for Oldenburg's correspondence with these mathematicians (who included Barrow, Gregory, Huygens, Leibniz, Newton, Pell, Sluse, Tschirnhaus, and Wallis among others); Isaac Barrow called him 'Mersennus Anglus'. Collins obtained current mathematical news and foreign books for the Royal Society and its fellows, often in exchange for British scientific publications' (ODNB). Collins's books were acquired sometime after his death by William Jones, and hence to Shirburn Castle. Collins's notes appear on 16 pages, mainly in the first book. In four instances he has made corrections to the text (not errata). Scarce on the market: since 1975 only 7 copies appear in ABPC, only 1 of them since 1993, and only 1 in a contemporary binding, and that rebacked. (Schreiber 26; Steck III.14; Thomas-Stanford 6). Bookseller Inventory # 50370

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Published by Jacobus Chriegher German, Pesaro (1572)

**Used**
**Hardcover**

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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 Pisa Comillo Franceschini 1572 (1572)

**Used**
** First Edition **

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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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**Used**
** First Edition **

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

**Item Description: **Paris, Henrici Stephani (Henri Estienne), (1516). Folio. (30x21 cm.). Bound in a fine recent full vellum. 262 leaves (last leaf I 11, blank). 8 leaves misnumbered. Numerous fine initials in various sizes throughout, numerous diagrams arranged in the broad outer margins. Title-page having the printer's name crossed out in old ink, leaving a small hole in paper. An ink-spot on title-page. A few small worm-tracts on the first 7 leaves and in inner margins on a few leaves at the end. A tear to one corner repaired. A few marginal repairs. The first 6 books extensively annotated in the margins in a contemporary hand (in Latin), comments and references, and sometimes proposing other ways of representing the problem, sometimes calculations added. In general fine and clean and printed on good, strong paper. The scarce first edition thus, being the most important edition of the text before the appearance of the Greek editio princeps (1533). The present edition is the first Euclid-edition printed in France, the first printed outside of Italy and the first to contain both Campanus's and Zamberti's translations. It was edited by the famous founder of the French humanistic School, Jacques Lefévre (Jakob Faber Stagulensis), who, in this edition, solved many of the editorial problems of the previously printed editions. This beautifully printed edition, with the diagrams presented in the margins of the text, became the standard for many following editions.The work also comprises the proofs of Theon of Alexandria. During the Middle Ages it was thought that the proofs were made by Theon alone and that Euclid himself only formulated the propositions. "The most notable of Theon's editions is that of Euclid's "Elements", which was so influential that it consigned the original text to near oblivion." (D.S.B. XIII:322)."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 judgment 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 Lanczos in "Space through the Ages"). Adams E 982 - Riccardi 1516 (4) - Thomas-Stanford No. 6. - Max Steck III.14. Bookseller Inventory # 31906

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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 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. Woodcut royal arms on title-page. Woodcut initials (6 to 8 lines high). Numerous woodcut diagrams in text (usually 10 to 11 lines high). (6), 60 ll. 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. 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. ---- 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. NUC: CU (lacking title page), WU. OCLC: 16934885 (University of California-Berkeley, Houghton Library, Linda Hall Library); 36792525 (Columbia University, University of Wisconsin-Madison, National Library of Wales); 560852201 (British Library); 16627982 (Brown University); and 80597537 (microfilm copy: University of California-Berkeley). CCPBE locates 24 copies, a significant number of which are incomplete and / or in poor condition. Rebiun locates five copies: Universidad Politécnica de Madrid, Bookseller Inventory # 21312

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Published by Melchior Mondiere, Paris (1625)

**Used**
** First Edition **

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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 Basle, J. Herwagen (1546)

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**Hardcover**

Quantity Available: 1

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

**Item Description: **Basle, J. Herwagen, 1546. Hardcover. Book Condition: Very Good. 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 contemp. 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 ms. c.1400 with decorative initials, eps. from Galen’s De Compositione medic., Basle 1530. C16th autograph and ms. 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 reprod. 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 ed.). 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). Bookseller Inventory # 1822

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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)

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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 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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**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 Paris, apud Vascosamum (1551)

**Used**
**Hardcover**

Quantity Available: 1

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

**Item Description: **Paris, apud Vascosamum, 1551. Hardcover. Book Condition: Very Good. FIRST EDITION thus. 4to, ff. (xviii) 140. Theorems in Roman letter, explanations in Italic, a little Greek, printed diagrams illustrating text throughout . Contemporary autograph repeated and partially inked or written over on t.p. (one dated 1551) and inside rear corver, C19 armorial blind-stamp of double horse shoes surmounted by plumed helmets with motto 'Je maintiendrai' on second f.e.p., autograph of Sir Rowland Hill (1795-1879) on fly, C19 armorial bookplate inside front cover. Light waterstain to lower blank margins of first few gatherings, slight age yellowing, a good, clean copy in contemporary limp vellum, lacking ties, in 1/4 morocco folding box. **** First edition of Pierre de Montdoré's translation and commentary on the tenth book of Euclid's elements, dedicated to the Cardinal du Bellay. In his 36 page preface Montdoré explains that whilst the earlier books of Euclidian geometry are relatively easy for students, the tenth is considerably more complex - the book of 'irrational magnitudes' - based on Archimedes' 'method of exhaustion'. Its main achievements are the classification of irrational straight lines, making for much easier reference and the calculation of complex areas by a primitive form of integral calculus. Montdoré systematically explains these by reference to the earlier books and to other authors, especially Proclus. In his preface he fulsomely praises the work of Pythagoras but is scathingly dismissive of Ramus (named in contemporary ms) whose Latin version of the Elements had appeared in 1545. Montdoré (b. 1570), poet, mathematician, master of the Court of Requests and sometime Royal librarian at Fontainebleau was a protestant humanist scholar from Orleans, much admired by Montaigne. Ultimately his religious beliefs cost him his position and his splendid library and collection of mathematical instruments was pillaged after the St. Bartholomew's Day Massacre. Sir Rowland Hill, inventor and entrepreneur, is celebrated as creator of the world's first mass postal service 'the penny post', but as a young man he taught mathematics at his father's groundbreaking experimental school, becoming an expert Trigonometrical doubtless the present volume was put to good use. **** BM STC Fr. p. 157. Thomas Stanford IV:XII. Bookseller Inventory # 1450

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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 together. Numerous geometrical diagrams in text. Colophon of Vol. 2 missing. The first edition of The Elements of Euclid by Clavius with his comprehensive annotations. Clavius (1537-1612) a German Jesuit staid 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) (in Chinese 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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Published by Russell Maret, New York (2014)

**Used**

Quantity Available: 1

From: Jeremy Norman's historyofscience (Novato, CA, U.S.A.)

**Item Description: **Russell Maret, New York, 2014. Maret, Russell. Interstices & intersections or, an autodidact comprehends a cube. Thirteen Euclidean propositions. Translated by Thomas Little Heath with commentary by Russell Maret. [pagination etc., accordion-folded.] New York: Russell Maret, 2014. [size; binding by Daniel Kelm] One of 71 numbered copies printed by Maret on a special making of Zerkall paper. Preserved in a clamshell box. Prospectus included. A Letterpress Color Printing Tour de Force based on Euclid’s Elements, designed by Russell Maret and set in type designed by him, and with X [need numbers] beautiful color illustrations by Maret derived from Euclidean diagrams, each one requiring from ten to fourteen or more impressions to produce. Maret’s book has been compared Oliver Byrne’s The First Six Books of the Elements of Euclid (1847), but it is vastly superior in its design and execution, and includes color images that it is unlikely that any other letterpress printer could achieve. Maret described his design process for this work as follows: "I am beginning the project by reading and drawing proofs for all the propositions in Euclid’s thirteen books [of the Elements]. In the process, certain propositions stand out as having a particular interest or relevance: they spark associations in literature, letter forms, or life experience (or all three). I then develop visual ideas, write sections of text, and read books that might inspire or relate to the proposition at hand. Eventually, I will choose one proposition from each of the thirteen books and pair them with accompanying textual and visual commentaries of my own. For the illustrations, I am first painting them in pencil, ink, watercolor, and/or acrylic. Once I am satisfied with an illustration, I redraw it in separations to prepare it for printing. For the translation from painting to print to work, most of the spreads I have designed so far involve between ten and fourteen press runs each. The text of the book will be set in my proprietary type family, Gremolata & Cancellaresca Milanese, and printed from photo-polymer plates. The binding will be executed by Daniel Kelm" (Prospectus). Russell Maret is a fine printer and type designer working in New York City. He began printing in San Francisco as a teenager before apprenticing with Peter Koch in Berkeley and Firefly Press in Somerville, Massachusetts. He set up his own press at the Center for Book Arts, New York in 1993 and has been printing and publishing ever since. In 1996 Russell began teaching himself how to design typefaces, which led to a twelve-year study of letter forms before he completed his first typeface in 2008. The next year Russell was awarded the Rome Prize in Design from the American Academy in Rome. In 2011, he began working with the Dale Guild Type Foundry to convert some of his designs into new metal typefaces. Bookseller Inventory # 43151

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Published by Antonio Blado, Rome (1545)

**Used**
**
soft cover
**
** First Edition **

Quantity Available: 1

From: Rodger Friedman Rare Book Studio, ABAA (Tuxedo, NY, U.S.A.)

**Item Description: **Antonio Blado, Rome, 1545. soft cover. Book Condition: Very Good. 14cm; [109], [3 blank] pages. Text in Greek (except the dedicatory epistle from Angelo Caiano to Antonio Altoviti, in Latin). Woodcut portrait figure on title page; woodcut historiated initial. Bound in contemporary flexible vellum with overlapping fore-edges. Binding quite soiled with long split along upper joint, peeling a bit onto spine. Text clean, bright, with good margins and no blemishes. References: Thomas-Stanford, #26; Adams, E-996. A Greek edition of Euclid that includes, by design, the Propositions only (without proofs or diagrams). The Sixteenth Century believed that the Demonstrations were the work of a later commentator, a belief that was disproved by Henry Savile early in the 1600s. In true Humanist fashion, the editor of this text, Angelo Caiano, sought to pare away later accretions considered extraneous to the original text, leaving the Propositions only. The printer, Antonio Blado, has not inherited the popular recognition that fell to his contemporary peers, Paolo Manuzio and Bernardo and Benedetto Giunta. This repressed fame is due in part to Blado's onerous obligations as printer to the Apostolic Camera. Nevertheless, he took initiative, under patronage of Cardinals Farnese and Cervini, to produce fine humanist editions of Greek texts, both classical and patristic, from manuscripts in the Vatican Library. For this project, he studied Greek typography with Paolo Manuzio, gathered an impressive working group of Greek scholars, and entered into a sort of partnership with the Giunta. The venture ran out of money after only a few remarkable and high-priced editions. In order to bring matters under control, Blado commissioned a smaller Greek font from Giovanni Onorio Magliese, head of the Vatican Library's Greek division. The new Greek types make their debut in this volume of Euclid, which Blado struck of his own accord apart from the larger project. He called in the humanist Angelo Caiano to prepare the Greek text and produce an Italian translation, published as a "companion volume" (Thomas-Stanford) the same year. The volume was dedicated to the 24-year-old Antonio Altoviti, later Bishop of Florence and secretary to Pope Paul III. The result is the first Greek edition of a Euclidian text printed in Italy, preceded only by the Basel editio princeps of 1533 and the Paris edition of 1536. Bookseller Inventory # 5477

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Published by Venturio Rossinelli ad instantia e requisitione de Guilielmo de Monferra, & de Pietro di Facolo da Vinegia libraro, [Vinegia (i.e. Venice) (1543)

**Used**
** First Edition **

Quantity Available: 1

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

**Item Description: **Venturio Rossinelli ad instantia e requisitione de Guilielmo de Monferra, & de Pietro di Facolo da Vinegia libraro, [Vinegia (i.e. Venice), 1543. First edition in Italian and first edition in a modern language, folio, 242 leaves, large woodcut device on colophon and on verso of final leaf; woodcut arms on title-p.; geometrical woodcut diagrams in the margins throughout; a good, complete copy in dirty old vellum, recased in the 19th century, with extensive paper repair to margins of the title-p. and following leaf, also with paper repairs to corners of a number of pages throughout; some leaves washed. The translation and commentary is by Niccolo Tartaglia, one of the most noted mathematicians of the 16th century who here has added his own preface, commentary and eulogy on the utility of mathematics. According to Stillman Drake, Galileo at Work, pp. 2-4, it is probably this translation that was used by Galileo. "Tartaglia's Italian translation of Euclid - the first published translation of the Elements into any living language of Europe - was an event of great importance to the progress of mathematics, and indeed of all applied sciences. For the first time the principal treasury of rigorous mathematical reasoning was open to men who knew neither Greek nor Latin. The implications of that event for the science of mechanics were great because literacy in Europe was very high, especially among engineers and artisans" (Drake & Drabkin, Mechanics in Sixteenth Century Italy, pp. 21-22). Adams E-992; Thomas-Stanford, Early Editions of Euclid's Elements, no. 34. Bookseller Inventory # 26575

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Published by Pisauri [Pesaro], M D LXXII. Cum Privilegio Pont. Max. Publisher's statement from colophon (on verso of 3S3): Pisavri Cum Licentia Superiorum. Apud Camillum Francischinum. [Francischino, Camillo]., , (1572)

**Used**

Quantity Available: 1

From: Collectable Books (London, United Kingdom)

**Item Description: **Pisauri [Pesaro], M D LXXII. Cum Privilegio Pont. Max. Publisher's statement from colophon (on verso of 3S3): Pisavri Cum Licentia Superiorum. Apud Camillum Francischinum. [Francischino, Camillo]., , 1572. The first edition of the first Latin translation from the Greek. Folio, leaf size: 318x212mm. In period vellum binding, somewhat scuffed and worn, small manuscript calculation on back board. Spine with four raised bands, recently rebacked, relaying old spine with title manuscript in black. Book-plate: 'Ex libris Monastery St Augustinians Ramsgate' partially torn away at foot, on front pastedown. [12], 255, [1] leaves; signatures: [rosette]-2[rosette]6, A-3R4, 3S4 (the last leaf is blank). Ownership inscription at foot of front free end-paper. Title-page: text set within woodcut architectural border signed Iacobus Chriegher German[us]; three ink spots on the border; monastery stamp at lower foredge corner and on verso of final leaf. A few minor squiggles on front and rear pastedowns and on front free end-paper, recto and verso. Small singe mark on 2A3 (fol.95) affecting a few letters. Some light brown (ink?) splashes on 2L1 (fol. 133). Woodcut diagrams and most attractive historiated initial letters throughout. With printed marginal notes. Includes index. Printed in roman and italic type. See Thomas Heath, ‘The Thirteen Books of Euclid's Elements’, vol. 1, p. 104: 'The most important Latin translation . it was the foundation of most translations which followed it up to the time of Peyrard [1814]'. Extraordinarily crisp and clean. (Further information and photographs available on request.). Bookseller Inventory # 14418

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Published by Domenico Frisolino, Urbino (1575)

**Used**
**Hardcover**

Quantity Available: 1

From: Rodger Friedman Rare Book Studio, ABAA (Tuxedo, NY, U.S.A.)

**Item Description: **Domenico Frisolino, Urbino, 1575. Hard cover. Book Condition: Very Good. Folio; [16], 278 pages. Title page and all text pages ruled in typographic border. Typographic ornament on title page, 18 historiated initials (some duplicates) showing putti with geometer's instruments against a background of Italian hill towns. Numerous geometric figures in text. Bound in c19 (?) full mint green sheep, with red leather title label lettered and tooled in gilt. Edges stained indigo. Binding somewhat scuffed, with upper joint cracked; spine darkened and scuffed. Early ownership inscription on title page, later bookplate on front pastedown. Few marginal notes in contemporary hand. Very light occasional foxing present. References: Moranti, #4 ("un vero capolavoro tipografico" p.14); Gamba 1386 ("Nobile edizione"). The first book printed in Urbino in the 16th century, and only the fourth overall. Urbino's presses lagged behind those of other Italian cities, due in part to Duke Federico's predilection for manuscripts. It seems Federico Commandino, the foremost mathematician of the generation before Galileo, had a press set up in his house. He hired in a printer, Domenico Frisolino, and there he published his translation into Italian of Euclid, based on his own Latin translation of 1572. Commandino died just as the sheets were coming off the press. His brother-in-law hastily attached a dedicatory letter (to Francesco Maria II della Rovere) explaining that the Commandino wanted the text to be available to "all who are served by mathematics," that is, even those who do not understand classical languages. Euclid's text is glossed by Commandino's running commentary, and illustrated with figures. Bookseller Inventory # 5476

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