[3] De Motu is known for expressing Galileo's ideas on motion during his Pisan period prior to transferring to Padua.
Galileo would later incorporate select arguments and examples from his De Motu into his subsequent works Le Meccaniche (On Mechanics), Discorso intorno alle cose che stanno in su l'acqua (Discourse on Floating Bodies), and Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences).
However, despite his frequent stinging criticism of Aristotle’s physics, Galileo’s De Motu still clung to the classical elements as a foundational cause for motion in which all matter moves toward its respective natural place in the universe.
This is due to the underlying unity of conception, the skillful linking of ideas, the constant recourse to mathematics, and the lucidity of the reasoning and the style.
Pierre Duhem proposed that Galileo’s Pisan dynamics was a continuation of the tradition taught by Jean Buridan and Nicole Oresme, in which Galileo continued to perfect the impetus theory throughout his career, potentially drawing influence from Giambattista Benedetti whose dynamics are generally described as a partisan of the impetus physics.
[9] Ernest Moody pointed out that Galileo’s arguments that rejected Aristotle’s explanation for projectile motion were exactly the same as those used by Buridan and Albert of Saxony, and was therefore not original; however, Moody argued against Duhem and Koyré that Galileo’s early dynamics were not modeled after the Buridan impetus, but rather based upon 11th-century Avenpace’s dynamics, which stemmed from the ideas of 6th-century John Philoponus of Alexandria.
Further, Galileo was also influenced by his senior colleague at Pisa, Francisco Bonamico, who also discussed the problem of projectile motion in his own De Motu and mentioned that Philoponus is the originator of the theory of impressed forces.
Moody suggests that Bonamico was acquainted with the medieval tradition of impetus physics, but only at a second- or third-hand account, especially in regard to the 14th-century contribution to mechanics, which is what led Koyré to assume that Bonamico’s views were an approximation of Buridan’s impetus and were the same as the impressed force theory of Philoponus, Peter John Olivi, and Francis of Marchia.
[10][11] Moody asserts that there is not only a developmental difference but also in meaning between Galilean impressed forces (virtus impressa) and Buridian impetus: Buridan’s impetus was an “enduring reality” (res permanens) that would remain undiminished forever if left unimpeded by air and gravity, much like the modern treatment of momentum; whereas Galileo’s impressed forces were primarily self-depleting that is supplementally impeded by air resistance.
[12] Buridan proposed that impetus wouldn’t need to posit angels or “Intelligences” as movers of the heavens, for if we suppose that God, at the creation of the world, set the heavenly bodies in motion at their present rates of rotation, no further action by a “mover” would be required, because their original impetus would endure undiminished forever, in the absence of resistance or of opposed forces.
Galileo begins by defining heaviness and lightness, which is effectively the equivalent of the modern concept of specific gravity or relative density.
Based on this arrangement, it appears Galileo assumes a Ptolemaic system that places Earth at the center of the universe, despite his later acknowledgment of Nicolaus Copernicus’s De revolutionibus orbium coelestium in Chapter 20.
Since natural motion results due to the heaviness/lightness of the medium and the body, and since the respective heaviness/lightness can be compared through respective weights with equal volumes, Galileo recognizes that the same can be said of weights on a balance, and that, in viewing the lever as an analogy for motion, it can be easily understood why solids lighter than water (e.g., wood) are not completely submerged in water – the heavier cannot be raised by the heavy.
In another example, Galileo proposes that a piece of wax be mixed with sand so that it becomes slightly heavier than water and begins to sink slowly.
The only way to correct the contradiction is to reject Aristotle’s claim and assume that the two bodies of same material but different size (and weight) fall at the same speeds.
A caveat is then recognized: the weights of the bodies of same material cannot be taken to the extremes, for even a thin plate or even a leaf of the same substance can be made to float on water.
Similar arguments are then made for the ratios of speeds of two bodies equal in volume but unequal in weight moving the same media in both upward and downward motion.
Galileo investigates the speeds of bodies moving down inclined planes; however, portions of his arguments are unrefined and contain errors.
Mathematician Vincenzo Viviani would later insert an amendment to the second edition of Two New Sciences that refers to and incorporates portions of Galileo’s refined discussion of inclined planes from Le Meccaniche.
In his argument, Galileo requires that objects hanging from a balance form perfect right angles with against perfectly straight horizontal lever arms, thus making the strings that hang the objects parallel to each other; an assumption that Galileo recognizes as flawed since the Earth is understood to be spherical, that bodies are drawn to the center of the Earth, and therefore the strings would actually draw lines that converge to the center and not parallel.
In the defense of his assumption, Galileo states, “To such objectors I would answer that I cover myself with the protecting wings of the superhuman Archimedes, whose name I never mention without a feeling of awe.
Galileo raises several objections to this explanation (most of which were recognized much before Galileo): the successive parts of air that push the projectile would always be accelerated, which is contrary to Aristotle’s assumptions; experience shows that arrows fly despite a strong opposing headwind; a ship propelled by oars against a current continues to move forward long after the oars are retracted from the water; iron balls can be flung at a great distance, and yet flaxen fibers fall to the ground sooner than the iron ball; lastly, a marble sphere can spin for a long time without displacing, thus leaving no space for air to push against it, nor is a flame placed underneath the sphere disturbed by any air currents.
Instead, Galileo argues that projectile motion results from an impressed force that gives the projectile a self-depleting impetus for its motion (as a side note, according to Drabkin, medieval philosophy historian E. A. Moody "sharply differentiates the development of Galileo’s theory of impressed force from Jean Buridan’s impetus theory"[15]).
Galileo analogizes this impressed force to a temperature of a body, such that when a mover acts upon the body, it is much like placing iron in a fire, and once the projectile has left the hand of the mover, the impressed force diminishes much like how iron, once pulled from the fire, loses its heat and returns to its natural coldness.
He then compares the impressed force transferred from a mover to the mobile much like what is transferred from a hammer to a bell: initially both silent, the hammer impacts and imparts a sonorous quality to the bell which is contrary to its natural silence, and over time the sound gradually diminishes, much like an impressed force applied to a projectile.
Galileo then discusses how certain opinions, however false they may be, remain persistent because, at first sight, they offer some appearance of truth, but no one bothers to examine whether they are worthy of belief.
Aristotle and his followers believed that two contrary motions could not be continuous with each other, and therefore when a stone is thrown upward and falls back down, it must necessarily remain at rest at the apex for an interval of time.
Furthermore, the approach of such terminal velocity would be asymptotic, such as the hyperbola as discussed in the Conics of Apollonius of Perga, or the first conchoid curve of Nicomedes in the commentary of Eutocius of Ascalon regarding Archimedes’ On the Sphere and Cylinder, book 2.
Averroes and his followers had proposed a solution to this question that supposed that elements were heavy in their own region, a proposition that Galileo rejected in Chapter 11.
However, he admits that there remains some difficulty with his proposed theory: even though heavier bodies begin with a greater amount of impressed force, they also have more weight that can overcome it, which suggests that the heavy and the light should fall with equal speeds.