EUCLID OF ALEXANDRIA.Livre Rare Book
34 résultats
154334704(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 front cover 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 remarkably 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.
158862780Colophon: Pisauri (Pesaro), Hieronymum Concordiam, 1588. (Having the reprinted title-page: Venetiis, Franciscum de Franciscis Senemsem, 1589). Folio. Contemporary limp vellum. Repairs to upper part of spine and small nicks to back repaired. Edges of covers with tiny loss of vellum. Covers slightly soiled. Calligraphed title on back. Title-page with and old, partly erased stamp. Woodcut printer's device on title-page. Ff (3), 334 (332) (= 664 pp). Numerous woodcut diagrams and illustrations in the text. Printed on good paper. Ff. 2-3 with an old repair to inner margin (no loss). F2 browned, but otherwise remarkably clean with only a few brownspots. A few small worm-tracts to some margins. In spite of its flaws, a very good copy of this monumental work.
158862780Colophon: Pisauri Pesaro Hieronymum Concordiam 1588. Having the reprinted title-page: Venetiis Franciscum de Franciscis Senemsem 1589. Folio. Contemporary limp vellum. Repairs to upper part of spine and small nicks to back repaired. Edges of covers with tiny loss of vellum. Covers slightly soiled. Calligraphed title on back. Title-page with and old partly erased stamp. Woodcut printer's device on title-page. Ff 3 334 332 = 664 pp. Numerous woodcut diagrams and illustrations in the text. Printed on good paper. Ff. 2-3 with an old repair to inner margin no loss. F2 browned but otherwise remarkably clean with only a few brownspots. A few small worm-tracts to some margins. In spite of its flaws a very good copy of this monumental work. <br/><br/><em>First edition title-issue with the fresh title-page stating 1589 but with nothing else reprinted and otherwise through and through the 1588-printing of Commandino's seminal Latin translation of the work that constitutes the culmination of Greek Mathematics. This printing which contains the complete extant text of Pappos in Latin translation is responsible for reviving ancient mathematics in the Renaissance and shaping much modern mathematics profoundly influencing the likes of Descartes and Newton. "Pappos was the greatest mathematician of the final period of ancient science and no one emulated him in Byzantine times. He was the last mathematical giant of antiquity." George Sarton Ancient Science and Modern Civilization. p.82. "Pappus of Alexandria in ab. 320 composed a work with the title Collection Synagoge which is important for several reasons. In the first place it provides a most valuable historical record of parts of Greek Mathematics that otherwise would be unknown to us. For instance it is in Book V of the Collection that we learn of Archimedes' discovery of the thirteen semiregular polyhedra or "Archimedian solids". Then too the Collection includes alternative proofs and supplementary lemmas for propositions in Euclid Archimedes Appolonius and Ptolemy. Finally the treatise includes new discoveries and generalizations not found in any earlier work. The Collection Pappus' most important treatise contained eight Books but the first Book and the first part of the second Book are now lost" Boyer A History of Mathematics p. 205. "Each book 8 is preceded by general reflexions which give to that group of problems its philosophical and historical setting. The prefaces are of deep interest to historians of mathematics and therefore it is a great pity that three of them are lost . Book VII is far the longest book of the Collection . and here we find in it the famous Pappo's problem: "given several straight lines in a plane to find the locus point such that when straight lines are drawn from it to the given lines at a given angle the products of certain of the segments shall be in a given ratio to the product of the remaining ones". This problem is important in itself but even so because it exercized Descartes' mind and caused him to invent the method of coordinates explained in his Geométrie 1637. Think of a seed lying asleep for more than thirteen centuries and then helping to produce that magnificent flowering analytical geometry . The final Book VIII is mechanical and is largely derived from Heron of Alexandria. Following Heron Pappos distinguished various parts of theoretical mechanics geometry arithmetic astronomy and physics. The Book is considered the climax of Greek mechanics and helps us to realize the great variety of problems to which the Hellenistic mechanicians addressed themselves. If Book VIII is the climax of Greek mechanics we may say as well that the whole collection is a treasury and to some extent the culmination of Greek mathematics. . The ideas collected or invented by Pappos did not stimulate Western mathematicians until very late but when they finally did they caused the birth of modern mathematics- analytical geometry projective geometry centrobaric method. That birth or rebirth from Pappos' ashes occurred within four years 1637-40. This was modern geometry connected immediately with the ancient one as if nothing had happened between." Georg Sarton op.cit. - It is from Pappus we have the famous words of Archimedes: "Give me a place to stand and I will move the earth" Se PMM No 72. - "Without pretending to great originality the whole work shows on the part of the author a thorough grasp of all the subjects treated independent of judgement mastery of technique; the style is terse and clear; in short Pappus stands out as an accomplished and versatile mathematician a worthy representative of the classical Greek geometry." Heath A History of Greek mathematics Vol. II: p.358. Adams P 224 The sheets of the Pisauris edition with a fresh title. </em> hardcover
1538126667Basel: Johann Walder 1538. Theon's valuable commentary on the Almagest Editio princeps. Theon father of the celebrated female mathematician and philosopher Hypatia composed his commentary on the Almagest as a redaction of his lectures said to have been given at the Museum in Alexandria. Edited by Joachim Camerarius 1500-1574 the commentary is of particular value to modern scholars because it preserves information about now-lost mathematical and astronomical treatises. The book was issued as a companion volume to the editio princeps of the Almagest published the same year by Walder. Folio 316 x 203 mm 1 vol. only of 2. Contemporary limp vellum sewn on three cords yapp edges ties lacking. Housed in a vellum-backed folding case spine lettered in gilt. Bookplate of Elizabeth Sprague. Light dampstain at head some gatherings lightly browned still a very good copy. hardcover
15882080Pesaro: Girolamo Concordia 1588. First edition. original boards. Very Good. FIRST EDITION of arguably the most important source book for the works of the Greek mathematicians. The magnificent Horblit copy in contemporary probably original boards. Pappus of Alexandria fl 320AD was "the most important mathematical author writing in Greek during the later Roman Empire known for his Synagoge "Collection" a voluminous account of the most important work done in ancient Greek mathematics. Pappus seldom claimed to present original discoveries but he had an eye for interesting material in his predecessors' writings many of which have not survived outside of his work. As a source of information concerning the history of Greek mathematics he has few rivals." Pappus's principal work "was the Synagoge c. 340 a composition in at least eight books corresponding to the individual rolls of papyrus on which it was originally written. The only Greek copy of the Synagoge to pass through the Middle Ages lost several pages at both the beginning and the end; thus only Books 3 through 7 and portions of Books 2 and 8 have survived. A complete version of Book 8 does survive however in an Arabic translation. Book 1 is entirely lost along with information on its contents. Such a range of topics is covered that the Synagoge has with some justice been described as a mathematical encyclopedia. "The Synagoge deals with an astonishing range of mathematical topics; its richest parts however concern geometry and draw on works from the 3rd century BC the so-called Golden Age of Greek mathematics. The longest part of the Synagoge Book 7 is Pappus's commentary on a group of geometry books by Euclid Apollo Eratosthenes of Cyrene and Aristaeus collectively referred to as the "Treasury of Analysis." "Analysis" was a method used in Greek geometry for establishing the possibility of constructing a particular geometric object from a set of given objects. The analytic proof involved demonstrating a relationship between the sought object and the given ones such that one was assured of the existence of a sequence of basic constructions leading from the known to the unknown rather as in algebra. The books of the "Treasury" according to Pappus provided the equipment for performing analysis. With three exceptions the books are lost and hence the information that Pappus gives concerning them is invaluable. "Pappus's Synagoge first became widely known among European mathematicians after 1588 when a posthumous Latin translation by Federico Commandino was printed in Italy. For more than a century afterward Pappus's accounts of geometric principles and methods stimulated new mathematical research and his influence is conspicuous in the work of René Descartes 1596-1650 Pierre de Fermat 1601-1665 and Isaac Newton 1642 Old Style-1727 among many others. As late as the 19th century his commentary on Euclid's lost Porisms in Book 7 was a subject of living interest for Jean-Victor Poncelet 1788-1867 and Michel Chasles 1793-1880 in their development of projective geometry" Britannica. Provenance: Harrison D. Horblit with his bookplate on front pastedown. Pesaro: Girolamo Concordia 1588. Folio 315x220mm contemporary probably original boards; old paper spine label and ink "Pappus" written on spine; "Pappi Alexandrini" written neatly on bottom edge. Soiling and light wear to boards. Early cross-out of early signature on title very light marginal dampstaining to a few early gatherings. An outstanding copy with exceptionally wide margins. Girolamo Concordia unknown books
15883991588. Numerous woodcut illus. & diagrams in the text. 4 p.l. the last a blank 334 i.e. 332 pp. Folio cont. limp vellum title a bit soiled last two leaves with some light dampstaining ties gone. Pesaro: H. Concordia 1588.<br/> <br/> First edition and a very fine and fresh copy of this uncommon book; this edition providing the complete extant text was the final work to be edited by Commandino and completes his life's work of reviving Renaissance mathematics by making available the best mathematical writings of antiquity. <br/> <br/> "In the silver age of Greek mathematics Pappus stands out as an accomplished and versatile geometer. His treatise known as the Synagoge or Collection is a chief and sometimes the only source for our knowledge of his predecessors' achievements. The Collection is in eight books perhaps originally in twelve of which the first and part of the second are missing. <br/> <br/> "Book VII is the most fascinating in the whole Collection not merely by its intrinsic interest and by what it preserves of earlier writers but by its influence on modern mathematics."D.S.B. X p. 293-95and see pp. 294-98 for a full discussion of the contents. <br/> <br/> This concerns in a passage on Apollonius' Conics the attempt to conceive of the product of more than three straight lines as geometrical entities known as "Pappus' Problem." Descartes devoted a major part of his own Géométrie to this and solved it by the use of algebraic notation. "Pappus' problem thus inspired the new method of analytical geometry that has proved such a powerful tool in subsequent centuries. In his Principia 1687 Newton also found inspiration in Pappus; he proved in a purely geometrical manner that the locus with respect to four lines is a conic section which may degenerate into a circle."D.S.B. X p. 296. <br/> <br/> Topics discussed in the other books include astronomy and mechanics. <br/> <br/> A very fine copy preserved in a green morocco-backed box. <br/> <br/> Rose The Italian Renaissance of Mathematics p. 214"Within 25 years of Commandino's death the first step in founding the mechanics of the seventeenth century was to be taken by Galileo when in criticising the inclined plane theorem of Pappus the Tuscan mathematician adumbrated the notion of inertia. This step was not taken in an intellectual vacuum but represents the culmination of the mathematical renaissance that had been achieved by the Restauratores."& see the whole of Chap. 9 for Commandino and this book. Smith History of Mathematics I pp. 136-37. unknown
15885234Pesaro: Girolamo Concordia 1588. <p>First edition of Pappus' Collection translated with commentary by Federico Commandino a princely copy from the notable collection of the great Papal family and patrons of learning the Piccolomini Dukes of Amalfi thence by marriage to the German nobleman von Troilo. The Collection is "by far the most important of Pappus' works . without it much of the geometrical achievement of his predecessors would have been lost forever" DSB.</p>. GREEK GEOMETRY - A CRUCIAL INFLUENCE ON DESCARTES. <p>First edition of Pappus' Collection translated with commentary by Federico Commandino a princely copy from the notable collection of the great Papal family and patrons of learning the Piccolomini Dukes of Amalfi thence by marriage to the German nobleman von Troilo. The Collection is "by far the most important of Pappus' works . without it much of the geometrical achievement of his predecessors would have been lost forever . The Collection deals with the whole body of Greek geometry mostly in the form of commentaries on texts which it is assumed the reader has to hand. It reproduces known solutions to problems in geometry; but it also frequently gives Pappus' own solutions or improvements and extensions to existing solutions. Thus Pappus handles the problem of inscribing five regular solids in a sphere in a way quite different from Euclid; gives a broader generalization than Euclid to the famous Pythagorean theorem and provides a demonstration of squaring the circle which is quite different from the method of Archimedes who used a spiral or that of Nicomedes who used the conchoid.<br /> Perhaps the most interesting part of the Collection measured by its influence on modern mathematics is Book VII which is concerned with the problems of determining the locus with respect to three four five six or more than six lines. Pappus' work in this field was called 'Pappus' problem' by René Descartes who demonstrated that the difficulties which Pappus was unable to overcome could be got round by the use of his new algebraic symbols. Pappus thus came to play an important if minor role in the founding of Cartesian analytical geometry. And it is another mark of his originality and skill that he spent much time working on the problem of drawing a circle in such a way that it will touch three given circles a problem sophisticated enough to engage the interest centuries later of both François Viète and Isaac Newton. For his own originality even if his chief importance is as the preserver of Greek scientific knowledge Pappus stands with Diophantus as the last of the long and distinguished line of Alexandrian mathematicians" Hutchinson Dictionary of Scientific Biography. "He formally defined analysis and synthesis as they are still commonly applied in the solution of geometrical riders. Pappus stumbled upon the projective invariance of the cross-ratio of four collinear points and other related results reclaimed by modern projective geometry; and he gave the first recorded statement of the focus-directrix property of the three conic sections. He formulated the 'centrobaric' theorems frequently attributed to Paul Guldin 1577-1643 for calculating the volume and surface generated by a plane figure rotating about an axis in its own plane. He discussed theoretical mechanics the equilibrium of a heavy body on an inclined plane the use of the mechanical powers and the construction of mechanical toys" Biographical Dictionary of Scientists.</p> <br /> <p>Provenance: Ex libris inscription of Princess Maria Piccolomini and signature of Count Franz Gottfried von Troilo on title; shelfmark on front free endpaper.</p> <br /> <p>Pappus of Alexandria c.  290 - c.  350 AD was the most important mathematical author writing in Greek during the later Roman Empire. Other than that he was born at Alexandria in Egypt and that his career coincided with the first three decades of the 4th century AD little is known about his life.</p> <br /> <p>"In the silver age of Greek mathematics Pappus stands out as an accomplished and versatile geometer. His treatise known as the Synagoge or Collection is a chief and sometimes the only source for our knowledge of his predecessors' achievements. The Collection is in eight books perhaps originally in twelve of which the first and part of the second are missing . The several books of the Collection many well have been written as separate treatises at different dates and later brought together as the name suggests . A. Rome concludes that the Collection was put together about AD 340 but K. Ziegler states that . the Collection may have been compiled soon after AD 320. It has come down to us from a single twelfth-century manuscript Codex Vaticanus Graecus 218 from which all the other manuscripts are derived .</p> <br /> <p>"The portion of book II that survives beginning with proposition 14 expounds Apollonius' system of large numbers expressed as powers of 10000. It is probable that book I was also arithmetical.</p> <br /> <p>"Book III is in four parts. The first part deals with the problem of finding two mean proportionals between two given straight lines the second develops the theory of means the third sets out some 'paradoxes' of an otherwise unknown Erycinus and the fourth treats of the inscription of the five regular solids in a sphere but in a manner quite different from that of Euclid in his Elements XIII. 13-17.</p> <br /> <p>"Book IV is in five sections. The first section is a series of unrelated propositions of which the opening one is a generalization of Pythagoras' theorem even wider than that found in Euclid VI.31 . The second section deals with circles inscribed in the figure known as the άÏβηλος or 'shoemaker's knife.' It is formed when the diameter AC of a semicircle ABC is divided in any way at E and semicircles ADE EFC are erected. The space between these two semicircles and the semicircle ABC is the άÏβηλος. In a series of elegant theorems Pappus shows that if a circle with center G is drawn so as to touch all three semicircles and then a circle with center H to touch this circle and the semicircles ABC ADE and so on ad infinitum then the perpendicular from G to AC is equal to the diameter of the circle with center G the perpendicular from H to AC is double the diameter of the circle with center H the perpendicular from K to AC is triple the diameter of the circle with center K and so on indefinitely. Pappus records this as 'an ancient proposition' and proceeds to give variants. This section covers as particular cases propositions in the Book of Lemmas that Arabian tradition attributes to Archimedes.</p> <br /> <p>"In the third section Pappus turns to the squaring of the circle. He professes to give the solutions of Archimedes by means of a spiral and of Nicomedes by means of the conchoid and the solution by means of the quadratrix but his proof is different from that of Archimedes. To the traditional method of generating the quadratrix Pappus adds two further methods 'by means of surface loci' that is curves drawn on surfaces. As a digression he examines the properties of a spiral described on a sphere.</p> <br /> <p>"The fourth section is devoted to another famous problem in Greek mathematics the trisection of an angle. Pappus' first solution is by means of a νευσις or verging-the construction of a line that has to pass through a certain point-which involves the use of a hyperbola. He next proceeds to solve the problem directly by means of a hyperbola in two ways; on one occasion he uses the diameter-and-ordinate property as in Apollonius and on another he uses the focus-directrix property. This property is proved in book VII. Pappus then reproduces the solutions by means of the quadratrix and the spiral of Archimedes; he also gives the solution of νευσις which he believes Archimedes to have unnecessarily assumed in On Spirals proposition 8.</p> <br /> <p>"In the preface to book V which deals with isoperimetry Pappus praises the sagacity of bees who make the cells of the honeycomb hexagonal because of all the figures which can be fitted together the hexagon contains the greatest area. The literary quality of this preface has been warmly praised. Within the limits of his subject Pappus looks back to the great Attic writers from a world in which Greek had degenerated into Hellenistic. In the first part of the book Pappus appears to be reproducing Zenodorus fairly closely; in the second part he compares the volumes of solids that have equal surfaces. He gives an account of thirteen semiregular solids discovered and discussed by Archimedes but not in any surviving works of that mathematician that are contained by polygons all equilateral and equiangular but not all similar. He then shows following Zenodorus that the sphere is greater in volume than any of the regular solids that have surfaces equal to that of the sphere. He also proves independently that of the regular solids with equal surfaces that solid is greater which has the more faces.</p> <br /> <p>"Book VI is astronomical and deals with the books in the so-called Little Astronomy-the smaller treatises regarded as an introduction to Ptolemy's Syntaxis Almagest. In magisterial manner he reviews the works of Theodosius Autolycus Aristarchus and Euclid and he corrects common misrepresentations. In the section on Euclid's Optics Pappus examines the apparent form of a circle when seen from a point outside the plane in which it lies.</p> <br /> <p>"Book VII is the most fascinating in the whole Collection not merely by its intrinsic interest and by what it preserves of earlier writers but by its influence on modern mathematics. It gives an account of the following books in the so-called Treasury of Analysis those marked by an asterisk are lost works: Euclid's Data and Porisms Apollonius' Cutting Off of a Ratio Cutting Off of an Area Determinate Section TangenciesInclinationsPlane Loci and Conics. In his account of Apollonius' Conics Pappus makes a reference to the 'locus with respect to three or four lines' a conic section. He also adds a remarkable comment of his own. If he says there are more than four straight lines given in position and from a point straight lines are drawn to meet them at given angles the point will lie on a curve that cannot yet be identified. If there are five lines and the parallelepiped formed by the product of three of the lines drawn from the point at fixed angles bears a constant ratio to the parallelepiped formed by the product of the other two lines drawn from the point and a given length the point will be on a certain curve given in position. If there are six lines and the solid figure contained by three of the lines bears a constant ratio to the solid figure formed by the other three then the point will again lie on a curve given in position. If there are more than six lines it is not possible to conceive of solids formed by the product of more than three lines but Pappus surmounts the difficulty by means of compounded ratios. If from any point straight lines are drawn so as to meet at a given angle any number of straight lines given in position and the ratio of one of those lines to another is compounded with the ratio of a third to a fourth and so on or the ratio of the last to a given length if the number of lines is odd and the compounded ratio is a constant then the locus of the point will be one of the higher curves .</p> <br /> <p>"In 1631 Jacob Golius drew the attention of Descartes to this passage in Pappus and in 1637 'Pappus' problem' as Descartes called it formed a major part of his Géométrie. Descartes begins his work by showing how the problems of conceiving the product of more than three straight lines as geometrical entities which so troubled Pappus can be avoided by the use of his new algebraic symbols. He shows how the locus with respect to three or four lines may be represented as an equation of degree not higher than the second that is a conic section which may degenerate into a circle or straight line. Where there are five six seven or eight lines the required points lie on the next highest curve of degree after the conic sections that is a cubic; if there are nine ten eleven or twelve lines on a curve one degree still higher that is a quartic and so on to infinity. Pappus' problem thus inspired the new method of analytical geometry that has proved such a powerful tool in subsequent centuries.</p> <br /> <p>"In his Principia 1687 Newton also found inspiration in Pappus; he proved in a purely geometrical manner that the locus with respect to four lines is a conic section which may degenerate into a circle .</p> <br /> <p>"Pappus observes that the study of these curves had not attracted men comparable to the geometers of previous ages. But there were still great discoveries to be made and in order that he might not appear to have left the subject untouched Pappus would himself make a contribution. It turns out to be nothing less than an anticipation of what is commonly called 'Guldin's theorem.' Only the enunciations however were given which state:</p> <br /> <p>'Figures generated by complete revolutions of a plane figure about an axis are in a ratio compounded a of the ratio of the areas of the figures and b of the ratio of the straight lines similarly drawn to sc. drawn to meet at the same angles the axes of rotation from the respective centers of gravity. Figures generated by incomplete revolutions are in a ratio compounded a of the ratio of the areas of the figures and b of the ratio of the arcs described by the respective centers of gravity; it is clear that the ratio of the arcs is itself compounded 1 of the ratio of the straight lines similarly drawn from the respective centers of gravity to the axis of rotation and 2 of the ratio of the angles contained about the axes of rotation by the extremities of these straight lines.'</p> <br /> <p>"Pappus concludes this section by noting that these propositions which are virtually one cover many theorems of all kinds about curves surfaces and solids 'in particular those proved in the twelfth book of these elements.' This implies that the Collection originally ran to at least twelve books.</p> <br /> <p>"Pappus proceeds to give a series of lemmas to each of the books he has described except Euclid's Data presumably with a view to helping students to understand them. He was half a millennium from Apollonius and elucidation was probably necessary. It is mainly from these lemmas that we can form any knowledge of the contents of the missing works and they have enabled mathematicians to attempt reconstructions of Euclid's Porisms and Apollonius' Cutting Off of an Area Plane Loci Determinate Section Tangencies and Inclinations. It is from Pappus' lemmas that we can form some idea of the eighth book of Apollonius' Conics" DSB.</p> <br /> <p>Adams P223; Pietro and Bonelli Catalogo della Biblioteca Mediceo-Lorense 151; Riccardi I 364 11.</p> <br/> <br/> Folio 307 x 204 mm ff. 4 including blank 334 recte 332 with woodcut printer's device on title several historiated woodcut initials and numerous woodcut diagrams in text small wormhole through blank area of last two leaves. Contemporary German half-pigskin over yellow boards pigskin dyed rose pink somewhat faded small split in upper joint and small wormhole in lower board with blind floral rolls gilt silver arms of Count Franz Gottfried von Troilo on upper cover and a phoenix surrounded by flames within a wreath on lower cover. A fine clean crisp copy. Girolamo Concordia unknown
151766901Editio Princeps and the First Book Printed at the press of the Greek Gymnasium HOMER. DIDYMUS OF ALEXANDRIA. LASCARIS Janus editor. Homeric Scholia on the Iliad. Homeri interpres pervetustus in Greek. Edited by Janus Lascaris Rome: Vittore Carmelio and/or Zacharias Callierges for Angelo Colocci at the Press of the Greek Gymnasium caballini montis gymnasium. Not before 7 September 1517. Editio Princeps and the first book that was printed at the press of the Greek Gymnasium in Rome. Folio 10 1/2 x 7 3/4 inches; 265 x 197 mm. 172 leaves. Text in Greek. With "To the Reader" and "Address to Pope Leo X" which is dates 7 September 1517 in Latin. Colophon and register in Greek. This is the Longleat Beriah Botfield copy. We were not able to locate any copies besides the present copy at auction in the past fifty years and only one library on OCLC with a copy. Beautifully bound in early 19th Century straight-grain morocco by Francois Bozerian His stamp "Rel. F. Bozerian jeune" at bottom of the spine. Boards tooled in gilt and blind. Spine elaborately stamped and lettered in gilt. Boards edges gilt. Gilt dentelles. All edges gilt. Silk endpapers. Blue silk page marker. Two old circular previous ownership stamps on recto of first leaf not affecting text. Stamps are one of which is red and one of which is black are from the Seminaire des Missions Etrangeres. "Pope Leo X Giovanni de' Medici called Janus Lascaris to Rome to found a Greek College in 1513 and three years later it began to issue Greek texts principally edited by Lascaris. The printer was once thought to be Angelo Colocci a rich Roman proponent of Greek learning in whose house the press almost certainly operated but it was most likely Vittore Carmelio Hobson foreman to Callierges first printer of Greek at Rome or Callierges himself Layton. The types were designed by Lascaris cut possibly by Callierges and first used in 1494-96 by Lorenzo di Alopa at Florence to print books Lascaris edited. Cf. A. Hobson 'The Printer of the Greek Editions "In gymnasio Mediceo ad Caballinum montem"' Studi di biblioteconomia e storia del libro in onore di Francesco Barberi Rome: 1976: 331-335; E. Layton The 16th-century Greek Book in Italy pp.323-329; D.E. Rhodes 'The Printing of a Group of Greek Books in Rome' Studies in Early Italian Printing London: 1982 pp.111-113; Barker Greek Script pp.74-75. This first edition of the Homeric scholia on the Iliad has no author attribution although it is sometimes given erroneously to Didymus c.65 B.C.-10 A.D. It was a standard text in the study of Homer and clearly a required text for the students at the Greek Gymnasium." Christies 2002 HBS 66901RSL. $40000 Vittore Carmelio and/or Zacharias hardcover books
15756346Basel: Eusebius Episcopius & Heirs of Nikolaus Episcopius 1575. First edition. <p>First edition of Diophantus - the first printing of the Arithmetica in any language in any form - owned annotated and signed by Giovanni Camillo Gloriosi 1572-1643 Galileo's successor in the chair of mathematics at the University of Padua. Gloriosi's mathematical annotations dating from 1611 and 1612 revise and correct the calculations of Diophantus and of his Latin translator Xylander; the long note at page 59 against Proposition II.19 is the working source for Gloriosi's 1613 Ad theorema geometricum Venice Baglioni whose publication with Galileo's recommendation secured the Padua chair in October of that year. After Gloriosi's death the library passed for five hundred gold coins to Ramiro de Guzmán Viceroy of Naples who bound the books in red morocco with his armorial. Bouza's 2024 catalogue of thirty-five Gloriosi books surviving in Madrid libraries records signatures only; this copy stands apart by the density of its 1611-1612 marginalia and by the direct textual link between the note at page 59 and pages 28-29 of the printed Ad theorema geometricum.</p>. Hardcover. Giovanni Gloriosi's Signed and Annotated Copy of the First Systematic Treatise on Algebra. <p>First edition of Diophantus - the first printing of the Arithmetica in any language in any form - owned annotated and signed by Giovanni Camillo Gloriosi 1572-1643 Galileo's successor in the chair of mathematics at the University of Padua and subsequently acquired from Gloriosi's estate for five hundred gold coins by Ramiro de Guzmán Duke of Medina de las Torres and Viceroy of Naples who bound the book in red morocco with the combined armorial of himself and his wife Anna Carafa de Stigliano on the covers. When Antonio Favaro undertook his 1904 study of Gloriosi in the series on Galileo's acquaintances and correspondents he posed what seemed a straightforward question - what had become of the mathematician's books and papers - and reported that every effort he had made to trace them had been entirely in vain. The present copy bound in the viceroy's unmistakable red morocco and carrying Gloriosi's signature on the last leaf with extensive mathematical annotations in his hand is distinguished among the now-identified survivors of that library by the density of the annotations and by their demonstrable bearing on Gloriosi's own published mathematical work.</p> <br /> <br /> <p>Gloriosi was a Neapolitan Jesuit-trained and came to mathematics through the algebraic tradition rather than through natural philosophy. In 1604 a friar asked Galileo to write on his behalf for a lectureship in mathematics; the appointment did not materialise but the correspondence opened a cordial if occasionally pointed relationship between the two men. By 1606 Gloriosi was in Venice moving in the circle around Paolo Sarpi and Giovanfrancesco Sagredo where he also met Antonio Santini and Marino Ghetaldi who introduced him to the algebra of François Viète - the immediate and decisive influence on his reading of Diophantus. In October 1613 with Galileo's recommendation and on the strength of his first publication Ad theorema geometricum Venice: Tommaso Baglioni 1613 Gloriosi was nominated to the chair Galileo had just vacated at Padua. He held the post until 1622 returning thereafter to Naples where he lived as a private gentleman maintained correspondence with the mathematical communities at Padua Venice Bologna and the Roman College and continued to exchange letters with Galileo until at least 1635. He died in January 1643 leaving four surviving letters to Galileo as the record of a thirty-year intellectual acquaintance.</p> <br /> <br /> <p>Gloriosi's annotations transform the copy from a bibliographical rarity into a document of working mathematical scholarship. Dating from 1611 and 1612 - the two years immediately preceding the Ad theorema geometricum and the Padua appointment - they fall into two kinds. Many are brief marginal identifiers a single Latin word most often Theorema placed beside the statement of a particular proposition to fix its status in the flow of Diophantus's argument. The majority however are substantive mathematical calculations in Gloriosi's fine italic hand revising extending and in a number of cases correcting the work of Diophantus and of the book's Latin translator and commentator Wilhelm Holtzmann of Augsburg Xylander. They are concentrated in Book II and in the later books in which the more intricate indeterminate problems occur and they are dense enough in places to fill margins on both sides of the printed page. Where Xylander's own calculation has gone astray Gloriosi writes out the corrected arithmetic to several orders of fractional precision; where a proposition requires a generalisation Diophantus had not offered he supplies it.</p> <br /> <br /> <p>The most consequential of these annotations occupies the lower margin of page 59 against Proposition 19 of Book II - the problem that asks a given number to be divided into three parts such that each part on donating a specified fraction of itself plus a fixed number of units to the next yields three equal results. For the number 80 with the fractions one-fifth one-sixth and one-seventh and the added units 6 7 and 8 respectively Xylander's solution failed: the parts summed to 80 but the distribution did not in fact satisfy the equations. Gloriosi noted the failure precisely - aequatio facta est ad 16 2/3 cum fieri debebant ad 26 2/3 the equation had been set at 16 2/3 when it should have been set at 26 2/3 - and then in the same annotation recorded the three correct fractional parts 1N 9530/363 10200/363 and 9310/363 obtained from the corrected equation. He rejected the possibility that Diophantus himself had erred insisting that the Alexandrian would not have proposed a problem without knowing its solution and argued instead that the Greek text had been mutilated in transmission. The task he set himself was to recover a solution using as Diophantus's method required a single hypothesis. This is exactly the reconstruction carried out on pages 28-29 of the Ad theorema geometricum of 1613 - the annotation and the printed text correspond point by point in the equation in the numerator 9530 over the common denominator 363 and in the subsequent reasoning - and the book prints no other source for the reconstruction. The margin of the present copy is the working source.</p> <br /> <br /> <p>The causal chain is tight. The marginal notes of 1611-1612 fed into the printed argument of 1613 the printed argument of 1613 supplied the published credential on which Galileo's recommendation built and the appointment to the Padua chair followed in October of the same year. The book at hand is therefore not merely an annotated copy of a famous mathematical work but the physical support for the single published achievement that elevated Gloriosi into the most visible Italian chair of mathematics. That it emerged from a library thought lost - and emerged intact bound by a seventeenth-century viceroy with the annotations complete and legible - is among the more unusual recoveries of the last generation of rare-science-book scholarship.</p> <br /> <br /> <p>Favaro's search had run up against a problem he could not solve from the evidence then available. Gloriosi had died a private gentleman in Naples; his nephew in Tomasini's words in the 1644 Elogia was a stranger to the study of letters who disposed of the entire library at a single stroke for five hundred gold coins to the viceroy. The viceroy then transferred the books to Spain and after his own death in 1668 the collection dispersed into the Madrid book trade where the Gloriosi association was no longer visible to anyone not already looking for it. Fernando Bouza working from Tomasini's text and from the catalogue records of Spanish libraries reconstructed the trajectory in a 2024 article in Galilæana and catalogued thirty-five printed books once belonging to Gloriosi almost all of them in Madrid - at the Biblioteca Nacional de España the Biblioteca Histórica of the Universidad Complutense the Biblioteca Francisco de Zabálburu and the Real Academia de Bellas Artes de San Fernando - together with a further two outside Madrid a 1521 Alfonsine Tables rebound in the eighteenth century and a 1545 Cardano Ars Magna sold at the 1861 Guglielmo Libri auction at Sotheby's. In each of the thirty-five Madrid books Gloriosi is identified by his characteristic signature alone set on the title verso or after the colophon; Bouza does not describe any of them as carrying substantive mathematical annotation. The present copy stands apart from that group in two respects: the density of Gloriosi's 1611-1612 marginalia and the specific point-for-point correspondence between the note on page 59 and pages 28-29 of the printed Ad theorema geometricum which ties this particular volume to a particular publication in a way no other survivor has yet been shown to do.</p> <br /> <br /> <p>Ramiro Núñez de Guzmán 1600-1668 second Duke of Medina de las Torres by marriage to Anna Carafa and son-in-law of the Count-Duke of Olivares served as Viceroy of Naples from 1637 to 1644 and was one of the most powerful Spanish grandees of his generation. His library-building followed the pattern common to seventeenth-century Italian viceregal courts in which the acquisition of a scholar's entire legacy was an act of cultural prestige as well as of intellectual collecting. The red morocco binding with his armorial stamps - exclusive bindings known to collectors as medines combining the viceroy's quartered arms on one cover with those of Anna Carafa REVOLUTA FOECUNDANT the Carafa stars and crescent on the other - was presumably executed in Naples or in Madrid after the purchase. Of the small number of these bindings that survive the one on the present volume is identical in tool format and armorial layout to that on the Bodleian sammelband Rigaud.e.148 which contains Gloriosi's own copies of Galileo's Sidereus nuncius 1610 and Il Saggiatore 1623 Giulio Cesare La Galla's 1612 De phoenomenis in orbe lunae Francesco Sizzi's 1611 Dianoia astronomica and Mario Guiducci's 1620 Lettera al padre Tarquinio Galluzzi. Taken together the sammelband and the present copy demonstrate that the viceroy bound the mathematical and the Galilean-astronomical portions of Gloriosi's library in a single uniform style and that Gloriosi himself had studied Galileo's principal works at first hand.</p> <br /> <br /> <p>After Medina de las Torres's death in 1668 the library began to disperse. The principal buyer was William Godolphin c. 1634-1696 the English diplomat and Catholic convert then resident at the court in Madrid whose prominent ownership inscriptions identify a substantial block of former Guzmán books. The present Diophantus was not among them. A second buyer identified only as 'Ãlvarez' signed his name on the title page; the inscription survives covered by a contemporary paper slip that has been preserved in place. The same 'Ãlvarez' signature appears on three other former Guzmán books currently traceable in the Spanish antiquarian market and in one of them - a 1600 Brescia edition of Alessandro Manerba's Moralis sylva - Godolphin's own title-page inscription overlaps Ãlvarez's showing that the two were contemporaries and that Ãlvarez transferred part of his collection on to Godolphin. The absence of Godolphin's characteristic title-page or colophon signature from the present copy indicates that Ãlvarez acquired the book directly from the viceroy's dispersal and retained it and that it never entered Godolphin's library. Ãlvarez is therefore the third known owner standing between Guzmán and the Earls of Macclesfield from whose library at Shirburn Castle the book came to the market as lot 636 in the 2005 sale.</p> <br /> <br /> <p>The edition Gloriosi annotated was in 1611-1612 the only printed Diophantus in existence. Wilhelm Holtzmann of Augsburg 1532-1576 who Hellenised his name as Xylander was a classical philologist and professor of Greek at Heidelberg and his Latin Arithmetica of 1575 was the first complete European rendering of the text. The Greek editio princeps would not appear for another forty-six years when Bachet de Méziriac printed it in Paris in 1621 item 20 in this catalogue Bachet's own large-paper copy. Xylander worked from a single Byzantine manuscript derived like every surviving Greek witness from a single lost archetype and the manuscript was in André Weil's phrase marred throughout by the numerical errors of professional scribes who had not been mathematicians. He laboured for several years under these conditions supplied the text with a running Latin commentary - the Xylandri sections set beneath each Diophantine proposition in the present volume - and dedicated the book to his pupil Prince Ludwig of Württemberg. Thomas Heath writing in 1910 observed that Xylander's achievement had been inadequately appreciated by later commentators largely because the book itself was so rare: Nesselmann preparing his 1842 Algebra der Griechen was unable to find a copy at all. The translation's immediate and enormous influence on the shaping of European algebra as Heath put it ran through Bombelli Stevin Viète and - through Bachet's 1621 reprinting with improvements - Pierre de Fermat. Xylander himself did not live to see that influence take hold: he died the year after publication.</p> <br /> <br /> <p>The Arithmetica itself composed at Alexandria in approximately AD 250 is the first systematic treatise on algebra and the founding text of the tradition now called Diophantine analysis: the search for rational or integer solutions to polynomial equations in several unknowns. Diophantus introduced the earliest sustained symbolism in Greek mathematics - a character for the unknown for its powers up to the sixth and for the operations of addition and subtraction - and treated roughly two hundred and sixty problems whose solutions though always given in specific numerical terms tend to suggest general methods. The work was originally in thirteen books. Six survived in Greek transmitted by Byzantine scholars from Michael Psellus through Maximus Planudes whose scholia on the first two books Xylander prints alongside the text to the codex Cardinal Bessarion rescued before the fall of Constantinople and that Regiomontanus discovered at Venice; four further books surfaced in 1968 in a ninth-century Arabic translation by QustÄ ibn LÅ«qÄ dispersing the suspicion that the ancient numbering had corresponded straightforwardly to the surviving Greek sequence. Three books remain lost. The Arab reception had in fact been considerable: al-NadÄ«m's index of the sciences 987-988 lists commentaries by QustÄ ibn LÅ«qÄ and by AbÅ«'l-WafÄ' and a substantial fraction of the problems in al-KarajÄ«'s algebra are drawn directly from Diophantus's first three books.</p> <br /> <br /> <p>Xylander's volume prints at the end a fragment of the only other surviving work by Diophantus - a treatise on polygonal numbers which is differentiated from the Arithmetica by its use of geometric proofs and which breaks off in the middle of its investigation of the number of ways in which a given number can be expressed as a polygonal. The full transmission history of both texts from Bessarion and Regiomontanus through Bombelli's partial assimilation in his 1572 Algebra 271 problems of which 147 were taken directly from Diophantus to Viète's Zetetica of 1593 and on to Bachet's definitive 1621 edition runs entirely through this 1575 volume. It was in the margins of a copy of Bachet's 1621 reprint that Pierre de Fermat in the mid-1630s wrote the forty-eight observations that founded modern number theory - among them on page 85 against Problem II.8 on the decomposition of a square into two squares the proposition now known as Fermat's Last Theorem whose proof by Andrew Wiles in 1995 closed a gap that had stood for three hundred and fifty-eight years. The 1670 reprint of Bachet's edition with Fermat's observations printed in the margins the book that carried the Last Theorem into circulation is item 19 in this catalogue.</p> <br /> <br /> <p>Auction records since Honeyman list only three other copies of the 1575 Xylander; each is in a nineteenth- or twentieth-century binding and none has significant provenance. OCLC records eight copies in North American libraries. Copies in contemporary armorial bindings with identifiable early mathematical ownership are essentially unrecorded in commerce of the last century and the present volume - the Gloriosi copy in the Medina de las Torres binding standing as the material support for the 1613 Ad theorema geometricum and for the Padua appointment that followed it - is without known parallel.</p> <br /> <br /> <p>Almost nothing is known of the life of Diophantus. He quotes Hypsicles and so must have worked after roughly 150 BC; he is quoted in turn by Theon of Alexandria and so must have worked before AD 364. The conventional placement around AD 250 rests on a single passage in an eleventh-century Byzantine letter and on the absence of Diophantus's name from the commentaries of Pappus. His place of birth is unknown his teachers unknown and the fourteen-line Greek epigram in the Palatine Anthology that purports to record his age at death is generally regarded as a mathematical exercise rather than a biographical document.</p> <br /> <br /> <p>References: Adams D-652 - DSB IV 110-19 - Honeyman 890 - Norman 641 - Macclesfield 636 this copy - Bouza 'The mathematician and the viceroy' Galilæana XXI 1 2024 pp. 201-220 - Favaro Amici e corrispondenti di Galileo Galilei. IX. Giovanni Camillo Gloriosi 1904 - Tomasini Elogia virorum literis et sapientia illustrium 1644 - Heath Diophantus of Alexandria: A Study in the History of Greek Algebra 2nd ed. 1910 - Heath A History of Greek Mathematics 1921 vol. II pp. 448-517 - Weil Number Theory: An Approach Through History from Hammurapi to Legendre 1984 - Katz & Parshall Taming the Unknown 2014 ch. 4 - Schappacher 'Diophantus of Alexandria: a text and its history' IRMA Strasbourg - Smith Rara Arithmetica p. 348.</p> <br /> <br/> <br/> <br /> <p>Folio 307 × 200 mm pp. xii 152. Printer's device on title legend Episcop woodcut initials printed marginal notes. Occasional foxing light damp stains to blank corners of some leaves. Mid-seventeenth-century red morocco with gilt arms of the Duke of Medina de las Torres and his wife on the covers elaborate gilt borders and corner fleurons spine gilt; damage to upper edge of front board affecting gilt border.</p> . / Hardcover. Eusebius Episcopius & Heirs of Nikolaus Episcopius unknown
