De motionibus naturalibus a gravitate pendentibus.
Bologna: Dominici Ferri, 1670.
A fine copy of one of the most important early treatises on fluid mechanics. In this work Borelli “argues against positive levity, discusses the Torricellian experiment, takes up siphons, pumps, and the nature of fluidity, tries to understand the expansion of water while freezing, and deals with fermentation and other chemical processes” (DSB). “This work is important as the first treatise on capillarity, and for containing important investigations on the action of capillary tubes, in which the author, inter alia, formulates the law that the height of the ascent of liquids in capillary tubes is inversely proportional to their diameters. His investigations also led him to the conclusion that the phenomenon of capillarity is independent of the pressure of air” (Zeitlinger in Sotheran, First supplement, 3060). “[De motionibus naturalibus] was well known among Borelli’s contemporaries and is quoted by Varignon in his Projet d’une nouvelle mechanique. It is reviewed in the first volume of Philosophical Transactions Abridged, where it is praised for its thoroughness, for the discussion of Torricelli's experiments and for Borelli’s stand against Descartes on the nature of fluidity” (Roberts & Trent). Borelli regarded this work, together with his De vi percussionis (1667), as necessary preparation for his masterpiece, De motum animalium (1680-81), on which he had worked since the early 1660s. The work appeared in three subsequent editions, testifying to its influence.
“While On the Force of Percussion laid out some foundational propositions relating to motion and colliding bodies, the subsequent work, On the Natural Motions, was intended to be far more wide reaching … In the concluding propositions to On the Force of Percussion, Borelli dismisses Aristotle’s views on falling bodies. Borelli begins On the Natural Motions in that same pose. He attacks Aristotle for supposing that elements possess either heaviness or lightness. According to Aristotle, positive levity (referring to the supposed intrinsic lightness of bodies that allows them to rise rather than fall in a natural state) is a quality of air and ﬁre. Earth and water, on the other hand, contain a gravity that impels them towards their natural place at the centre of the earth. Borelli makes it clear from the outset of this second book that he is determined to dispel these views” (Boschiero).
“Giovanni Alfonso Borelli, while embracing the doctrine of corpuscles in motion …, uniquely sought to constrain it by means of mathematics. In De motionibus naturalibus a gravitate pendentibus he was concerned ‘to show that all events in the world of body are up for explanation by the force of heaviness only, if only one attributes fitting shapes to the particles of bodies, so that the force of heaviness, directed toward the center of the Earth, compels them according to mechanical laws [i.e., those of statics] to move in other directions, too, depending on circumstance. He therefore regards the corpuscles as machines, which are moved by the force yet determined as to direction by their construction. Since the only driving force is thus the pressure of bodies upon others and themselves, he conceives of the totality of movements on Earth as a problem in hydrostatics’” (Cohen, pp. 393-4).
“Borelli’s analysis of the collision of elastic bodies relies on a notion of the spring-like and machine-like properties of some parts of nature. For example, air particles impact upon each other, transmitting a motive virtue one upon the other that is maintained through the compressive properties of these corpuscles. In other words, each corpuscle of air, when impacted, compresses, moves as a result of its attained motive virtue and recoils in order to re-acquire its lost space before impacting onto another particle. In such an environment, less dense particles of ﬁre, with their own shapes and properties inconsistent with those of air, are pushed upwards. Thus, Borelli debunks Aristotle’s theory of positive levity, which attributes motion only to intrinsic qualities of nature rather than extrinsic forces proportional to elastic properties of corpuscles. To illustrate his point, on several occasions Borelli discusses the ‘structure of air’: It is . . . reasonable to assign to the particles of air a structure which forces them to unfold when they are constricted against their natural requirement. We understand this if we conceive that the substance of air consists of countless juxtaposed small machines. Then we clearly perceive that an elastic virtue can be found in this aggregate since the small machines attempt at dilating after being compressed (Prop. XCCIII).
“After covering further ground with the description of theories and experiments to do with the vacuum, the Torricellian tube and the freezing process of liquids, Borelli reaches his conclusions reminding his readers of the ﬁnal destination of this project: This is enough on the motions resulting from the innate force of gravity. We indeed do not consider extending further these preliminaries nor delaying the edition of the main argument on the movements of animals longer (Prop. CCLXXVII)” (Boschiero). Born in Naples, Giovanni Borelli (1608-79) studied mathematics at Rome under Benedetto Castelli. Sometime before 1640 he was appointed professor of mathematics at Messina. In the early 1640s, he met Galileo in Florence. In 1656 Borelli was appointed to the chair of mathematics at the University of Pisa, a post previously held by Galileo. It was in Pisa that Borelli met the Italian anatomist Marcello Malpighi; the two men became founder members of the short-lived Accademia del Cimento. Motivated by Malpighi’s own studies, Borelli began his first investigations into the science of animal movement. This began an interest that would continue for the rest of his life, eventually earning him the title of the Father of Biomechanics.
In May 1665, Cardinal Michelangelo Ricci, Roman correspondent and adviser to the Tuscan Court, wrote to Prince Leopoldo de Medici, the patron of the Cimento, encouraging Borelli to apply himself to the composition of a treatise on motion. Borelli’s initial response was that he was instead concentrating on a treatise on anatomy, but, seemingly at Ricci’s insistence, Borelli eventually agreed, the result being the two works De vi percussionis and De motionibus naturalibus. Both works were composed, or at least drafted, before his departure from the Medici court in 1667, when he returned to Messina. At this point the Cimento effectively ceased to function, even though it apparently was not formally dissolved, and even though Prince, now Cardinal, Leopold continued to direct some experimental work until he died in 1675.
“On the way [to Messina, Borelli] passed through Rome and stopped for the summer in Naples. While there he was the guest of the Investiganti for whom he repeated many of the experiments he had performed at the Cimento. And he also repeated for his own edification some work that the Investiganti had accomplished independently. As a result of this visit, Concublet provided for the publication of De motionibus naturalibus, for which Borelli reciprocated by writing a warm dedication to him” (DSB). The Accademia degli Investiganti was founded in 1663 by Leonardo di Capua, under the patronage of Andrea Concublet, Marquis of Arena.
DSB II.306-14; Carli-Favaro 78 (329); Cinti 291 (147); De Caro 54; Krivatsy 1577; Riccardi I.159-60; Roberts and Trent p. 42; Wolf, History of science, technology, and philosophy I pp. 58-60. L. Boschiero, Introduction to Borelli’s On the Movement of Animals – On the Natural Motions Resulting from Gravity, P. Maquet (tr.), 2015; H. F. Cohen, How Modern Science Came into the World: Four Civilizations, One 17th Century Breakthrough, 2014.
4to (228 x 154 mm), pp. 4 p.l., 566, , half-title, woodcut device on title, woodcut diagrams in text. A few minor stains, some light finger soiling, occasional small marginal tears, Tt1 with two paper flaws outside of the text, 18th-century mottled calf, spine gilt (small wormholes in spine, foot of spine lightly rubbed).