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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| De motu antiquiora | 8/12 | https://en.wikipedia.org/wiki/De_motu_antiquiora | reference | science, encyclopedia | 2026-05-05T08:51:23.985272+00:00 | kb-cron |
=== Chapter 12: Disproving Aristotle’s claim that absolutely light and absolutely heavy exist; and even if they did, it would not be earth and fire === Aristotle defined that the “absolutely heaviest” are things that lay below everything else and always move towards the center of the universe, and he calls the “absolutely lightest” things that rise above everything else and always move up and never down. Thus, the heaviest is earth, and the lightest is fire. For if fire had heaviness, it would remain below something, which is not observed. Galileo rebuts that Aristotle’s argument is not conclusive, for it is sufficient for fire to be less heavy than everything else, and is not necessarily without weight. Aristotle argues that, if fire had weight, then a large amount of fire would be heavier than a small amount, thus the large amount would rise slower. Similarly, if earth had lightness, then a large amount of earth would fall slower than a small amount. But experience shows the opposite. Galileo rebuts that this is also an invalid argument, for weight of a body is modified by the medium it is in. In other words, fire does not have weight in air. Secondly, a larger amount of fire does rise faster than a small amount–this was shown in Chapter 8. Galileo proposes that the correct way to reason about fire is that a large amount of fire will be heavier than a small amount of air, but not in the medium of air where fire has no weight, but in some other medium lighter than fire or even in a void. Also, if we assume that fire has no weight, then it is without density, but that which is without density is a void. Therefore, fire is a void, which is absurd. Galileo then questions the claim that earth is the heaviest when we are unable to see below the earth. Moreover, it’s known that quicksilver (i.e., mercury) causes earth to float above it, so clearly there are things that are heavier than earth.
=== Chapter 13: Proof that differences in weights and motions are determined only in a void === Since in every medium the weights of heavy bodies are diminished by the weight of a portion of that medium equal in size to the solid, it is clear that whole and undiminished weights of solids are obtained in a medium whose weight is zero. Such medium can only be the void. Similar considerations hold for the speeds of motions and the ratio of these speeds.
=== Chapter 14: A discussion regarding the ratio of the speeds of bodies moving along various inclined planes === Galileo investigates the speeds of bodies moving down inclined planes; however, portions of his arguments are unrefined and contain errors. Galileo would later revisit this discussion (with corrections) in his lecture notes, Le Mecaniche, which utilizes his new abstract concept, momento, to roughly describe both modern concepts of moment and angular momentum. 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 Mecaniche. In this present discussion, Galileo recognizes from Chapter 9 that heavy bodies tend to move downward with as much force as is necessary to lift it up, thus if we can find how much force is needed to draw a body upwards on an incline, we would then know how much force the body would descends on the incline. To measure this force, Galileo reverts to the lever, but instead of lever arms that are parallel to each other, one lever arm is bent at an angle such that the force exerted at the bent lever arm is weakened. A weight positioned at the extremity of the bent lever arm would then experience the same force as if the same weight were on an incline that is tangent to the rotation of the bent lever arm. From there, a ratio of the force of the incline to a force that drives the weight vertically downward can be formed, which is then used to find the ratio of speeds (albeit erroneously). 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 other words, Galileo argues that his assumption relies on a small-angle approximation. 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. For he made this same assumption in his Quadrature of the Parabola…yet we must not suppose, in a moment of doubt, that his conclusion is false, since he had earlier demonstrated the same conclusion by another geometric proof.”