Sarpi and Galileo Drop Aristotle
Sarpi's Pensieri and Galileo's De Motu
In this post, I will focus on key passages in each of Paolo Sarpi’s Pensieri and Galileo Galilei’s De motu, which clearly show that these two were interacting as they were developing an alternate model to Aristotle’s for bodies in free fall.
My source for this post comes from an article entitled “Galileo Galilei e Paolo Sarpi”1 by the famous Italian translator Liberio Sosio, who was co-editor of Sarpi’s Pensieri.2 My thanks go to Gregorio Baldin,3 who refers to Sosio’s article.
Until the late sixteenth century, the preëminent model for motion was that of Aristotle (384-322 BC), which included four key points:
If an object moves continuously over a period of time, it is because something is pushing or pulling it along during this entire period.
Bodies are categorized into two categories: heavy bodies, which fall; and light bodies, which rise.
Heavier bodies fall faster than do less heavy ones.
There are two kinds of motion: natural motion, i.e., continuous motion; and violent motion, such as the tossing or striking of an object.
With respect to the first point, in the sixth century, John Philoponus (c.490-c.570) had proposed an alternative to Aristotle of “some incorporeal driving force imparted by the projector to the projected” (my translation). This force would later be called virtus impresa by Thomas Aquinas (1225-1274, who opposed it), virtus motiva by Peter John Olivi (1248-1298), and impetus by Jean Buridan (c.1301–c.1359/62). The idea of impetus is that once motion has been imparted to an object, it can move on its own, although unlike for the later concept of momentum, the impetus would degrade over time.
As for the second point, already in ancient Greek times, Archimedes (c.287–c. 212 BC) had, in his famous Eureka! moment, discovered the principle of specific gravity, i.e., the ratio of the density of an object to an object to a fluid (usually water). Archimedes' principle states that the buoyant force on an object equals the weight of the fluid it displaces.
From 1578 to 1584, when Sarpi was in Venice prior to going to Rome for three years, he critiqued on several occasions Aristotle’s distinction between heavy and light bodies, and agreed with the concept of impetus. As for the distinction between violent and natural motion, he wrote in his Pensiero 100 (my translation):
The violent and the natural are not two different natures, but two kinds of being of a single nature, for every motion is natural with respect to the passive principle, nor would the stone move upwards when it was not naturally acted upon to be moved.
So a violent motion results from an external force being applied, and being in contradiction to an internal force, although not all external forces are necessarily violent.
Galileo arrived in Padua in 1592, and stayed there for 18 years, until the publication of the Sidereus Nuncius, which made him famous. During those years, he spent a lot of time studying motion, working and reworking ideas and their presentation, as well as undertaking experiments. During this time, there was definite interaction with Sarpi, possibly as early as 1592, but definitely by 1597 there was documented interaction, and in 1604 there was written correspondence between the two on the subtleties of movement.
The key passages for the purpose of this post follow. This is from Sarpi’s Pensiero 536, dated to 1592 (all subsequent translations are mine, with the help of Deepl).
When the weight passes from ascending to descending, it only has a force impressed upon it that can sustain it, and as it begins to move downwards, that force is increasingly lacking, and so the natural motion grows the more the external force is lacking, and hence motus addit ponderi (the motion adds the weight).
And here is an extract from the dialogue component of Galileo’s De motu (Opere, I:405):
Let us therefore recall what we have stated above, namely, that the body, while moving with violent motion, moves to the point where the force imparted by the mover is greater than the weight that resists it: from this it follows that, when the body ceases to rise, the force imparted in it is equal to its weight; it follows clearly that, when the body begins to descend downwards, it does not simply move with natural motion. For, at the beginning of its motion, there is still in the body a part of that force imparted to it which used to push it upwards; this force, being now less than the same weight of the body, no longer pushes it upwards; and yet it still resists the weight that wants to descend downwards, not yet having been completely annihilated. For it is shown that it diminishes progressively; whence it follows that the body in the beginning of its motion moves slowly; and since the contrary force then diminishes and weakens, the body, finding less resistance, moves faster...
The style of the two passages is very different: Sarpi was writing for himself, in almost note form, while Galileo’s writing is much more explanatory, as if for some hypothetical future audience. Nevertheless, the two are essentially stating the same thing, namely that the force which initiated the rise of a body that ultimately reaches a point of stillness at the top before falling down, is over time being negated by the weight of the body, and as the body moves, it is accelerated by its weight.
Sosio, when he was still a student in 1958, studied De motu and concluded that the dialogue component is the oldest part of the text, notwithstanding the fact that in the Opere, this component is assumed to be the newest part. The dialogue is situated in Pisa on the shore of the Arno river, but there is no reason for Galileo not to have written this dialogue once he arrived in Padua, just as later he would situate the dialogues of the Discourses and the Dialogue in Venice after moving to Tuscany.
In the same dialogue, Alessandro, representing Galileo, also explains how just letting a body drop from one’s hand is no different from the violent motion needed to throw the same body in the air (Opere, I:405-406):
For even in natural motion preceded by violent motion, the [falling] body departs from the proportion of equality, which is the proportion of stillness…. And what I have said will also appear clearer if we consider that when something heavy is at rest in a hand, and presses downwards with its gravity, it is necessary that from something, that is, from the hand, it is pushed upwards with as much force as its gravity presses downwards.
Sarpi, although he did not write explicitly on this theme, did state in his Pensiero 449, dated to 1588, that “he who supports a weight feels the work he does in it,” which is consistent with what Galileo wrote above.
It should be noted that there are two key points that Sarpi and Galileo share at this time, that would later be rejected:
Bodies are assumed to fall at a rate proportional to their specific gravity, which is a slight adjustment of Aristotle’s assumption that heavier bodies fall faster than do less heavy ones, but still incorrect.
The velocity of a body in free fall depends on the distance travelled, as opposed to the time elapsed.
According to Sosio, the identity of Sarpi’s and Galileo’s solutions to the problem of acceleration in free fall can hardly be considered coincidental: to his knowledge, these are the only two who came up with this new solution, an important step towards the concepts of composition and independence of motions. Furthermore, they were both present in Padua at this time, and without doubt had ample opportunity to discuss these matters.
It is still not clear how exactly the two interacted. However, given their age difference of 12 years, and given the terse form in which Sarpi wrote his Pensieri, I could easily imagine a relationship in which they would have met from time to time, discussed a bit, with comments on Sarpi’s part of the kind, “Have you thought about this?” and then Galileo would have gone on and worked on these ideas, and conducted experiments.
Whatever the exact details of their interaction might have been, it seems clear to me that for centuries the influence of Sarpi on Galileo’s work on motion has been greatly underestimated.
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Liberio Sosio. Galileo Galilei e Paolo Sarpi, Galileo Galilei e la cultura veneziana, Venezia: Istituto Veneto di Scienze, Lettere ed Arti, 1995, pp.269-311.
Paolo Sarpi, Pensieri naturali, metafisici e matematici e altri scritti, a cura di Luisa Cozzi e Libero Sosio, Ricciardi, Milano-Napoli 1996. I tried to get a copy of this book, but it is sold out and there are no online copies. It is available in many academic libraries in North America and Western Europe.
Gregorio Baldin. Hobbes and Sarpi: Method, matter, and natural philosophy, GALILÆANA: Journal of Galilean Studies X:85-118, 2013.