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

Venice: Bernardinus Bindonus, 1537.

First edition of any part of Apollonius’ *Conics*, “one of the greatest scientific books of antiquity” (Stillwell), alongside those of Euclid and Archimedes. “Apollonius’s theory of the conic sections (about 220 BC) 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 Kepler’s use of the *Conics* in his *Astronomia Nova*, where it was fundamental for his proof of the ellipticity of the orbit of Mars. This first edition is very rare, preceding by 29 years the Commandino edition of the same four books canonized by Horblit (and taken over by Dibner and Norman), and 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. “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. OCLC lists five copies in America (Harvard, Louisville, MIT, UNC, Yale). ABPC/RBH list only three complete copies since Honeyman: Christie’s New York, April 9, 2013, lot 33, $327,750 (John Dee’s copy); Sotheby’s 2002, lot 27, £17,500 = $25,254 (de Vitry copy, rebacked); Sotheby’s, December 10, 1999, lot 51, £18,400 = $29,817.

“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 II.667-8; Macclesfield 171 (lacking two leaves of text); Riccardi I 247 (‘raro libro’); Sander 480; Stillwell II.139; not in Adams; Horblit 4, Dibner 101 and Norman 57 for the Commandino edition of 1566. Neugebauer, The Astronomical Origin of the Theory of Conic Sections, in: *Astronomy and History Selected Essays*, 1983. Rose, *The Italian Renaissance of Mathematics*, 1975.

Folio (306 x 220), pp. [1], 2-88, [1], [1, blank], woodcut of the author with his mathematical attributes on title, wide historiated six-block title-border showing classical poets, philosophers and scientists, and an enclosed garden, numerous woodcut geometrical diagrams in text, and portrait of St. Peter beneath colophon at end (small red stamp to the bottom margin of title and colophon covered). Contemporary vellum. A fine copy of this very rare work.

Item #3075

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Price:
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