Euclid, First Edition (89 results)

First edition. PMM 25 - the oldest textbook in the history of science. First edition of the "oldest mathematical textbook still in common use today" (PMM), This book "has exercised an influence upon the human mind greater than that of any other work except the Bible" (DSB). 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 20th century. It is the foundation work not only for geometry but also for number theory. Euclid's Elements of Geometry 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. The text is the standard late-medieval recension of Campanus of Novara, based principally on the 12th-century translation from the Arabic by Adelard of Bath. In fact, Adelard left three Latin versions of Euclid. Campanus's text is a free reworking of earlier Latin translations, mainly Adelard's second version (an abbreviated paraphrase), with additional proofs that make it "the most adequate Arabic-Latin Euclid of all With an eye to making the Elements as self-contained as possible, he devoted considerable care to the elucidation and discussion of what he felt to be obscure and debatable points" (DSB). This text was printed more than a dozen times in the late-15th and 16th century. The "decisive influence of Euclid's geometrical conception of mathematics is reflected in two of the supreme works in the history of thought, Newton's Principia and Kant's Kritik der reinen Vernunft" (DSB). Ratdolt's edition is one of the most beautifully printed of early scientific books, and is the first dated book with diagrams (Stillwell). His method of printing diagrams in the margins to illustrate a mathematical text became a model for much subsequent scientific publishing. The method used to is still a matter of scholarly debate: although traditionally described as woodcuts, it is probable that printer's "rules" were used, i.e., thin strips of metal, type high, which were bent and cut and adjusted and set into a substance that would hold them (and pieces of type) in place. Born ca. 300 BC in Alexandria, Egypt, "Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 BC), not to be confused with the physician Hippocrates of Cos (c. 460375 BC). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384322 BC). The older elements were at once superseded by Euclid's and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own "Euclid understood that building a logical and rigorous geometry depends on the foundationa foundation that Euclid began in Book I with 23 definitions (such as "a point is that which has no part" and "a line is a length without breadth"), five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem "The subject of Book II has been called geometric algebra because it states algebraic identities as theorems about equivalent geometric figures. Book II contains a construction of "the section," the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. (This division was renamed the gol.

First edition. THE FIRST EDITION OF EUCLID IN ARABIC A TSAR OF RUSSIA'S COPY. First edition of Euclid in Arabic, "possibly the most remarkable of all printed editions of Euclid" (Thomas-Stanford). Euclid's Elements, the "oldest mathematical textbook still in common use today" (PMM), "has exercised an influence upon the human mind greater than that of any other work except the Bible" (DSB). It 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 20th century. It is the foundation work not only for geometry but also for number theory. Euclid was first re-introduced to medieval Europe through Adelard of Bath's Latin translation of an Arabic manuscript of the Elements a testament to the enduring importance of intellectual exchange between Europe and the Islamic world. This first printed Arabic edition (the only Arabic edition printed in Europe until the 19th century) is a ta?r?r of the Elements not a translation but a redaction, a re-working of older Arabic translations, with additions and commentary. The most significant of the additions is an attempted proof of the 'parallel postulate' (pp. 28-33) that through any point not on a given straight line passes a unique line that does not intersect the given line. This attempted proof exerted a considerable influence on the historical development of non-Euclidean geometry. A Latin translation of it was published by the great Oxford mathematician John Wallis in his Opera mathematica (1693) (based upon a lecture he had delivered 30 years earlier), and this in turn "became the starting point for the work of Saccheri and ultimately for the discovery of non-Euclidean geometry" (Katz, p. 271). This redaction of the Elements has traditionally been ascribed to the great Persian polymath Na??r al-D?n al-??s? (1201-74) (and is so ascribed on the title page), but this is no longer accepted by scholars. The actual author, usually designated 'Pseudo-??s?', is unknown, although some believe it may have been al-??s?'s son, Sadr al-Din. This beautiful edition of the Elements was printed at the press established by Ferdinando de' Medici under Pope Gregory XIII to disseminate works in oriental languages. Some copies (including the present one) contain the first 12 books of the Elements, others also contain the 13th book. The reason for the omission of the 13th book in some copies is unknown, but copies of the 'shorter' version are held in many great libraries (Oxford, Christ Church and Trinity; one, if not more, of the copies in Cambridge University Library, plus other Cambridge copies (see Adams); Göttingen; Munich; the Vitry copy in a contemporary German binding (Sotheby's 10-11 April 2002, lot 352); and others). In addition, while in the present copy the title page is partly in Arabic and partly in Latin, some copies have a title page entirely in Arabic (and the title verso is also reset see Thomas Stanford). Provenance: Tsar of Russia (ink stamps on title). Adam Litawor Chreptowicz (1768-1844), philanthropist and patron of science, Knight of Malta, Knight of Honor and Devotion of the Grand Catholic Priory in Russia (inscription at foot of title page, marginal annotations). He augmented the library of the Counts of Chreptowicz in Szczorsy (now in Belarus) which contained more than 10,000 volumes. The library was founded by his father Joachim Litawor Chreptowicz (1729-1812), Polish-Lithuanian nobleman, writer, poet, politician of the Grand Duchy of Lithuania, marshal of the Lithuanian Tribunal, and the last Grand Chancellor of Lithuania. Born ca. 300 BC in Alexandria, Egypt, "Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 BC), not to be confused with the physician Hippocrates of Cos (c. 460375 BC). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (38.

Hardcover. Condition: Very Good. 1st Edition. Oliver BYRNE (1810-1880). The First Six Books of the Elements of Euclid. London: [printed by Charles Whittingham for] William Pickering, 1847. Small 4to. (9 x 7 ¼ inches; 230 x 183mm). First edition of one of the oddest and most beautiful books of the whole century (McLean). Oliver Byrne was an Irish mathematician and engineer who focused greatly on improvements in educational materials for school children. In this marvelous effort, he elucidated the first six books of Euclid s Elements by coloured graphic explanations of each geometric principle. He designated the angles and lines of geometric figures instead of usual letters throughout the entire book, envisioning such a visual appeal will make it easier for schoolchildren to learn plane geometry. Exhibited at the Great Exhibition in London 1851, the book was praised for the beauty and artistry of the printing. It was quite unusual of a Science book to showcase such glamour and lavish richness of decorated printing and stands as a true masterpiece of the Victorian era. The book has become the subject of renewed interest in recent years for its innovative graphic conception and its style which prefigures the modernist experiments of the Bauhaus and De Stijl movements.

First edition of "one of the oddest and most beautiful books of the whole century" (McLean). The use of colour is its most iconic feature, with equal angles, lines, or polygonal regions assigned one of the three primary colours. It is rare in both the original cloth (as here) and in the original wrappers. Byrne (18101880) was a self-educated Irish mathematician and engineer who "considered that it might be easier to learn geometry if colours were substituted for the letters usually used to designate the angles and lines of geometric figures. Instead of referring to, say, 'angle ABC', Byrne's text substitued a blue or yellow or red section equivalent to similarly coloured sections in the theorem's main diagram" (Friedman). His style remarkably prefigures the modernist experiments of the Bauhaus and De Stijl movements. Exhibited at the Great Exhibition in London 1851, the book was praised for the beauty and artistry of the printing. However, the selling price of 25 shillings was almost five times the typical price for a Euclidean textbook of the time, placing it out of reach of educators who might make use of this new way of teaching geometry. The technical difficulty of keeping the coloured shapes in register greatly increased production costs, and it was therefore never a viable book for cheap mass-production, preventing Byrne's method from becoming widespread or effecting any major change in the teaching of geometry. Even so, its beauty and innovation ensure it remains among the most desirable of illustrated books from the Victorian period. Friedman, Color Printing in England 43; Keynes, Pickering, pp. 37, 65; McLean, Victorian Book Design, p. 70. Susan M. Hawes & Sid Kolpas, "Oliver Byrne: The Matisse of Mathematics", Convergence (Mathematical Association of America), Aug. 2015. Quarto. Original red straight-grain cloth, expertly rebacked preserving the original gilt-blocked spine, covers with ornamental blind panelling, front with gilt tooling, pale yellow endpapers, gilt edges. Geometric diagrams printed in red, yellow, and blue; printed in Caslon old-face type with ornamental initials by C. Whittingham of Chiswick. Bookseller's blindstamp (G. W. Holdich, Hull) to front free endpaper. Extremities gently rubbed, spine darkened, corners and inner hinges professionally restored, foxing and offsetting to contents as usual, the diagrams sharp and bright. A very good copy.

Hardcover. Condition: Near Fine. 1st Edition. 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).

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. Crisp. Light dampstain in lower blank margin of final 20 leaves. 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 six 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, Bibliografia euclidea, 1576 (1). Not in HSA. CCPBE locates sixteen copies. Not located in Rebiun (which cites Salamanca 1999 and Mairena del Aljarafe 2006 editions). Jisc repeats the two copies at Cambridge University. Not in Orbis (which lists the Salamanca 1999 edition at SML). KVK (51 databases searched) adds one copy at Biblioteca Nazionale Centrale-Roma, and one at Biblioteca Casanatense-Roma. NUC: MiU, MB.

Hardcover. Condition: Very Good. 1st Edition. FIRST EDITIONS. Folio. Three works in one, ff. (xii) 255 (iv) 55 (ii) 63 (i), first lacking last blank, separate t-p to each. Roman and Italic letter, pages double-ruled in red. First t-p within architectural border t-p, allegorical figures, grotesques, cornucopiae and small geometrical diagrams; second and third with printer's device to last; hundreds of fine geometrical diagrams; decorated initials. Occasional light yellowing, first t-p with odd marginal thumb mark, light marginal water stains to second t-p and a few ll. where annotations were washed, a few marginal tears without loss, old repairs to 3 ll. and one outer margin of final ll. of first work. Very good, well-margined copies in superb C17 French brown goatskin, gilt to a single- and double-ruled panel design, centre panel with gilt arms of Louis Bizeau surmounted by a plumed helmet, gilt monogram LB to corners, gilt roll of lozenges and circles to edges, all edges gilt and marbled. Spine triple gilt ruled in seven compartments, six with monogram LB, one with gilt lettering, floral scrolls with dentelles at head and foot, raised bands gilt to a roll of interlacing circles. Early casemark 'FF. 8. 31.' and armorial bookplate of Viscount Bruce of Ampthill and Baron Bruce of Whorleton, 'Robert Bruce 1729' to ffep, a few washed-out early marginalia. In modern slip box. The superb binding bears the monogram and arms (a fess, two stars in chief, a crescent in point) of Louis Bizeau (fl. first half of C17), a prominent bibliophile of whom little is known (Olivier, 'Manuel de l'amateur de reliures', V, pl. 486). Some of his bindings c.1645-50 have been linked to the same workshop as worked for Dominique Séguier (Quaritch, 'Examples of the Art of Book-Binding', 108-9). His books, like this, had ruled pages, gilt edges and marbled pastedowns. Excellent, well-margined copies, in fine impression, of Francesco Commandino's Latin translations of Euclid's 'Elements' and Archimedes's 'opera omnia', with Commandino's commentary, the last two issued together. These texts provided the foundations of modern mathematics and physics. Commandino (1509-75) was a humanist from Urbino renowned for his translations of the ancient Greek mathematicians including Aristarchus of Samos and Pappus of Alexandria. Several of his Latin renditions of Greek mathematical terms, for which he relied on previous adaptations by Roman authors like Cicero and Vitruvius, became the standard. Euclid (4 th century BC) was the first to reunite mathematical findings from the ancient world into a coherent, bi-dimensional system centred on simple axioms of plane geometry, based on angles and distance, from which further propositions (or theorems) could be deduced. His 'Elements' began with the crucial definition of 'point', 'that which has no part nor size' and which is only determined by two numbers defining its position in spacethe fundamental notion on which the Euclidean geometrical system is based. Archimedes (287-12BC) was a mathematician, inventor, astronomer and engineer from Syracuse. The 'Opera non nulla' includes all his recorded writings, except for the treatise on floating bodies and that on the method of mechanical theorems, which was discovered later. This editionthe sole Aldine of Archimedes's worksillustrates superbly his theorems on the area of circles, parabolae, spirals, spheres and cones, concluding with the famous 'De arenae numero', a calculation of the amount of sand grains needed to fill the universe. It is followed by Commandino's commentary on Archimedes's works, where geometrical diagrams are substituted by numerical calculations. Charles Bruce (1682-1747), Earl of Ailesbury, Viscount Bruce of Ampthill and Baron Bruce of Whorleton, was a keen book collector. A catalogue of his vast library, comprising over 8,000 volumes, at Tottenham in Wiltshire, was printed in 1733the second earliest catalogue of an English private library ever published (Pollard & Ehrman, 274-75).

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. Contemporary 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.

Hardcover. Condition: Very Good. 1st Edition. 4to (236 x 186 mm). [7] viii-xxix [1], 268 pp. Including half-title, four-line woodcut initials, color diagrams throughout printed in red, blue, yellow and black. Contemporary three-quarter calf over cloth, spine-ends and raised bands with gilt-decoration, gilt-lettered red morocco spine-label, original blue endpapers (extremities rubbed, corners bumped). Some pale brown spotting of text as usual*, minor age-toning of paper, but in all a better-than-average, crisp and clean copy. ---- FIRST AND ONLY EDITION OF BYRNE'S SPECTACULAR RENDERING OF EUCLIDEAN GEOMETRY USING FOUR-COLOR PRINTING, AND "THE MOST ATTRACTIVE EDITION OF EUCLID THE WORLD HAS EVER SEEN" (Oechslin). 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). "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). 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). "According to Julie L. Mellby, graphic arts librarian at Princeton University, in her online article "Euclid in Color," Byrne's Euclid was exhibited in London at the Great Exhibition of 1851. Praise was given for its beauty and the artistry of the printing, which may have influenced future publications and artwork. However, the book was sold for an extravagant price by contemporary standards, placing it out of the reach of educators who were supposed to make use of this new way of teaching geometry." *Virtually all copies of this print show more or less heavy brown spotting (or foxing) due to the used paper stock, but this copy is less affected than most copies we have seen. References: Janet Ing, Charles Whittingham, Printer, 46; Keynes, Pickering, pp. 37, 65; R. McLean, Victorian Book Design and Colour Printing p. 50-51 (illustration facing p. 53); E. R. Tufte, Envisioning Information, p.84; P. Lynch, That's Maths: The rebel who brought Technicolour to Euclid, Irish Times, February 20, 2014; W. Oechslin, ed., Oliver Byrne: The Elements of Euclid (Cologne, Germany: Taschen America LLC, 2013), p.15; J. L. Mellby, Euclid in Color, Princeton University Library, Princeton, New Jersey, 2008. - Visit our website to see more images!.

Hardcover. First edition. EDITIO PRINCEPS OF EUCLID'S DATA. 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. Euclid's Data opens with the passive perfect participle '????????,' which means 'given'; its Latin form 'data' remained in the title in modern times. "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. Rectilinear 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). The Data is more concerned with 'problems' than with 'theorems'. In theorems, the goal is to show the truth of a claim; in problems, it is to perform a task after being given certain objects (e.g., given a straight line segment, construct an equilateral triangle on it). The more you are 'given', the easier is the fulfillment of the task. The Data provides a mechanism for extending what one has been given by the terms of the problem. This is a tool for the solution of problems. "A clue to the purpose of the Data is given by its inclusion in what Pappus calls the Treasury of Analysis [or Collection] The Data is a collection of hints on analysis" (DSB). The relative obscurity of the Data, compared to the Elements, might be explained by the evolution of Greek mathematics, which in its early stages focused on the solution of special problems, but later concentrated more on the systematic arrangement of theorems. This is a very rare book. OCLC lists copies at Chicago, Harvard, New York Public, Stanford, and Wisconsin in US. ABPC/RBH lists only three other copies. There are "two characteristic features of a classical analysis of a [geometrical] problem: it proceeded by means of a concept 'given,' and it was performed with respect to a figure in which the required elements were supposed to be drawn already. The latter was indicated by such phrases as 'factum jam sit,' 'Let it be done.' Which served as a standard reminder that the subsequent argument was an analysis. The at-first-sight contradictory approach, namely to assume a problem solved in order to find its solution, was seen as the essential feature of analytical reasoning. In the supposed figure some elements were given at the outset; some were directly constructible from those originally given, and some required more steps. The analysis used a kind of shorthand, codified largely in Euclid's Data, for finding the constructible ('given') elements in the figure. The geometer used that shorthand as it were to plot a path from the primary given elements to the elements he ultimately wanted to construct. "In the Data Euclid distinguished between three modes of being given: given in magnitude, given in position, and given in kind. Geometrical entities (line segments, angles, rectilinear figures) were 'given in magnitude' if, as Euclid phrased it: 'we can assign equals to them.' The third mode applied to rectilinear figures (triangles, polygons); such a figure could be 'given in kind', which meant that its angles and the ratios of its sides were given, but not its size. Thus i.

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.

4to. 2 parts. (4 pp.), 5-16, 10 ff. Text in Greek and Latin. With woodcut printer's device as well as several floral headpieces and initials. Later full vellum with handwritten spine-title. First edition. Greek text and Latin translation of the "Introduction to Harmonics" by the Greek scholar Cleonides, the pupil of Aristoxenus, erroneously ascribed to Euclid, and of the "Division of the Scale", about whose true authorship there is no agreement. Edited by the French mathematician and educator Péna (ca. 1528-68), the book reflects the influence of classical mathematicians on Renaissance music theory and was a key work for the wide distribution of music theory of the classical period. - The attribution of the "Eisagoge" to Euclid (or to Pappus in some manuscripts) is incompatible with the Aristoxenian approach adopted in the treatise, namely that "the scale is formed of notes separated by a tone identified by the ear" (DSB IV, 430). Cleonides's treatise is the clearest account of the technical aspects in the work of the philosopher Aristoxenus, who defined key terms of music theory, including the interval, whole tone and semitone, pitch space, and rhythm. - The other musical work here ascribed to Euclid, the "Sectio canonis", expounds a quite contrary theory, namely "the Pythagorean doctrine that the musical intervals are to be distinguished by the mathematical ration of the notes terminating the interval [.] All that it seems possible to say with certainty is that Euclid wrote a book entitled 'Elements of Music' and that the 'Sectio canonis' has some connection with it" (DSB). Wechel printed both works in Greek as the first part and followed them with both Latin translations in the second. - Modern binding a little soiled and occasionally scratched; upper cover slightly bowed. Contemporary handwritten table of contents to second flyleaf (preserved from the first binding), mentioning another work by Péna, his translation of Euclid's "Optica & Catoptrica", also published in 1557, which appears to have been bound with the "Eisagoge" at the time. Second half shows a few light waterstains to the margin. Traces of an erased handwritten ownership on title-page. Rare; not seen at auction for nearly two decades. - RISM BVI 296. Gregory/Sonneck 85. Gesch. der Musiktheorie 7, 25 & 320. Davidsson 1962, 27. Gregory 85. Adams E 1023. Hoffmann II, 41. Schweiger I, 111. Not in Damschroder/Williams. OCLC 257567017.

Hardcover. Condition: Very Good. 1st Edition. [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). - Visit our website for additional images!.

Folio (314 x 209 mm). Complete Contemporary limp vellum. First edition in both Greek & Latin.Provenance: Contemporary annotations on pp. 83 (correction of the figure of propositio ii), 107 (additional drawing to propositio xxxi), 147 (marginal notes in book ii, propositio v), 153; in a different hand: 3, 114, 151."It is a handsome book, with the diagrams on a large scale and printed on better paper than the other Basle editions." (Thomas-Stanford p. 8).The introduction by Johann Scheubel (1494-1570) on pages 1-76 was printed separately as Algebra compendiosa facilisque descriptio . in 1551and 1552 in Paris (Smith, Rara Arithmetica, p. 252), and later in Basel. The German algebraist Johannes Scheubel lectured in Tübingen; he is known as one of the forerunners of algebra in Europe. In 1555 he published his translation into German of Euclid's books vii-ix. - Steck, Bibliographia Euclideana, p. 64 (III 49); Adams E 1012; Hoffmann II 39; VD16 E 4145. Except for a few scattered ink stains here and there a fine, unsophisticated copy with ample margins.

Condition: Very Good. First edition. RARE HISTORICALLY-IMPORTANT EDITION OF THE WORLD'S MOST INFLUENTIAL MATHEMATICAL TREATISE: THE FIRST "COMMANDINO" EDITION. Having established himself as a noted scholar, Federico Commandino of Urbino at the behest of his pupil Prince Francesco Maria translated into Latin Euclid's Elements, configuring it into 15 books and adding extensive commentary. A gorgeously printed work, profusely illustrated with 865 in-text diagrams, Commandino's edition, first published in 1572, was "made use of by subsequent editors for centuries" (Thomas-Stanford). EUCLID; COMMANDINO, FEDERICO. Euclidis Elementorum Libri XV. Unà cum Scholijs antiquis. A Federico Commandino Urbinate nuper in Latinum conversi, commentarijsq'ue quibusdam illustrati. Pesaro: [Camillo Franceshini], 1572. First edition. Folio (8.5 x 13 in; 216 x 330 mm); *,**6, A-Z, Aa-Zz, Aaa-Sss4: [12] (title-page, papal authorisation, dedication to Prince Frederico Maria of Urbino, contents), 255 ff., [1]. Bound in early eighteenth-century calf-backed decorated boards. With broad woodcut title page border by J. Chrieger, and woodcut illustrations throughout text and historiated initials at the start of each book. Ff. [100] and [192] misprinted as "110" and "129", respectively. Repair to hinge of title-page, some foxing and soiling to title-page, with tear (4 ¾ x 1 in) repaired later paper along right of bottom edge just clipping line of boarder, faint evidence of early stamp on top right margin; tear to bottom corner of f. 49; occasional foxing (most significant on ff. 38-39, 94-95, 146-47, 229, 232), otherwise crisp text throughout with extremely large margins. Thomas-Stanford 18. References: Dennistoun, James, Memoirs of the Dukes of Urbino, 3 vols. (London: Bodley Head, 1909), III Encyclopedia of the Scientific Revolution, ed. by Wilbur Applebaum (New York: Taylor & Francis, 2005) Thomas-Stanford, Charles, Early Editions of Euclid's Elements (London: Bibliographical Society, 1926).

(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.

18th century vellum over boards, spine with six (6) almost flat bands; gilt lettered title on morocco label on two; all edges speckled rose., Euclid or Euclid of Alexandria (~ 300 B.C.), "was a Greek mathematician, often referred to as the 'founder of geometry' or the 'father of geometry'. He was active in Alexandria during the reign of Ptolemy I (323?283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.? The Italian Federico Commandino (1509?1575) "studied at Padua and at Ferrara, where he received his doctorate in medicine. He was most famous for his central role as translator of works of ancient mathematicians. In this, his sources were primarily written in Greek and secondarily in Arabic, while his translations were primarily in Latin and secondarily in Italian. He was responsible for the publication of many treatises of Archimedes. He also translated the works of Aristarchus of Samos (On the sizes and distances of the Sun and the Moon), Pappus of Alexandria (Mathematical collection), Hero of Alexandria (Pneumatics), Ptolemy of Alexandria (Planisphere and Analemma), Apollonius of Perga (Conics) and Euclid of Alexandria (Elements). Among his pupils was Guidobaldo del Monte and Bernardino Baldi. Commandino maintained a correspondence with the astronomer Francesco Maurolico. The proposition known as Commandino's theorem first appears in his work on centers of gravity." The present work is the first edition of the Italian translation by Commandino; it is one among only few works printed in Urbino during the 16th century. , Size : Folio (303x212mm). , Illustrated printed title with woodcut device; large historiated woodcut initials at openings of chapters/ book with depictions of engagement in mathematical studies; moreover, numerous in-text woodcuts throughout the work depicting mathematical figures, concepts, and number lines.Text in Italian; panelled.Roman and Italic script. First Edition in Italian with Commandino?s commentary., References : Adams: E995; Brunet II: 1090; Gamba: 1386: , Ll: bl., [8], 278; collation: bl., [2] with title and dedication, **1-4, ***1-2, A1-Z4, AA1-ZZ4, AAa1-ZZz4, AAAa1-2, bl. Occasional scattered foxing and light marginal water stains, otherwise very good example.

8vo., 107, (3) pp., including woodcut portrait of Euclid on title. Bound in old cartonnage, title in ink on front cover. Lightly toned, old repair to wormhole in blank right corner of title, minor waterstaining at extreme lower edge of blank margin. Very good. Rare first edition of Euclid extracts in Italian, preceded only by Tartaglia's translation of 1543, of which it is independent. The first Italian translation made directly from the Greek. According to Rose, (Italian Renaissance of Mathematics, p. 189), the editor and translator Cainai omitted the proofs and figures of most editions because they were not Euclidean. According to Thomas-Stanford, it was issued along with (but is bibliographically separate from) a Greek language selection which the Roman publisher Blado published the same year. (Cf. Thomas-Stanford 26). The work was possibly intended for the use of young people, as in the preface, we read that it is dedicated by the translator, Angelo Caiano, 'allo eruditissimo Giovane, Messer Antonio Altovitti", the scion of a great Roman family. (Raphael painted a great portrait of the young man's relation Bindo Altovitti, now in the National Gallery, Washington). In the preface, Caiani affirms that he made the translation himself from the Greek. Of course, like the Tartaglia, the translation could also have been used by any Latinless reader. OCLC lists UCLA, Brown, Utah, Burndy, Harvard and Michigan. The only copy of the Greek is held by Burndy. Little is known about Caiani. He had a connection with the learned secretary of Ranuccio Farnese Annibal Caro, having copied one of the latter's manuscripts (Rose, ibid., p. 189). * Thomas Stanford 35; Fumagalli/Belli, Blado [1891]. Vol. I, fasc. I., No. 78; Riccardi I.208.

Hardcover. Condition: Very Good. 1st Edition. Folio (341 x 223 mm). [12], 282 pp., including half-title, title with engraved vignette of the Sheldonian theater, final blank leaf Qq4, numerous woodcut and typographic text diagrams throughout. Signatures: pi2 a-b2 A-G2 H-Z4 Aa-Qq4. Contemporary Cambridge-style speckled calf, spine with 6 raised bands richly gilt in compartments and with gilt-lettered red morocco label in second compartment, red-sprinkled edges, original endpapers (boards rubbed and scratched, joints partially split but cords sound, wear to extremities, corners bumped). Light pale dampstaining to first 4 leaves, leaf a2 of prelims with paper repair of tears (without loss), very minor occasional spotting, generally quite crisp and clean throughout. Provenance: Sir William Beauchamp Proctor* (his armorial bookplate with motto "tria juncta in uno" to front pastedown). ---- FIRST EDITION of Scarburgh's translation of Euclide, published from his manuscript by his son. Physician and mathematician Sir Charles Scarburgh was an original fellow of the Royal Society. John Evelyn described his library as "the very best collection, especially of mathematical books, that was, I believe, in Europe." *Sir William Beauchamp-Proctor, 1st Baronet (1722-1773) was an English politician who served as a member of Parliament from Middlesex from 1747 to 1768. He was the first of the Proctor-Beauchamp baronets. References: Wallis, British Euclids, p.5. - Visit our website to see more images!.

Uppsala, Eschillus Matthiæ, 1637. Small 4to. Cont. full vellum over wood. Spine ends worn, tears to hinges, but not broken, lower edges of boards with old repairs. Some old ink annotations on boards. Inside frontcover and on title many old owner names, small wholes cut in titel without loss of letters. First ab. 20 leaves with a faint dampstain in upper margin, inkspots on last page. Internally clean. (24),350,(2) pp., numerous geometrical diagrams in the text. Scarce first edition of the first Swedish edition of Euclid's Elements (Book I-VI) with Gestrinius' commentaries to the axioms and porpositions and with his attempt of a proof of the "Parallel-axiom" (The Fifth Postulate). In the preface he discusses the use of plane-geometry in the theories of Aristoteles, Eudoxus, Ptolemy and Kepler. - Gastrinius (1594-1648) became professor of mathematics in Uppsala in 1621 after studies in Greifswald.Collijn (1600-Talet) I:310. - Riccardi p. 436 (1637,2) - Poggendorff I:889. - Not in Max Steck.

Hardcover. Condition: Good. Small 8vo (13.5 cm), early vellum rebacked, with ms. title on spine a good clean copy (light repair to the lower corner of last leaves, far from text). A woodcut depicting Euclid's portrait at centre of title-page, pp. 107, (5, last 2 orig. blank). First edition of this rare translation made directly from the Greek into Italian of Euclid (in extract) preceded only by Tartaglia's translation of 1543 (Venice, Rossinelli), of which it is independent. This translation was probably intended for didactic use, also given the dedication to a young member of the noble Roman Altoviti family. Fumagalli/Belli, Blado I/1°, n. 78; Smith pp. 236-7; Thomas-Stanford n. 35; Riccardi I/1°, c. 208; BMC STC Ital. p. 239.

Quibus, cùm ad omnem Mathematicae scientiae partem tùm ad quamlibet Geometriae tractationem, facilis comparatur aditus. 8°. 14 Bll. (a1-8, b1-6), 203 S. Mit Druckermarke, zahlr. Diagrammen u. geometr. Figuren in Holzschn. Flex. Pgmt. d. Zt. Rückensch. abgelöst. Wurmgänge a. d. ersten u. letzten Bll. vgl. BMC 288 (Ausg. 1587); vgl. Benzig 228; VD16, E4160 - Beigeb.: ZALLAMELLA, Pandulpho. Tabula quaestionum omnium scoti; Cum reductione illarum ad unitatem triplicem, alphabeti scilicet, materiae, & propositionis. Venedig, N. Morettus 1591. 80 S. - Erste Ausgabe, im Todesjahr d. Verf. erschienen. Pandolfo Zallamella wurde 1551 in Ravenna geboren u. war seit 1568 Schüler von G. Porta, der ihn sehr geschätzt haben muß, da er ihn bei seinem Abschied 1574 als Nachfolger für das Domkapellmeisteramt in Ravenna vorschlug. Gewicht in Gramm: 500.

Hardcover. Condition: Good. 1st Edition. Two volumes. Second edition of Clavius's main work, his rare and influential edition of Euclid. Clavius (1538-1612), was called by his contemporaries "the Euclid of the sixteenth century", a Jesuit mathematician who gave the Gregorian Calendar of New Style its present form and made all the calculations necessary for its verification. His edition contains the fifteen books with very full scholia, and the addition of a sixteenth, De solidorum regularium comparatione. It was first printed at Rome in 1574 in the same form, and in folio at Cologne in 1591. [Clavius's] "Elements, which is not a translation, contains a vast quantity of notes collected from previous commentators and editors, as well as some good criticisms and elucidations of his own. Among other things, Clavius made a new attempt at proving 'the postulate of the parallels.'In a scholion, to the twelfth proposition of the ninth book of Euclid, Clavius objects to Cardanus' claim to originality in employing a method that derives a proposition by assuming the contradictory of the proposition to be proved. According to Clavius, Cardanus was anticipated in this method by Euclid and by Theodosius of Bithynia in the twelfth proposition of the first book of his Sphaericorum."-D.S.B., III, p. 311. Very rare to find complete in two volumes. Full 18th century vellum binding. Pictorial Title-page with the engraved figures of Archimedes and Euclides; many geometric illustrations within the text. Ex libris from the noble family Doria of Genoa. Doria is an old and extremely wealthy Genoese family who played a major role in the history of the Republic of Genoa and in Italy, from the 12th century to the 16th century. Ships from U.A.E.

Euclid's Optics is a work on vision written around 300 BC. The earliest surviving manuscript of Optics is in Greek and dates from the 10th century AD. It focuses almost completely on the geometry of vision with little reference to either the physical or psychological aspects of sight. No Westerner had previously given such mathematical attention to the subject of vision. Euclid's work influenced many later Greek, Islamic, and Western European Renaissance scientists and artists. Heliodorus of Larissa (fl. 3rd century?) first propounded the axiom that light on being reflected always chooses the shortest way. Small quarto. [8], 110, [2, blank with small vignette on verso]. [34] pp. Geometrical diagrams in text. Woodcut printer's device on title-page, decorative initial letters, tail-pieces, and other vignettes. Separate title-page for La Prospettiva di Elidoro Larisseo, with small typographic vignette. Contemporary vellum over stiff boards, title in manuscript on spine. Covers soiled, with a few stains, one wormhole at spine, light worming to pastedown endpapers. Dampstain at top edge and fore-edge in first and last few leaves, first few leaves closely cropped at top edge, grazing a few words, but not affecting legibility. A little light foxing and toning, and a few additional small stains. One inch tear at fore-edge of blank between the two works. A good, sound copy. First Italian edition of Euclid's Optica (La prospettiva di Euclide), together with a translation of the spurious Catoptrica (Gli specchi di Euclide). La prospettiua di Eliodoro Larisseo follows, first in the Italian, and then in the Greek and Latin versions, in parallel columns Adams E 1021. Riccardi I, 391. Wellcome I - 2085; Gamba, 1385.

(26 x 20 cm). XLII (statt XLIV?) 518 (2) S./ XLIV, 518 (1) S./ (4) XVIII, 616 S. Mit zahlreichen Textholzschnitten. Moderne Pappbände im Stil der Zeit. Erste Ausgabe dieses hervorragenden Werkes, der einzigen trilingualen Edition der euklidschen Werke. - "Das dreibändige Hauptwerk von Peyrard, mit dem er den Höhepunkt seiner Quellenforschung zu Euklid erreicht und die Grundlage für die abschließende Ausgabe der Heiberg-Menge u.a. schafft, indem er die ortheonische Redaktion der Euklidischen Elemente in einer griechisch-lateinisch-französischen Ausgabe bietet" (Steck). Peyrard ist der Erste, der auf die Vatikan-Handschrift "Vaticanus Graecus 190" zurückgreift; sie ist die einzige vollständige vortheonische und damit die älteste bekannte Fassung der 'Elemente'. - Vereinzelt leicht stockfleckig. Die ersten Blätter von Band 3 in der rechten oberen Ecke mit kleinem Fleckenrand. Möglicherweise fehlt ein Blatt der Vorstücke von Band 1. Insgesamt gut erhaltenes Exemplar. - Steck VI.6; Riccardi, Bibliografia Euclidea S. 484.

Hardcover. Condition: Good. 1st Edition. FIRST EDITION IN ENGLISH. Leather-bound, hardcover, small octavo (15.5 x 10 x 2.5 cm.), pp. [4], 380. Signatures: A-3B [sup]4. English text, with diagrams in the text throughout. Bound in contemporary full calf. Title-page enclosed within double line border. Condition: GOOD. Binding secure, however, the joints are rubbed and starting to split slightly. Corners rubbed and bumped. Lacking front blank leaf, else complete. Interior lightly toned, a couple of corners slightly torn away not affecting text, title-page with slightly ragged fore edge. Otherwise well-preserved. Scarce. Notes: An attractive copy in a contemporary English binding of the first edition of this English translation of Dechasles's Euclidis Elementorum libri octo, a paraphrase of Euclid's Elements [according to Backer's Bibl. de la Compagnie de Jesus, the translation was made by William Halifax]. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's Elements. Another, more common English edition was published in London by Phillip Lea in the same year, the translation being by Reeve Williams. 'Dechales [is also known to have] adopted Galileo's theory of motion, where he introduced several original views and developments. [Wing E-3400; ESTC R21479; OCLC 926232929].

Kjøbenhavn, Ernst Henrik Berling, 1744. 4to. Samt. hldrbd. over træ. Ryg lidt slidt Overtrækspapiret på permer med mangler.(12),20,311 pp. samt 5 foldede kobberstukne plancher, i teksten talrige geometriske figurer. De første blade og de 5 plancher med en svag vandskjold. Svag skjold på de sidste ca 20 blade. En del blade med brunplet i øvre margin.4to. Contemporary half calf over wooden boards. Spine a bit worn and lacing some of the paper over boards. Faint damp stain to first leaves, to plates, and to the last ab. 20 leaves. Some leaves with a brown spot to upper margin. (12), 20, 311 pp + 5 folded engraved plates. Numerous geometrical figures in the text. Første udgave på dansk af Euclids "Elementer", omfattende Bog 1-6 og 11-12. J.F. Ramus have allerede nogle år tidligere udgivet Euclid, men disse var mindre lærebøger i uddrag og på latin. Oversættelsen indeholder en lang introduktion af Ramus "Betænkning om Euclidis Elementer og om deres Oversættelse i det Danske Sprog."Ziegenbalg var teologisk kandidat, men havde studeret matematik i flere år, både i Jena og i England. Han blev udnævnt til professor i matematik ved Københavns Universitet efter Ramus, og havde i nogle år forinden fungeret som dennes assistent. Hans oversættelse er dedikeret Christian den VI, og i forordet introducerer han den således "offereres (oversættelsen) Deres Kongelige Majestæt.disse udi det Danske Sprog oversatte Elementa Geometriæ, som ere Hoved=Kilden til alle Mathematiske Videnskaber og have nu i 2000 Aar været i saa stor Estime, at alle de største og erfarne Mathematici have grundet deres Skrifter paa dem og at de til almindelig Nytte og Brug ere bekientgiorte næsten udi alle Europæiske, men ey tilforn i dette Sprog."First edition of the first Euclid-translation into Danish, comprising Book 1-6 and 11-12. Bound in cont. hcalf. Rebacked in old style. A good copy. - Riccardi, Bibl. Euclideana, Parte 4, p. 47. - Bibl. Danica IV:96.

7 Bll., 342 S. Mit zahlreichen Textholzschnitten. Pergament der Zeit (Hardcover). Erste Ausgabe. First Edition. Einband fest. Hinterdeckel am unteren Rand mit festgeklebtem Papierrest. Innen papierbedingt gebräunt. Ältere Besitzvermerke. Guter Zustand. Sprache: la.

Hardcover. First Edition; First Printing. Near Fine, Leather Bound, Accented in 22kt gold. Printed on archival paper with gilded edges. The endsheets are of moire fabric with a silk ribbon page marker. Smyth sewing and concealed muslin joints. This book is in full leather with hubbed spines. Notes from editors neatly laid in. ; First Franklin Library Edition.

Half-Leather. Condition: Very Good. First Thus. Marbled 1/2 leather, gray paper covered boards, 5 raised bands with gilt-stamped compartments, lacking title label, marbled endpapers (perhaps not original to issue). Surface rubbing to boards, several scratches to back cover, leather mostly intact though with rubbed corners. Edges rubbed with exposure, modest leather loss to top front and bottom rear corners. Firm binding. Former owner's signature on blank opposite main title, dated 1782, another signature dated 1825 on main title. [xvi],366,[1] pp., illus. w/ figures in text. Interior nicely intact, with minimal toning or foxing, all leaves firmly anchored. Very scarce. Size: 8vo - over 7¾" - 9¾" tall. Book.