## Opera per doctissimum Philosophum Ioannem Baptistam Memum patritium Venetum, mathematicharumque artium in urbe Veneta lectorum publicum. De Graeco in Latinum Traducta & Noviter impressa.

[Colophon:] Venice: Bernardinus Bindonus, 1537.

First edition, **an extraordinary copy of the greatest importance, signed and heavily annotated by the celebrated English polymath John Dee (1527-1608), and later acquired and signed by John Winthrop Jr. (1606-76), the first Governor of Connecticut, whose library was one of the most important in the early American colonies**. The present volume, no. 74 in Roberts & Watson’s listing of Dee’s 2292 printed books, is one of only three which they record as being in private hands; others are located in institutional collections on three continents. “Dee’s library, the ‘Bibliotheca Mortlacensis,’ was not only a monument to his scholarly interests and achievements; it was one of the great monuments of English Renaissance culture. By the time it was catalogued in 1583 he had assembled England’s largest and – for many subjects at least – most valuable collection of books and manuscripts. Its dispersal, which began even while he lived, was perhaps the most significant redistribution of textual resources since the dissolution of the monasteries” (Sherman, p. 30). Dee’s interests extended into many fields, but he published relatively little; “his ideas on many topics must be teased out from his manuscripts and from the copious notes that he entered in many of the books in his enormous library” (Grafton). “One collector provided John Dee after his death with the link with the New World which would not have been wholly uncongenial to him. The large library of John Winthrop Jr. (1606-1676), first governor of Connecticut, has been described in detail as befits one of the first major accumulations of books in the American colonies … Whether John Winthrop was able to acquire any of Dee’s books as soon as they came on the market is uncertain. His first dated acquisition is the 1537 Apollonius Pergaeus which Dee had acquired in Antwerp or Louvain in 1549. Winthrop bought it in 1631 and it was probably he who added Dee’s monad to the title page. As Winthrop sailed for Boston at the end of August it would have been in the barrel of books that went with him” (Roberts & Watson, p. 67). Winthrop “was especially attracted to the pansophic Christian alchemical philosophies of Paracelsus, John Dee, and the supposed secret order of the Rosicrucians” (DSB). The *Opera* is the first printing of any part of Apollonius’ *Conics*, “one of the greatest scientific books of antiquity” (Stillwell), alongside those of Euclid and Archimedes. It contains the first four books – Books V-VII were not published until 1661, and Book VIII is lost. “Apollonius’s theory of the conic sections (about 220 BCE) is undoubtedly one of the masterpieces of ancient mathematics and will remain one of the great classics of mathematical literature” (Neugebauer, p. 295). To understand its importance in modern science, we need only recall that it was fundamental to Kepler’s discovery in the *Astronomia Nova* that Mars follows an elliptical orbit, and to Galileo’s finding that projectiles follow parabolic trajectories. “The verso of the flyleaf [of the present volume] bears a detailed set of notes by Dee, based chiefly but not only on the prefaces to books 1 and 4 of this text, which he annotated in the margins. These notes deal with an intricate and technical subject: the relative chronology of Hellenistic mathematicians. Dee laid out their names in brackets, in the form of a sort of a table, on the left side of the page, along with notes recording their chronological relationships to one another. In a second column on the right, Dee argued at length that Archimedes came before Apollonius” (*ibid*.). A complete transcription and translation of Dee’s annotations, by Professor Anthony Grafton of Princeton University, is available upon request (his description of this copy has already been referred to above). Apollonius’ *Opera* is very rare – OCLC lists five copies in the US (Harvard, Louisville, MIT, UNC, Yale); ABPC/RBH list only two other complete copies since Honeyman.

*Provenance*: John Dee (1527-1608), philosopher, mathematician, and astrologer (his ownership inscription dated 1549 on the title-page, 'Joannes Deeus: Anglus: 1549.', some marginal notes and underlining, autograph table on flyleaf of Ramist systematization of the mathematics in Apollonius, Archimedes, and Eutocius of Ascalon); John Winthrop, Jr. (1606-1676), son of the Massachusetts Bay Colony's first governor, physician, governor of Connecticut (ownership signature dated 1631, 'John Winthrop. 1631.', and his sigil, the hieroglyphic monad invented by Dee, on the title-page, another ownership inscription on the recto of the front flyleaf, 'Winthropi', combined with a smaller monad symbol); by descent to Waitstill Winthrop (1642-1717) son of John, Jr., chief justice of Massachusetts (signature on recto of front flyleaf); Frederick Winthrop of New York (ownership entry dated 18 May 1812 on title-page, ‘Fred.k Winthrop New York May 18.th 1812’); Robert Charles Winthrop (1809-1894), Speaker of the House, senator from Massachusetts); Charles Fraser (presentation inscription on the flyleaf ‘Washington, May, 1850’); Arthur & Charlotte Vershbow, acquired from Goodspeed’s Book Shop, 1975 (inked note on the recto of the front flyleaf ‘75-46-14’, ex-libris on recto of front flyleaf); see *The Collection of Arthur & Charlotte Vershbow*, Christie’s New York, April 9, 2013, lot 33).

Mathematician, magician, astronomer, astrologer, imperialist, alchemist and spy, John Dee **continues to fascinate and inspire centuries after he entered the court of Elizabeth I.** “Over the past four centuries, John Dee has proven one of the most interesting and enigmatic figures of the English Renaissance. Books from his library and from his own pen have always been treasured (witness the large number of volumes in the British Library that were once part of his collection – and, for that matter, his letter to Queen Elizabeth displayed in the British library textual hall of fame, the Manuscript Gallery) … He is one of the few Elizabethan figures who – like Queen Elizabeth herself – remain vivid, or at least colourful, enough to inspire historians and novelists alike” (Sherman, p. xi).

Born in London, “Dee entered St. John’s College, Cambridge, in 1542, where he earned a bachelor’s degree (1545) and a master’s degree (1548); he also was made a fellow of Trinity College, Cambridge, on its founding in 1546. Dee furthered his scientific studies on the Continent with a short visit in 1547 and then a longer stay from 1548 to 1551 (both times to the Low Countries) under the mathematician-cartographers Pedro Nuñez, Gemma Frisius, Abraham Ortelius, and Gerardus Mercator, as well as through his own studies in Paris and elsewhere. Dee turned down a mathematical professorship at the University of Paris in 1551 and a similar position at the University of Oxford in 1554, apparently in hopes of obtaining an official position with the English crown.

“Following his return to England, Dee attached himself to the royal court, offering instruction in the mathematical sciences to both courtiers and navigators. He also served as consultant and astrologer to, among others, Queen Mary I. The latter activity landed him in jail in 1555 on the charge of being a conjurer, but he was soon released. Following the ascent of Elizabeth I to the throne in 1558, Dee became a scientific and medical adviser to the queen, and by the mid-1560s he established himself at Mortlake, near London. There he built a laboratory and amassed the largest private library in England at that time, which was said to number more than 4,000 books and manuscripts. He was as generous in making his library accessible to scholars as he was in assisting numerous practitioners who applied for advice.

“Dee was intimately involved in laying the groundwork for several English voyages of exploration, instructing captains and pilots in the principles of mathematical navigation, preparing maps for their use, and furnishing them with various navigational instruments. He is most closely associated with the expeditions to Canada led by Sir Martin Frobisher in 1576–78 and with discussions in 1583 regarding a proposed but never commissioned search for the Northwest Passage. He was equally active in publicly advocating a British empire in *General and Rare Memorials Pertayning to the Perfect Arte of Navigation* (1577). In 1582 Dee also recommended that England adopt the Gregorian calendar, but at that time the Anglican church refused to embrace such a ‘popish’ innovation.

“Dee’s scientific interests were far broader than his involvement in English exploration might suggest. In 1558 he published *Propaedeumata Aphoristica*, which presented his views on natural philosophy and astrology. Dee continued to discuss his occult views in 1564 with the *Monas hieroglyphica*, wherein he offered a single mathematical-magical symbol as the key to unlocking the unity of nature. In addition to editing the first English translation of Euclid’s *Elements* (1570), Dee added an influential preface that offered a powerful manifesto on the dignity and usefulness of the mathematical sciences. Furthermore, as passionately as he believed in the utility of mathematics for mundane matters, Dee expressed conviction in the occult power of mathematics to reveal divine mysteries.

“Perhaps frustrated by his failure to arrive at a comprehensive understanding of natural knowledge, Dee sought divine assistance by attempting to converse with angels. He and his medium, the convicted counterfeiter Edward Kelley, held numerous séances both in England and on the Continent, where the two traveled together – mainly to Poland and Bohemia – between 1583 and 1589. By all accounts Dee was sincere, which is more than can be said for Kelley, who may have duped him.

“On Dee’s return to England, his friends raised money for him and interceded on his behalf with Queen Elizabeth. Though she appointed him warden of Manchester College in 1596, Dee’s final years were marked by poverty and isolation. He was long said to have died at Mortlake in December 1608 and to have been buried in the Anglican church there, but there is evidence that his death occurred the following March at the London home of his acquaintance (and possible executor) John Pontois.

“It is almost certain that William Shakespeare (1564–1616) modeled the character of Prospero in *The Tempest* (1611) on the career of John Dee, the Elizabethan magus” (Britannica). Dee was probably also the inspiration for the title character of Ben Jonson’s *The alchemist*.

Dee claimed to have owned over 3,000 books and 1,000 manuscripts, which he kept at his home in Mortlake. He compiled an inventory of his library shortly before his departure for Poland in 1583 (photographically reproduced and interpreted in Roberts & Watson). He entrusted the care of his library and laboratories to his brother-in-law Nicholas Fromond. But according to Dee, he ‘unduely sold it presently upon my departure, or caused it to be carried away’. Roberts & Watson blame other losses on John Davis, a sea captain, and Nicholas Saunder, who may have been a former pupil of Dee’s; many of the latter’s ‘acquisitions’, often mutilated by having Dee’s inscriptions effaced or cut out, found their way into the library of the Royal College of Physicians in London. Dee was devastated by the destruction of his library. He later recovered some items, but many remained lost. The present volume seems to have escaped these depredations. In his last years Dee found himself in penury and some of his books, but more especially his manuscripts, were sold off. Most of the remaining books were dispersed in sales of 1625 and 1626.

Dee’s library was particularly rich in mathematics and in fields such as astronomy, mechanics, and navigation in which mathematics plays a crucial role. “The supreme virtue of mathematics for Renaissance thinkers was its (relative) demonstrative certitude. As Dee notes in his ‘Mathematicall Praeface’ to the English Euclid, ‘In Mathematicall reasonings, a probable Argument, is nothyng regarded: nor yet the testimony of sense, any whit credited: But onely a perfect demonstration, of truthes certaine, necessary, and inuincible: vniuersally and necessarily concluded: is allowed as sufficient for an Argument exactly and purely Mathematical.’ For mathematicians like Dee, the mathematical disciplines were not only the most persuasive but the most *useful* for the apprehension of natural causes and effects and the application of these principles to the benefit of humanity – and, as Dee would have added, the glory of God, whose miraculous creation is uncovered and celebrated” (Sherman, p. 95)

Like many of Dee’s books, the present volume is extensively annotated by him. “However messy, modest, and (as it were) marginal they at first appear, it is no exaggeration to say that Dee’s marginalia are central to the recovery of his intellectual activities and, indeed, his role in society. In terms of the intellectual historian’s traditional search for sources and influences, the marginalia allow us to move beyond an exclusive reliance on his library catalogue, which is not at all an adequate basis for discussion. Roberts and Watson find in the notes valuable evidence of Dee’s bibliographical and biographical details, as well as an indication of his ‘tastes and interests.’ But they offer much more than this. They document the ways in which Dee interacted with his sources: and since he was one of the most source-oriented scholars in a source-oriented age, this is essential to our appreciation of his life and livelihood … it is in Dee’s marginal scribbles that we catch the most vivid and intimate glimpses of him in action, doing what he must have spent most of his time doing” (*ibid*., pp. 79-80).

Dee signed the book on its title page and dated its acquisition to 1549. The binding, which comes from Louvain, confirms the date, since Dee visited Louvain in 1547 and returned for a longer stay, which he devoted to mathematical studies, from 1548 to 1550 (Roberts and Watson, #74, with the note on 82). Many of the manuscript notes in this book, including the table on the flyleaf, deal with the chronology of Hellenistic mathematicians. “The history of the exact sciences in antiquity greatly interested sixteenth-century scholars. Their accounts often configured the data, sometimes violently, to support highly ideological claims about the nature and development of the sciences (for example, in the case of Dee’s correspondent Petrus Ramus, the thesis that astronomy had reached its zenith in ancient Babylon and Egypt, and degenerated when it fell into Greek hands; see Goulding).

“At their most detailed, as in Henry Savile’s Oxford lectures, these inquiries required precise reading, dating and assessment of complex, abstract texts, which resisted efforts to force them into historical pigeonholes. Most humanists agreed on at least one point: the mathematicians of the Hellenistic world had formed a creative, contentious community, centered in Alexandria, whose members challenged and criticized one another (*ibid*., 103-105). Before anyone could be sure what each of them had accomplished, the chronological relations among them and their works had to be established.

“Dee’s interests in mathematics had to do, for the most part, with the nature and divisions of the subject as a whole – though he shied away, in his ‘Mathematicall Preface’ to Henry Billingsley’s English Euclid of 1570, from discussing the relation between mathematics and the alchemy and astrology to which he devoted much of his life and work (see Rampling).

“In the notes in his copy of Apollonius, however, he carried out a different kind of classification, using a rigorous philological method to construct a historical timeline of Hellenistic mathematics. He worked by close reading of texts and elimination of apparent contradictions. At the start of the left-hand column, Dee made clear that he had started work by compiling the names of mathematicians older than or contemporary with Apollonius from this very text. He explicitly cited the prefaces to books 1 and 4. And in fact he noted the names of all mathematicians referred to in these texts in the margins of the pages in question.

“But Dee did not stop there. For example, the list of names shows that he also drew the name of one of Apollonius’s predecessors, Philonides, from the preface to book 2, though he did not annotate the page in question. Then he moved on to other sources, especially the works of Archimedes and of Eutocius of Ascalon, who wrote commentaries on Archimedes and Apollonius. More than once he stated the chronological relationship between a group of authors, or between one group and another.

“In the right-hand column Dee pulled these facts together into a formal set of arguments. In each stage he mustered evidence to show that Apollonius must have been later than Archimedes. Interestingly, he set this material out in syllogistic or geometrical form, rather than in prose: he offered arguments for his view, raised an objection, responded, and finally provided further arguments in confirmation of his original thesis. Perhaps Dee thought this rigorous approach appropriate to the subject matter. In this column he drew on Proclus’s commentary on book I of Euclid, a favorite source of Ramus and others, and other texts …

“The methods that Dee used here were typical of his approach to annotating works of history, as William Sherman showed in his classic book on Dee as a reader (Sherman, 87, 90-95). In particular, they were typical of his approach to what was beginning to be called ‘*historia literaria*,’ the history of literature, the discipline whose practitioners established the histories of all the other disciplines. Dee knew the guides to this subject, the standard bibliographical handbooks by Bale, Gesner and others, and his notes in his copies of these books (now in the library of Christ Church, Oxford) resemble those found here.

“As a practitioner of *historia literaria*, Dee cited his evidence explicitly, formulated his arguments with rigor and precision, and reached sound conclusions. When Dee wanted to, in other words, he could turn to the work of scholarly divination with as much enthusiasm and expertise as he showed for other forms of that pursuit. Like others better known for their scholarship, when he did so, he made no appeal to supernatural sources of wisdom, but argued from the texts” (Grafton).

The present volume’s American provenance is no less remarkable. “The life of John Winthrop Jr. exemplifies the physical and intellectual links that spanned the Atlantic. Governor of Connecticut and son of the founding governor of Massachusetts, Winthrop was one of the most important men in colonial English America. Born in 1606, he was a political leader from his arrival in New England in 1631 until his death in 1676. He was also a leading undertaker of three new towns and the promoter of New England’s first ironworks. Winthrop was a cosmopolitan intellectual and world traveller who journey through Europe and the Middle East searching for knowledge of scientific mysteries. He was a successful suitor for a royal charter for Connecticut in the restoration court of Charles II and a founding member of the Royal Society …

“During the years when English puritans were undertaking godly colonies in the Atlantic world, scientific reformers were working to synthesise Baconian empiricism and Rosicrucian millennialism into practical reform programs to improve world conditions in preparation for Christ’s return. Winthrop was drawn to such religioscientific schemes. In his early twenties he began to study alchemy, the branch of natural philosophy many believed was the key to all understanding … From the initiation of his alchemical studies in the 1620s, which he began with Edward Howes, his friend and fellow student at London’s Inner Temple, Winthrop was committed to the use of alchemy as a means of understanding Christian service and as a key to unlocking the hidden mysteries of nature. He and Howes became enthusiastic supporters of the Rosicrucian movement, which led Winthrop to undertake journeys to Europe and the Islamic world in search of alchemical knowledge. Among the important alchemical influences on Winthrop were Paracelsus, the English magus John Dee, the English physician and Hermetic theorist Robert Fludd, the utopian English alchemical entrepreneur Gabriel Plattes, and the great synthesist of the seventeenth-century universal reformation movement, Jan Comenius” (Woodward, pp. 1-3).

The building of what would become one of colonial New England’s most eminent book collections began with John Jr.’s grandfather Adam (1548-1623) and his father John (1588-1649), who in 1630 would become the governor of Massachusetts and in time the family’s most famous member. John Jr.’s book collecting began years before his departure to America, when “he was a student who read at Trinity College Dublin, travelled the Mediterranean, and found himself frequently in need of books. Whenever John Jr. requested a text (and there were many such requests), his father turned to his family and his network in London. John’s go-to book buyer was his brother-in-law Thomas Fones, whose daughter Martha would become John Jr.’s first wife … While the foundations of the Winthrops’ collection were laid by members of the family, many books came from other sources. The letters of John Jr., who by 1641 owned ‘above a thousand’ books, shed light on precisely how one generation of Winthrops succeeded in obtaining such a large quantity of books from all corners of the early modern market. Both before and after he sailed for New England, he was part of a global network of scholars and alchemists who exchanged texts along with their correspondence. As Ronald Wilkinson showed in a pioneering study, John Jr.’s suppliers included the London merchant Francis Kirby, the alchemist and remonstrant Robert Child, the polymath Samuel Hartlib and John Jr.’s dearest friend, Edward Howes, a clerk of his uncle Fones and, like the younger Winthrop, a student at the Inner Temple” (Grafton *et al*., pp. 75-76).

Winthrop Jr. purchased the present volume in 1631, but it is not known exactly how he acquired it. He had already become a follower of Dee’s in alchemical matters, and the detailed annotations in the book were no doubt particularly appealing for him. “For him, the provenance of a book, especially an annotated book, offered a precious link to the past, but also lent authority to contemporary practices” (*ibid*., p. 94).

As well as his signature and date of acquisition, Winthrop added Dee’s monad to the volume. Dee devised this symbol and explained its significance in *Monas hieroglyphica*. It is composed of four parts, which can be identified as lunar, solar, element and fire, or as lunar, solar, earth and spirit.Dee summarized his monad thus: ‘The Sun and the Moon of this Monad desire that the Elements in which the tenth proportion will flower, shall be separated, and this is done by the application of Fire.’

This first edition of Apollonius’ *Conics* is very rare, and precedes by 29 years the Commandino edition of the same four books canonized by Horblit (and taken over by Dibner and Norman). This first edition is known to have been used by Tartaglia, Benedetti and, however critically, Maurolico (see Rose). Books I-IV were the only ones to survive in the original Greek; Borelli discovered Arabic versions of books V-VII and published them, in Latin translation, in 1661; the Greek *editio princeps* did not appear until 1710, edited by Edmund Halley, who also attempted a reconstruction of the lost eighth book. “Apollonius (ca. 245-190 BC) was the last of the great Greek mathematicians, whose treatise on conic sections represents the final flowering of Greek mathematics” (*Hutchinson’s DSB*, p. 16). Apollonius synthesized the work of his predecessors as well as contributing new methods and techniques of his own. “Hipparchus and Ptolemy absorbed his work and improved on it. The result, the Ptolemaic system, is one of the most impressive monuments of ancient science (and certainly the longest-lived), and Apollonius’ work contributed some of its essential parts … Apollonius has, in a way, suffered from his own success: his treatise became canonical and eliminated its predecessors, so that we cannot judge by direct comparison its superiority to them in mathematical rigor, consistency and generality … It is hard to underestimate the effect of Apollonius on the brilliant French mathematicians of the seventeenth century, Descartes, Mersenne, Fermat, and even Desargues and Pascal, despite their very different approach. Newton’s notorious predilection for the study of conics, using Apollonian methods, was not a chance personal taste … It was not until Poncelet’s work in the early nineteenth century … revived the study of projective geometry that the relevance of much of Apollonius’ work to some basic modern theory was realized” (DSB I: 97-99). The text was passed down by Eutocius, a Byzantine mathematician of the Justinian period, and translated from the Greek by Giovanni Battista Memo (1466-1536), Public Professor of Mathematics at Venice. A patrician who held a number of important government posts, he was instrumental in establishing the mathematical chair of which he became the first occupant in 1530. This is his principal work, published just a year after his death by his nephew. The Greek manuscript he employed is unknown, though Rose suggests it might have been the one which once belonged to the family of the present work’s dedicatee, Cardinal Marino Grimani. Rose groups Memo with the successors of Valla, Zamberti and Gaurico, who applied the new philology to Greek scientific treatises, especially mathematics.

“The work on which Apollonius’ modern fame rests, the *Conics*, was originally in eight books. Books I–IV survive in the original Greek, Books V–VII only in Arabic translation. Book VIII is lost, but some idea of its contents can be gained from the lemmas to it given by Pappus. Apollonius recounts the genesis of his *Conics* in the Preface to Book I: he had originally composed a treatise on conic sections in eight books at the instance of one Naucrates, a geometer, who was visiting him in Alexandria; this had been composed rather hurriedly because Naucrates was about to sail. Apollonius now takes the opportunity to write a revised version. It is this revised version that constitutes the *Conics* as we know it.

“In order to estimate properly Apollonius’ achievement in the *Conics*, it is necessary to know what stage the study of the subject had reached before him. Unfortunately, since his work became the classic textbook on the subject, its predecessors failed to survive the Byzantine era. We know of them only from the scattered reports of later writers. It is certain, however, that investigation into the mathematical properties of conic sections had begun in the Greek world at least as early as the middle of the fourth century BC, and that by 300 BC or soon after, textbooks on the subject had been written (we hear of such by Aristaeus and by Euclid). Our best evidence for the content of these textbooks comes from the works of Archimedes. Many of these are concerned with problems involving conic sections, mostly of a very specialized nature; but Archimedes makes use of a number of more elementary propositions in the theory of conics, which he states without proof …

“Drawing mainly on the works of Archimedes, we can characterize the approach to the theory of conics before Apollonius as follows. The three curves now known as parabola, hyperbola, and ellipse were obtained by cutting a right circular cone by a plane at right angles to a generator of the cone. According to whether the cone has a right angle, an obtuse angle, or an acute angle at its vertex, the resultant section is respectively a parabola, a hyperbola, or an ellipse … With the above method of generation, it is possible to characterize each of the curves by … a constant relationship between certain magnitudes which vary according to the position of an arbitrary point taken on the curve (this corresponds to the equation of the curve in modern terms) …

“Apollonius’ approach is radically different. He generates all three curves from the double oblique circular cone [by intersecting them with a plane of variable angle] … This approach has several advantages over the older one. First, all three curves can be represented by the method of ‘application of areas’ favored by classical Greek geometry [this was a method of constructing (‘applying’) a rectangle on a given base whose area is equal to that of a given rectilinear figure]; the older approach allowed this to be done only for the parabola. In modern terms, Apollonius refers the equation of all three curves to a coordinate system of which one axis is a given diameter of the curve and the other the tangent at one end of that diameter …

“We cannot doubt that Apollonius’ approach to the generation and basic definition of the conic sections, as outlined above, was radically new. It is not easy to determine how much of the *content* of the *Conics* is new. It is likely that a good deal of the nomenclature that his work made standard was introduced by him; in particular, the terms ‘parabola,’ ‘hyperbola,’ and ‘ellipse’ make sense only in terms of Apollonius’ method … That [many of Apollonius’ results in the *Conics* were already known to his predecessors] at least for the first four books is suggested by his own Preface to Book I. He says there:

‘The first four books constitute an elementary introduction. The first contains the methods of generating the three sections and their basic properties developed more fully and more generally than in the writings of others; the second contains the properties of the diameter and axes of the sections, the asymptotes and other things …; the third contains many surprising theorems useful for the syntheses of solid loci and for determinations of the possibilities of solutions; of the latter the greater part and the most beautiful are new. It was the discovery of these that made me aware that Euclid has not worked out the whole of the locus for three and four lines, but only a fortuitous part of it, and that not very happily; for it was not possible to complete the synthesis without my additional discoveries. The fourth book deals with how many ways the conic sections can meet one another and the circumference of the circle, and other additional matters, neither of which has been treated by my predecessors, namely in how many points a conic section or circumference of a circle can meet another …’

“We will only supplement Apollonius’ own description quoted above by noting that Book III deals with theorems on the rectangles contained by the segments of intersecting chords of a conic (an extension to conics of that proved by Euclid for chords in a circle), with the harmonic properties of pole and polar (to use the modern terms: there are no equivalent ancient ones), with focal properties, and finally with propositions relevant to the locus for three and four lines …

“Although the mathematical stature of Apollonius was recognized in antiquity, he had no worthy successor in pure mathematics. The first four books of his *Conics* became the standard treatise on the subject, and were duly provided with elementary commentaries and annotations by succeeding generations. We hear of such commentaries by Serenus (fourth century AD?) and Hypatia (*d*. AD 415). The commentary of Eutocius (early sixth century AD) survives, but it is entirely superficial. Of surviving writers, the only one with the mathematical ability to comprehend Apollonius’ results well enough to extend them significantly is Pappus (*fl*. AD 320), to whom we owe what knowledge we have of the range of Apollonius’ activity in this branch of mathematics. The general decline of interest in the subject in Byzantium is reflected in the fact that of all Apollonius’ works only *Conics* I-IV continued to be copied (because they were used as a textbook). A good deal more of his work passed into Islamic mathematics in Arabic translation, and resulted in several competent treatises on conics written in Arabic; but so far as is known, no major advances were made. The first real impulse toward advances in mathematics given by study of the works of Apollonius occurred in Europe in the sixteenth and early seventeenth centuries” (DSB).

Apollonius “was born at Perge in Pamphylia (an important Creek city on the southern coast of Asia Minor) about 240 BC, and published the work for which he is famous, the *Conics*, probably not long after 200 BC. Since, furthermore, Apollonius tells Eudemus in the Preface to Book II that he is sending it by the hand of his son (also named Apollonius), the *Conics* was a work of Apollonius’ mature age. We know from the Preface to Book I that Apollonius was living in Alexandria when he composed the original version of the *Conics*. We learn from Apollonius himself that he was at other times in Ephesus and Pergamum, but we do not know where (if anywhere) his permanent domicile was. It is probable that, like most of those engaged in intellectual pursuits in Hellenistic times, Apollonius possessed the independent means which enabled him to devote himself to study.

“After his retirement from public life, Memmo persuaded the Senate to set up a public chair of mathematics at Venice. This was done on 8 October 1530, and on 17 October Memmo himself was appointed at a salary of 100 ducats per year. On 3 November, the new professor inaugurated a series of lectures on Euclid which were held at the church of SS. Gionanni e Polo …

“The main work of Memmo was his Latin translation of the Greek text of Apollonius … published a year after the translator’s death by his nephew Giovanni-Maria Memmo. The dedication to Cardinal Marino Grimani concludes with the hope that by this edition Apollonius may be *vitae restitutus*. There is no indication of the Greek text used, although in 1650 the Venetian library of San Antonio di Castello (which had inherited many of the Grimani family’s books) owned a manuscript *Axiomata ex Apollonio de Pyramidibus*.

“Memmo advocated the place of mathematics in *cultura filosofica*. The title page of the Apollonius translation depicts a portrait gallery of classical authors, ranged in pairs around the margin. The 18 named figures run from Plato and Aristotle to Plutarch and Lucian. Of the unnamed portraits, two are geometers and two astronomers, while a central portrait is presumably of Apollonius …

“Memmo’s circle of friends included both humanists and mathematicians. Nicolò Tartaglia recounts how Memmo discussed with him the squaring of the circle; this was in 1534, the year of the Brescian mathematician’s arrival in Venice … Another friend was Pietro Bembo who wrote in 1530 of his delight that Memmo had been appointed public professor of mathematics” (Rose, pp. 52-53).

Brunet I.347; Essling 667-668; Hoffmann I, p. 205; Macclesfield 171 (lacking two leaves of text); Riccardi I 247 (‘raro libro’); Roberts & Watson 74; Sander 480; STC Italian 34; Stillwell, *Awakening* 139; Wilkinson 11; not in Adams; see Horblit 4, Dibner 101 and Norman 57 for the Commandino edition of 1566. Goulding, *Defending Hypatia*:* Ramus, Savile, and the Renaissance Rediscovery of Mathematical History*, 2010. Grafton *et al.,* ‘Passing the book: cultures of reading in the Winthrop family, 1580–1730,’ pp. 69-141 in: *Past & Present*, 2018. Neugebauer, ‘The Astronomical Origin of the Theory of Conic Sections,’ in: *Astronomy and History Selected Essays*, 1983. Rampling, ‘The Elizabethan mathematics of everything: John Dee’s ‘Mathematicall praeface’ to Euclid’s *Elements*,’ *BSHM Bulletin* 26 (2011), pp. 135-146. Roberts & Watson (eds.), *John Dee’s Library Catalogue*, 1990. Rose, *The Italian Renaissance of Mathematics*, 1975. Sherman, *John Dee: The Politics of Reading and Writing in the English Renaissance*, 1995. Wilkinson, ‘The Alchemical Library of John Winthrop, Jr. (1606–1676) and His Descendants in Colonial America,’ *Ambix*, 13 (1966), pp. 139-186. Woodward, *Prospero’s America*:* John Winthrop, Jr., Alchemy, and the Creation of New England Culture*, *1606-1676*, 2013.

Folio (303 x 203mm), ff. [1], 2-88, [89] (of 90, lacking the final blank), Roman and italic type, title-page printed in red and black, within a four-sided border of six different woodblocks, depicting a series of philosophers, poets, and scientists from Antiquity, in the lower panel an enclosed garden with fountains, on the title-page woodcut depiction of the author with his mathematical attributes on a landscape ground, woodcut vignette, depicting an enthroned pope, with the letters '.S.' and '.P.', on fol. P5v, numerous woodcut diagrams in text (first two leaves slightly browned, a few fingermarks). Contemporary Louvain binding of blind-panelled polished fawn calf over pasteboards, covers within a frame of blind fillets, with small floral tools in gilt at each outer corner, central blind fillet-lozenge, the small tool of the double-headed Habsburg eagle at centre (“which appears on several of Dee’s Antwerp or Louvain acquisitions of this time” – Roberts & Watson), a small rampant lion-shape tool in gilt at each outer corner, spine with five small raised bands, gilt fleur-de-lis and dolphin alternately tooled in compartments, front pastedown is a fragment of a twelfth-century vellum manuscript on divination in a late-Carolingian hand, rear pastedown is a fragment of a thirteenth-century vellum manuscript Evangeliary in an early Gothic hand with musical notation (corners worn, spine defective at head and foot, front cover almost detached, some pencilled bibliographical notes on the pastedowns and recto of front flyleaf). Housed in a modern half-brown morocco box, on the spine ‘APOLLONIUS OF PERGA DEE-WINTHROP COPY’ in gilt on red morocco lettering-piece, and the imprint ‘VENICE 1537’.

Item #5650

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Price:
$650,000.00
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