Aristarchi Samii de mundi systemate, partibus et motibus ejusdem libellus. Adjectae sunt AE. de Roberval ... notae in eundem labellum

Paris: Antoine Bertier, 1644. First edition.

THE LAW OF UNIVERSAL ATTRACTION

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First edition, exceptionally rare, of Roberval's cosmology, in which he expresses, covertly, his support for Copernicus, and also formulates for the first time the law of universal attraction - that any two material bodies in the universe attract each other. This principle is normally ascribed to Robert Hooke, who published it three decades later, and to Newton in the Principia (1687). Roberval (1602-75) was one of the most brilliant members of Mersenne's circle. He developed indivisibles independently of Cavalieri, invented an original method of drawing tangents, and solved many of the problems on the cycloid that were formulated and solved by Pascal two decades later. However, since almost nothing of his work was published in his lifetime, he was for long eclipsed by Fermat, Pascal, and, above all, by Descartes, his irreconcilable adversary. In fact, Roberval himself published only two works, the Traité de mécanique (1636), and the Aristarchi offered here; several of his other works appeared posthumously in the Divers ouvrages de mathématique et de physique (1693), but many remain unpublished even today. "Roberval's positivism appears in a particularly nuanced form in the book De mundi systemate of 1644, where he claimed to have translated an Arabic manuscript of Aristarchus, to which he had added his own notes, all of them favorable to the author. Yet he did not adhere to the system of Aristarchus to the exclusion of those of Ptolemy and Tycho Brahe. In the dedication of the work, Roberval wrote: 'Perhaps all three of these systems are false and the true one unknown. Still, that of Aristarchus seemed to me to be the simplest and the best adapted to the laws of nature.' It is with this reservation that Roberval expressed his opinion on the great system of the world (the solar system), the minor systems (planetary), the motions of the sun and the planets, the declination of the moon, the apogees and perigees, the agitation of the oceans, the precession of the equinoxes, and the comets. Despite this reservation, Roberval appeared convinced of the existence of universal attraction, which-under the inspiration of Kepler-he put forth as the foundation of his entire astronomy: 'In all this worldly matter [the fluid of which the world is composed, according to our author], and in each of its parts, resides a certain property, or accident, by the force of which this matter contracts into a single continuous body'" (DSB). Like Copernicus, Aristarchus (ca. 310-230 BCE) maintained that the Earth rotates on its axis and revolves around the Sun. However, Aristarchus's work has not survived and the Arabic manuscript which Roberval claimed to have translated almost certainly did not exist. Roberval uses it as a cover to express his support, albeit nuanced, for heliocentrism, still a dangerous idea at the time. OCLC lists Cornell, Huntington and Linda Hall in US. No other copies in auction records.

"Gilles Personne was born in the village of Roberval, near Senlis, in 1602. Nothing is known about his early education; his father was a poor farmer or farmworker, and the young mathematician (who would later add 'de Roberval' his surname) seems to have led the peripatetic life of an impoverished student, passing through several universities and alternately studying and teaching. In 1628 he settled in Paris; there he got to know Mersenne, who recognised his talents and encouraged him to work on the problem of the curve known as the 'trochoid,' 'roulette', or 'cycloid.' In 1632 Roberval was given a teaching post at the Collège de Maître Gervais; two years later he obtained a more eminent position, the Ramus chair of mathematics at the Collège Royal. He would remain in this professorship for forty-one years - a permanent fixture, as it were, of Parisian intellectual life - until his death in 1675. But the peculiar terms on which holders of this Ramus chair were appointed had a very negative influence on both his work and his later reputation. The chair was tenable for a period of three years; at the end of that time it was opened to a public competition, in which anyone, including the incumbent, could apply for it. Candidates were required not only to lecture but also to demonstrate theorems and solve problems put to them by all comers. As a result, the practice grew up of the incumbent trying to ensure his reappointment by proposing problems which only he could solve. Whatever were the most advanced discoveries Roberval was making at any time, therefore, he had an incentive to keep them secret so that he could use them to confound his competitors on these triennial occasions. One consequence was that most of his important work in his special field - geometry - remained unpublished in his lifetime. And another consequence was that Roberval would more than once become embroiled in disputes about precedence, insisting that he had made key discoveries long before they were published by others; in 1646, for example, he would make bitter accusations against Torricelli, alleging that his analysis of the cycloid had been derived in an underhand way from Roberval's unpublished work. Even when he did allow some of his work to circulate, he favoured a method of publication that was both limited and carefully monitored. As the English mathematician John Pell would later recall, 'many yeares agoe, some pieces of Mr Roberval were published after the old fashion. That is, they were not given to a Printer; but any man that would pay for the transcribing might have had a coppy of them.'

"Roberval was, by all accounts, a prickly character, quick to take offence, and with a high opinion of his own worth. As those were also the most prominent characteristics of René Descartes, it is hardly surprisingly that a fierce enmity quickly sprang up between them. Roberval was almost ostentatiously unimpressed by Descartes' 'Géométrie' (one of the essays published with his Discours de la méthode in 1637); his cool and critical comments, transmitted to the author by their mutual friend Mersenne, elicited an angry reaction. Relations between them were further soured by Descartes' quarrel with Fermat about the construction of tangents in 1638, in which Roberval became one of Fermat's leading defenders; not long afterwards, Descartes accused Roberval of purloining his own ideas about the cycloid. Meanwhile Mersenne himself remained on the best of terms with both of these disputants. Indeed, he seems to have had not only a deep admiration of Roberval's mathematical talents - he described him as scarcely inferior to Archimedes - but also a real personal fondness for him. Mersenne made a special effort to promote the writings of this far from prolific author: he added Roberval's brief treatise on mechanics at the end of book 3 of his own Harmonie universelle (Paris, 1636); he included material from the Latin version of that treatise in his compilation of 1644, Cogitata physico-mathematica; he encouraged and assisted the publication of Roberval's astronomical work, Aristarchi Samii de mundi systemate libellus, in 1644; he also reprinted that entire work in his own later compilation of 1647, Novarum observationum ... tomus III. And throughout his own writings, Mersenne referred to Roberval in terms both laudatory and affectionate, calling him simply 'our geometer' - 'Geometra noster'" (Malcolm, pp. 157-8).

"In 1644, Gilles Personne de Roberval published a small cosmological treatise entitled Aristarchi Samii de Mundi Systemate, partibus, & motibus eiusdem, libellus. The book is attributed to the ancient Aristarchus of Samos, and Roberval claims it to be an annotated translation of a recently recovered Arabic manuscript ... Roberval tells the reader that the Arabic manuscript was translated under his and Mersenne's supervision, at the expense of the royal counsellor. He does not explicitly defend the authenticity of the manuscript, or even its origin as a true ancient source. Roberval does, however, imply the manuscript's authenticity, at least by the style and disposition of the treatise. The epistle informs us that, in addition to the translated text, Roberval will also help the reader by inserting certain notes. These are given within the text, are labelled as 'NOTA', and end with the abbreviation 'P.N.E.M.' ['pondere, numero et mensura', the motto of the mathematicians of the Collège Royal]. Usually, the notes present new discoveries which were unknown by the author, in order to corroborate or refute Aristarchus's opinions.

"Not many took the book to be an authentic ancient treatise. Most philosophers, mathematicians or scientists realized that the book was not authentic, and that the name of Aristarchus was used just as a cover for a seventeenth century author. They were, of course, right. However, as Heath observed more than a hundred years ago, 'there was every excuse for Roberval. The times were dangerous.' Only ten years before he wrote the Aristarchi, Galileo's Dialogue on the Two Chief Systems of the World was condemned. The French context was uncertain, as geocentric systems were actively defended in the 1630s. In 1632, Libert Froidmond, arguing against Philip and Jacob Lansbergen's heliocentric system, published the Anti-Aristarchus, sive Orbis-terrae immobilis. Two years later, Froidmond followed up with another treatise, the Vesta, sive Ant-Aristarchi Vindex. Furthermore, Roberval's Parisian colleague Jean Baptiste Morin had published the Famosi et antique problematis de telluris motu, strongly arguing against Galileo and Copernicanism" (Babeş, pp. 95-97).

In the Aristarchi, Roberval not only discusses heliocentrism, he gives a complete theory of the motion of the Earth, Moon and planets. It is based on three principles.

"The Sun as a cause of motion. From the very first chapter of the Aristarchi, Roberval explains all motion of the system of the world by two principles. One of them is a principle of attraction, stating that the fluid heavenly matter has, in every one of its parts, a certain property by which it tends to unite with all the other parts of matter. If the Sun would be absent from the world, all heavenly matter would reunite in a perfect sphere. The second principle concerns the action of the Sun. By its heat, the Sun continuously rarefies the surrounding matter. The rarefaction results in the elongation of matter, which is pushed towards the extremity of the system. The sun also has an axial motion of its own, by which the eviction of the rarefied matter takes place. This motion impresses upon the celestial bodies their periodical movement around the Sun. However, throughout the Sun's axial rotations, the ejections of rarefied matter do not have a constant flux, and thus the motions of heavenly bodies around the sun are not uniform.

"The movements of the Earth's system. As one of the planetary systems, the Earth is moved around the Sun by the continuous pushing of the elongated matter, coupled with the attractive property of the celestial matter. The system of the Earth retains its quasi-spherical shape due to an analogous attractive property of the elemental matter, which accounts for the weight of terrestrial bodies. The terrestrial matter is, however, different from the heavenly matter. It is very mixed, and it is unevenly disposed on the surface of the Earth. Therefore, the Sun unevenly elongates the airy and fiery atmosphere surrounding the Earth and, as a result, the diurnal motion of the Earth is irregular. To this is added a third reason of the irregularity, the influence of the Moon.

"The periodical movement of the Moon. According to Roberval, the Moon is a part of the system of the Earth. Its density is similar to that of the superior atmosphere, such that it revolves, together with the air and fire, around the Earth. Roberval claims that the moon floats in the superior atmosphere in the same way as a submerged piece of wax floats in water. Its orbit, however, in not circular but oval-shaped. This shape is responsible for the ebb of the seas: at its perigee, the Moon compresses the air below it which, in turn, exerts a pressure on the ocean. Likewise, the Moon disturbs the flow of rarefied matter coming from the Sun, which also affects the diurnal motion of the Earth" (Babeş, pp. 110-111).

What is particularly noteworthy here is the "property [of matter] by which it tends to unite with all the other parts of matter," the first suggestion of the 'universal attraction' between material bodies.

"In his System of the World, Roberval asserts that each part of the (fluid) matter which fills the universe is endowed with a certain property that makes all parts draw together and attract each other reciprocally (p. 39). At the same time he admits that in addition to this universal attraction there are other, similar, forces proper to each of the planets (something that Copernicus and Kepler also admitted) which hold them together and explain their spherical shapes ...

"Roberval's cosmology, as it is presented in his System of the World, ... was heartily condemned by Descartes, and Newton was deeply angered by Leibniz's identification of Newton's views with those of Roberval. Yet, historically, Roberval's work is interesting not only because it was the first attempt to develop a 'system of world' on the basis of universal attraction, but also because it presented some characteristic features, or patterns of explanation, which, or at least the analogues of which, we shall find discussed later by Hooke and advocated by Newton and Leibniz.

"Thus, according to Roberval, the fluid and diaphanous matter which fills or constitutes the 'great system of the world' forms a huge - but finite - sphere in the center of which is the sun. The sun, a hot and rotating body, exerts a double influence on this fluid matter: (a) It heats and thus rarefies it; it is this rarefaction and the ensuing expansion of the world-matter that counterbalances the force of the mutual attraction of its various parts and prevents them from falling upon the sun. This rarefaction also confers on the world-sphere a particular structure; the density of its matter increases with the distance from the sun. (b) The sun's rotating motion spreads through the whole world-sphere, the matter of which turns around the sun with speeds diminishing with its distance from the sun. The planets are considered as small systems, analogous to the great one, which swim or place them selves at distances from the sun corresponding to their densities, that is, in regions the density of which is equal to their own; thus they are carried around the sun by the circular motion of the celestial matter, as is the case with bodies swimming in a rotating vessel. Strangely enough, Roberval - who never takes any account of centrifugal forces - believes that these bodies will describe circular trajectories!" (Koyré, pp. 59-60).

The engraved plate, which is repeated in this copy, appears to be often lacking: it is not present in the BNF copy digitized on Gallica, for example. In the reprint of the work in Mersenne's Novarum observationum ... tomus III, the two astronomical diagrams on the plate are printed within the text, each of them several times.

Babeş, 'Roberval's scepticism in the Aristarchi Samii De Mundi Systemate,' Studia Ubb. Philosophia 65 (2020), pp. 95-114. Koyré, Newtonian Studies, 1965. Malcolm, Aspects of Hobbes, 2002.

12mo (142 x 83mm), pp. [viii], 148, with one engraved plate showing two astronomical diagrams, bound before title and repeated at end (two small paper flaws in aii affecting three letters but not the sense, occasional light browning and foxing). Contemporary vellum (darkened and stained). A genuine, untouched copy of an extremely rare book.