Theoricae mediceorum planetarum ex causis physicis deductae.

Florence: Ex Typographia S M D, 1666.

First edition, very rare, and an exceptionally fine copy, of Borelli’s important work on celestial mechanics, prefiguring the Newtonian theory of universal attraction. Borelli revived “Kepler’s theories on the planetary orbits … However, unlike Kepler, he believes natural motion to be in a straight line rather than a circle, hence requiring a form of gravitational force to maintain the planets in orbit. Borelli suggests that the elliptical orbit results from a balance between an attractive force of gravity between the sun and the planet and an opposing centrifugal force” (Parkinson, Breakthroughs). During the summer of 1665 Borelli established an astronomical observatory in the fortress of San Miniato, a pleasant site on a hill a short distance from Florence. Here he used an excellent Campani telescope and some instruments of his own design to try to determine with extreme accuracy the motions of Jupiter’s satellites. From this work came his Theoricae mediceorum planetarum ex causis physicis is deductae (1666), in which, among other things, he explained how the elliptical orbits of planetary bodies could be understood in terms of three types of action. In the first place, a planetary body has a tendency toward a central body and would move toward that central body if no other factors intervened. Then, a central body, such as the sun, sends out rays and as that body rotates the rays also rotate. The cumulative effect of the impacts of these seemingly corporeal rays is to impart to the planet a motion around the central body. This motion in revolution thus produces a centrifugal tendency which balances the original centripetal one and thereby establishes the planet in a given mean orbit. Small self-correcting fluctuations account qualitatively for the observed ellipses. There are some obvious difficulties in accommodating these proposals to the satellites of the major planets, and it is clear that Borelli had much more in mind than just explaining the motions of the moons of Jupiter. The Copernican implications of his scheme, however, could be masked by seeming to focus attention on Jupiter” (DSB). “In the work of Borelli we find a fulfillment – imperfect, but nonetheless decisive – of that identification of celestial physics with terrestrial physics which was the dream of modern science, and which Kepler and Descartes thought they had achieved, but only Newton realized. It appears in the work of Borelli by an admission that celestial forces (circular planetary motions) produce centrifugal forces … Borelli decided to reverse the modus procedendi, and to attack the problem theoretically, seeing that the observations did not provide the desired conclusion; that is to say, he developed first of all a priori, a theory of periodic motion for the planets, as well as for their satellites or moons, starting from certain data or physical requirements, and then made the appropriate deductions. These deductions were then compared with the empirical data from observations. By considering the observations after, instead of before, working out his theory, his task was greatly facilitated, for he knew what to look for; and knowing it, could easily find it” (Koyré, The astronomical revolution. Copernicus - Kepler - Borelli, p. 468). ABPC/RBH list only one copy since Macclesfield (a copy in a modern binding with a partially erased stamp on the title), and only one other copy since the Bute sale in 1961.

“Borelli’s Theoricae Mediceorum planetarum sought to provide a purely theoretical analysis of the motions of the Medicean planets as part of the European debate arising in the wake of the recently observed shadows of the satellites of Jupiter on the body of the planet—a required topic for a Medici mathematician. The dispute on the Medicean planets allowed forays into the solar system while avoiding dealing directly with Copernicanism, a dangerous topic in Italy in those years. Despite this precaution, Borelli established an analogy with planets that left little doubt as to his cosmological beliefs. Theoricae was published by the Medicean press and circulated among a select group of intellectuals and patrons. Borelli’s work is of interest in several respects, such as his integration of celestial and terrestrial physico-mathematics; his attempt in a Keplerian tradition to conceptualize curvilinear motion as resulting from an imbalance between an outward and an inward tendency; his effort to provide a quantitative analysis of those two components; and his experiments in the tradition of the Cimento. Borelli’s method of investigation was heavily dependent on analogies among different phenomena and fields, on the assumption that nature’s method of operation is both uniform and simple. He often extended his analogies from physico-mathematics to medicine and anatomy, and even his work on the Medicean planets starts with analogies between the solar system and the animal body. At times one finds so many analogies in Borelli’s work that one wonders which one he adhered to, since those presented early on were later modified or cast aside.

“It is not difficult to detect the strong Keplerian flavor of Borelli’s account, not just in his attempt to bring together physics and astronomy but also in his claim that the satellites’ trajectories are elliptical and that the sun pushes the planets with a lever, as it were. Borelli conceived orbital motion as if it were taking place on a rotating lever moved by the rotating sun. The inward tendency was due to an appetite of the satellites, or planets, to move toward the central body, whereas the outward tendency was due to their circular motion generated by the light emitted by the central body. Throughout his account Borelli provided examples and experiments with pendulums, magnets, and rotating bowls, thus treating celestial and terrestrial phenomena in a similar fashion. For example, Borelli described a device meant to illustrate the motion of celestial bodies by means of rotating wooden sticks and magnets [Fig. 15]. Without mentioning his name, Borelli examined Roberval’s hypothesis whereby planets float on a fluid whose density increases away from the center, occupied by the sun. The fluid’s density depended on the sun’s heat, and the planets’ distance from the sun depended on their specific gravity, following the laws of hydrostatics.

“Borelli believed the speed of a body moving in a circular motion, due to the same motive power, whether from an internal and natural or external and violent action, to be constant. He tried to support this claim by means of an experiment with a strong Galilean flavor, allegedly showing that the speed of a pendulum bob is not affected by a nail on the vertical hindering its oscillations [Fig. 16]. The choice of the vertical pendulum was unfortunate, because the bob’s speed varies at each point.

“In the case of orbiting bodies, however, we see that their speeds are not constant but rather increase closer to the central body, whether the sun or a planet. Thus Borelli argued that the light of the rotating sun pushes the planets with a force inversely as the distance, much as Jupiter does with its satellites. Here Borelli seemed unconcerned that Jupiter is not a luminous body like the sun. At this point he had recourse to the impact laws and implicitly criticized Descartes for refusing to accept that a large body cannot be set in motion by a smaller one. The action of the central body is assimilated to a lever, increasing further the barrage of mechanical analogies. Borelli argued that the rotation of the central body, either the sun or Jupiter, moves orbiting bodies with an equal force, opposed by the body’s resistance. Since the resistance increases with the distance from the center, the circular component of the speed will be inversely as the distance from the center. As to radial motion, Borelli considered the tendency of orbiting bodies toward the center to be constant. The outward tendency, however, was variable and produced an oscillating motion that, composed with the circular one, generated ellipses. Borelli compared the oscillating motion with that of a cylinder floating vertically in a bucket of water removed from its equilibrium position. Removing accidental perturbations, the oscillations would not stop, a situation much more likely to occur in the celestial aether.

“Borelli’s aim was to find analogies between planets and satellites, but like several of his contemporaries he failed to mention Kepler’s harmonic or third law, originally formulated in Harmonice mundi (Linz, 1619). Moreover, again like several of his contemporaries, Borelli did not distinguish between a planet’s orbital speed and its circular component. Without this distinction, his claim that the motion of the planet (or satellite) is inversely as its distance from the center is incorrect and implies an inaccurate understanding of Kepler’s second or area law. In his treatment of the outward tendency, which Huygens called centrifugal, Borelli seems to have believed that it varied inversely as the distance from the center; therefore the outward tendency was proportional to the orbital speed. Borelli did not carry out an investigation of how the outward tendency varied and simply adopted an intuitively simple relation. In conclusion, Borelli’s ingenious work contains valuable insights but betrays the haste with which it was composed. Borelli introduced outward tendencies in the account of orbital motion, but Koyré’s claim that this would represent his great innovation seems grossly overstated, given that Descartes’ Principia had unequivocally had recourse to them in 1644. Borelli’s mathematics appears remarkably simple, and nowhere did he prove that the orbital motion resulting from the conditions he had stated was indeed an ellipse. He often tried to follow a Galilean style and relied extensively on geometry and proportions, as well as some theorems on conic sections from Apollonius. Unlike Galileo, however, Borelli did not attempt to use indivisibles or infinitesimal procedures” (Meli (2006), pp. 192-7).

Several historians have noted that the date on the title page of the Theoricae has been altered by adding a ‘I’ on the dot at the end of MDCLXV., thus giving MDCLXVI, or 1666. It has been suggested that this was the result of a delay caused by the censor (the dedication is dated 20 October 1665, the imprimatur was granted on 10 March 1666). However, Borelli’s unpublished correspondence shows that, at the beginning of 1666, he decided to have the work printed with the date of the previous year to forestall the potential charge of having found inspiration in the Dialogi physici of his arch-rival Honoré Fabri.

“Around 1660 Fabri had put forward the idea that the appearance of Saturn could be accounted for in terms of dark and light satellites oscillating behind the planet. Fabri thought that the satellites of Jupiter moved in the same way because they are never seen in front of Jupiter, even though they are very bright, and because their shadows on the body of Jupiter had not been observed. Both observations, however, had just become available, and Fabri found himself in an awkward position. At the end of his Dialogi physici in quibus de motu terrae disputatur (Lyon, 1665), Fabri added two letters to his Lyon friend Claude Basset outlining his revised views. Fabri believed the orbital trajectory to be composed of two parabolic arcs with a common basis. He ruled out circular or elliptic trajectories on the grounds that the motion of the satellites, as seen from the Earth, is uniform—a claim disputed by most of his contemporaries” (Meli (2006), pp. 192-3).

“Borelli became aware of Fabri’s Dialogi physici in January 1666, when the grand duke showed him a published letter by Campani to Cassini mentioning Fabri’s book. From Pisa, Borelli asked Prince Leopold at Florence to send him a copy of Fabri’s Dialogi in order to make sure that he had not missed anything significant just before consigning his own work to the press. On seeing Fabri’s Dialogi Borelli was greatly distressed and replied immediately to Leopold in a style betraying his state of mind.

‘I have received yesterday afternoon Father Fabri’s book, which astonished me for that little that I have seen, because I see that to that cranky brain occurred concepts very similar to mine, with which I explain the physical causes of planetary motions. Although he talks a lot of nonsense as usual, I would not like it if others were to suspect that I had used his inventions and I, though innocent, considered to be a thief. Therefore I thought it appropriate to have recourse to the goodwill of Your Most Serene Highness, begging you most humbly and urgently to help me and protect my innocence – known to Your Highness – in the manner you deem appropriate. In the meantime I thought it absolutely necessary to have my work printed as soon as possible at Florence, no longer at Bologna, disregarding the higher costs involved, as long as it appears quickly under last year’s date.’

“This extraordinary passage highlights some of the background to the publication of the Theoricae, including the probably cause of the change of publication year on the title-page. Although we do not know exactly what Leopold and his brother Ferdinand II did to help Borelli, some inferences can be made. In the preface we read that the manuscript was submitted to Leopold’s ‘most severe judgment’ and that Leopold had urged Borelli to publish. By mentioning Leopold’s request, Borelli would have been shielded from potential accusations of plagiarism … Another macroscopic and yet apparently unnoticed feature testifies to the support Borelli obtained from the Medici. Theoricae was not published by any commercial printed in Florence, but at the printing press of the grand duke, ‘Ex Typographia S[erenissimi] M[agni] D[ucis].’ Even the Saggi di naturali esperienze fatte nell’Accademia del Cimento sotto le protezione del Serenissimo Principe Leopoldo di Toscana did not come out of the Medici press, but were published by ‘Giuseppe Cocchini all’Insegna della Stella.’ Thus it is probable that by mentioning to Leopold the higher costs involved in publishing his book in Florence rather than Bologna, Borelli may have had the Theoricae printed at his patron’s expense” (Meli (1998), pp. 392-3).

Newton’s own annotated and dog-eared copy of the Theoricae is in Trinity College, Cambridge. “In 1672 John Collins asked Isaac Newton for his opinion on Giovanni Alfonso Borelli’s De motionibus naturalibus a gravitate pendentibus. Newton replied that he esteemed Borelli ‘among the middle sort of Authors’ … A decade and a half later, Newton had another occasion to reflect on Borelli’s merit, and now he proved more complimentary, in part because Borelli served as a whip with which to lash out at Hooke. ‘I am told,’ Newton wrote to Halley, that Hooke pretended ‘I had all from him.’

‘This carriage towards me is very strange and undeserved, so that I cannot forbeare in stating that point of justice to tell you further, that he has published Borell’s hypothesis [in the Theoricae mediceorum planetarum] in his own name and the asserting of this to himself and completing it as his own, seems to me the ground of all the stir he makes. Borel did something in it and wrote modestly, [while Hooke] has done nothing and yet written in such a way as if he knew and had sufficiently hinted all but what remained to be determined by the drudgery of calculations and observations, excusing himself from that labour by reason of his other business, whereas he should rather have excused himself by reason of his inability’” (Feingold, The New Science and the Jesuit Science, p. 121).

Carli and Favaro 299; Crawford Library 55r; Lalande p 266; Parkinson Breakthroughs; Riccardi 158.9. Meli, ‘Shadows and deception: from Borelli’s ‘Theoricae’ to the ‘Saggi’ of the Cimento,’ British Journal for the History of Science 31 (1998), pp. 383-402. Meli, Thinking with Objects, 2006.

4to, pp. vii [-viii], 184, [4, imprimatur and errata], with woodcut vignette on title, woodcut head- and tailpieces, woodcut initials, and 5 folding engraved plates. Contemporary Italian vellum, faded manuscript number (?) on spine, edges speckled red (some spots on back cover).

Item #5221

Price: $65,000.00