Euclid, First Edition (91 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. 460-375 BC). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384-322 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 foundation-a 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 golden section in the Renaissance after artists and architects rediscovered its pleasing proportions.) Book II also generalizes the Pythagorean theorem to arbitrary triangles, a result that is equivalent to the law of cosines. Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon. "Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus (along with Book XII) to Eudoxus of Cnidus (c. 395/390-342/337 BC). While Book V can be read independently of the rest of the Elements, its solution to the problem of incommensurables (irrational numbers) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms, culminating in the "application of areas," a procedure for solving quadratic problems by geometric means. "Books VII-IX contain elements of number theory, where number (arithmos) means positive integers greater than 1. Beginning with 22 new definitions-such as unity, even, odd, and prime-these books develop various properties of the positive integers. For instance, Book VII describes a method, antanaresis (now known as the Euclidean algorithm), for finding the greatest common divisor of two or more numbers; Book VIII examines numbers in continued proportions, now known as geometric sequences (such as ax, ax2, ax3, ax4, .); and Book IX proves that there are an infinite number of primes. "According to Proclus, Books X and XIII incorporate the work of the Pythagorean Thaetetus (c. 417-369 BC). Book X, which comprises roughly one-fourth of the Elements, seems disproportionate to the importance of its classification of incommensurable lines and areas (although study of this book would inspire Johannes Kepler [1571-1630] in his search for a cosmological model).

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 taá ¥rÄ«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 Naá £Ä«r al-DÄ«n al-á Å«sÄ« (1201-74) (and is so ascribed on the title page), but this is no longer accepted by scholars. The actual author, usually designated 'Pseudo-á Å«sÄ«', is unknown, although some believe it may have been al-á Å«sÄ«'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. 460-375 BC). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384-322 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 foundation-a 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 golden section in the Renaissance after artists and architects rediscovered its pleasing proportions.) Book II also generalizes the Pythagorean theorem to arbitrary triangles, a result that is equivalent to the law of cosines. Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon. "Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus (along with Book XII) to Eudoxus of Cnidus (c. 395/390-342/337 BC). While Book V can be read independently of the rest of the Elements, its solution to the problem of incommensurables (irrational numbers) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of rati.

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 wrappers (as here) and in the original cloth. Byrne (1810-1880) 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 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 the reach of educators who were supposed to 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 consequently never a viable book for cheap mass-production, effectively 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, available online. Quarto (240 x 192 mm). Original buff wrappers, printed paper label on front cover, untrimmed. Housed in a custom red, yellow, and blue geometric solander box. Title page vignette and numerous geometric diagrams printed in colour within text, engraved headpieces, floriated initials. Wrappers soiled, spine creased and cracked resulting in loss at ends, evidence of printed paper label missing from head of spine, front joint split but holding, contents generally bright, some light foxing as usual, sporadic damp staining to lower margins, a handful of neat later pencil annotations demonstrating close reading: a notably well-preserved copy in the fragile original wrappers.

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.

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. 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 'ΠεΠοΌεΜα,' 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 if a figure was given in kind, this meant that another figure similar to it could be placed anywhere in the plane. For ratios there was only one mode of being given: a ratio was given if a ratio equal to it could be obtained, which meant in effect that two magnitudes could be produced whose ratio was equal to the given ratio. "Euclid's Data contained some 100 problems of the form 'If A is given in mode α, then B is given in mode Π.' In all these propositions, the consequent (B) was constructible by straight lines and circles from the antecedent (A). These propositions, then, provided the steps by which the geometer planned the route from the given elements to the required ones. Once that route was planned, the construction could be written out along the same path. "Once a route from the given to the required elements was planned in the analysis by means of the Data, the geometer could then proceed to the synthesis, i.e., the actual construction, by writing out the separate construction steps along that route . Nevertheless, the locus classicus on analysis, Pappus's explanation at the beginning of Collection VII, stressed that the arguments in analysis and synthesis were each other's reverse . It appears, however, that the actual practice of analysis was we find it in classical and early modern sources calls for a more nuanced view. Beyond the fact that analysis started with the assumption of the required, its direction of argument was not so definite . In the case of analysis on the basis of the Data, the obvious order was the same as that of the synthesis, namely from the given to the required" (Bos, Redefining Geometrical Exactness (2012), pp. 100-102). 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;" Propos.

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.

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 Ÿ 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.

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.

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.

14. Londini (London), Excudebat R. Daniel, Impensis Guil. Nealand Bibliopolæ cantabrig. 1659, small in-8°, 15 x 9 cm, title page with woodengraved vignette + (14) nn pp + 399 pp + (1)(bl), with numerous small woodengraved geometrical designs in the text. Contemporary full calf, raised back with gilt title and compartments, upper lower joint split over 2 cm, but a very nice copy with only some very slight browing or staining on the inside. First work by Isaac Barrow, this latin edition published 4 years after the first edition and one year before the english translation.

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 7Ÿ" - 9Ÿ" tall. Book.

FIRST HILL EDITION 1726. Small folio, approximately 220 x 160 mm, 8œ x 6œ inches, woodcut and line diagrams, head- and tailpieces, pages: [12] - title page with recommendation from Edmund Halley on verso, Dedication, Preface, Explanation of Signs etc., and List of Subscribers, pages: [1]-267 followed by Errata, bound in full calf, rebacked in lighter leather, gilt lettered label to spine, gilt rules to raised bands and edges of covers, edges red, engraved armorial bookplate of the Earl of Roden and private library ticket with case and shelf number. Some shelf wear to edges and corners, light rubbing to label slightly affecting gilt, pale dampstaining to top margins, not affecting text, pale age-browning affecting a few pages at rear, neat old ink numbering to top corners of rectos throughout with no relation to the actual numbering, 2 small closed tears neatly repaired, not affecting text, 3 old ink ownership names on last blank margin, occasional small ink spot to top corner of last page, small stain to red edges, otherwise a very good tight copy. See: THE LIBRARY OF THE EARLS OF MACCLESFIELD. PART IV: SCIENCE, No. 736, the copy listed lacking list of subscribers; ESTC T131718. MORE IMAGES ATTACHED TO THIS LISTING, ALL ZOOMABLE, FURTHER IMAGES ON REQUEST. POSTAGE AT COST.

Hardcover. First Edition; First Printing. Very Good+, Leather Bound. Book 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 to ensure the highest quality binding. This book is in full leather with hubbed spines. Faint bumping on side text block edge. ; First Easton Press Edition.

Condition: Fair. 8vo, [iv],466,[ii]32pp (21x13cms), recent full panelled calf with title gilt on label, 3 copper plates of trigonometrical diagrams, one corner tear not affecting text (C4). The plates fold out for ease of reference, (creased along the folds and dust marked and creased on edges), has a new ffep. Overall the text is clean.Comments: published by one of the important British Classical publishers of the the 18th Century. Publication of this edition was overseen by Andrew, son of Robert Foulis who took over the firm after the death of his brother, the older Andrew Foulis. The press was already struggling financially during this period. Robert Simson (1687 - 1768), attended the University of Glasgow in 1702 at age 14, studied classics and oriental languages, later pursued interests in mathematics especially of the early Greeks. In 1711 was appointed Professor of Mathematics at Glasgow University, devoting much energy to restoring and editing the works of the early Greek geometers. His first edition of Euclid's elements was published in 1756, was immensely successful, becoming for many years the standard work, being republished in various editions as late as 1944. Refer to Gaskell "A Bibliography of the Foulis Press", item 648.

Lugdunum Batavorum (Leiden), Danielem à Gaesbeek, 1691. Small8vo. Contemp. full vellum. Spine gone and frontcover detached. Some soiling to covers. Wood-cut printers device on titlepage. (24),468 pp. and many diagrams in the text. A few scattered brownspots and a few quires with light browning. First edition of Heinrich Coetsius' translation of the six first books of Euclid.Riccardi 1691, 7 - Max Steck p. 109, 1691.