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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| De motu antiquiora | 7/12 | https://en.wikipedia.org/wiki/De_motu_antiquiora | reference | science, encyclopedia | 2026-05-05T08:51:23.985272+00:00 | kb-cron |
=== Chapter 9: In view of all the above, bodies moving naturally are reduced to the weights of a balance === Galileo investigates the force responsible for the motions explained in Chapter 8, specifically, the amount of force necessary to hold wood underwater, to which he concludes that wood moves upward with a force measured by the amount by which the weight of a volume of water equals to the wood exceeds the weight of the wood. Similarly, he investigates the force of a lead sphere as it moves downward in water, and he concludes that the sphere moves downward with a force equal to the weight by which it exceeds the weight of an aqueous sphere of the same size. He then revisits the conclusion of the previous chapter: in the case of bodies of different material, provided that they are equal in size, the ratio of the speeds of their natural downward motions is the same as the ratio of their weights–and not their weights as such, but the weights found by weighing them in the medium in which the motion takes place. From this, Galileo recognizes that, when objects occupy a medium and we weigh the object on a balance, we don’t have the proper weight of the object since buoyancy in the medium will always modify it. He proposes that, if the objects could be weighed in a void, then hypothetically the proper weight could be found; however, Aristotle claims that motion in a void is impossible and that all things would be equally heavy in the void – a notion that Galileo rejects in the following chapter.
=== Chapter 10: Proof that, if there were a void, motion in it would not take place instantaneously === Aristotle cited several arguments in his attempt to deny the existence of a void. In one argument, he assumes that motion cannot take place instantaneously, and then attempts to show that if a void existed, motion in it would take place instantaneously; and, since that is impossible, he concludes that a void is also impossible. He further deduces that, assuming that motion can occur over time in a void, then the same body will move in the same time in a plenum and in a void, which he claims is impossible. Galileo argues that Aristotle failed to prove his assumptions, that they were actually false and led to false conclusions. In particular, Galileo asserts that Aristotle assumes that the ratio of the speeds of the same body moving in different media is equal to the ratio of the rareness of the media, which Galileo proved to be false in Chapter 8. Aristotle’s proof also states that it is impossible for one number to have the same relation to another number as a number has to zero. Galileo argues that this is true for geometric ratios (i.e., the ratio of a/b), but is not true for arithmetic relations (i.e., a - b). Moreover, if the ratio of the speeds were made to depend on the ratio in the arithmetic sense (i.e., a ratio of differences), then no absurd conclusion would follow, and therefore the body will be able to move in a void in the same way as in a plenum. In a plenum, the speed of motion of a body depends on the difference between its weight and the weight of the medium through which it moves; and likewise, in a void, the speed of its motion will depend on the difference between its own weight and that of the medium, but since the void is zero, then the difference between the weight of the body and the weight of the void will be the whole and proper weight of the body. Therefore, the speed of its motion in the void will depend on its proper weight, which is undiminished by any weight of the medium. Galileo then rejects Aristotle’s claim motion in a void would be instantaneous since a void is infinitely lighter than any plenum and that motion in it will be infinitely swifter than any plenum. Galileo accepts the premise of Aristotle’s argument, but rejects the conclusion of instantaneous motion. Rather, he argues that the motion takes place in less time than the time of motion in any plenum.
=== Chapter 11: Disproving Aristotle’s claim that air has weight in its own place === Aristotle claimed that, with the exception of fire, everything, even air itself, has weight in its own region; for an inflated bladder weighs more than a deflated one. Galileo disagrees: it’s understood that water has weight when in air, and that it moves downward because of its weight, but it’s absurd to believe that water sinks in water, as a first amount of water would need to displace upward a second amount of water. Moreover, if a portion of water is heavy and must move downward in water, then that would imply that the portion is heavier than another portion of water of equal volume – but this would be absurd since this would make water heavier than water. In response to the inflated bladder, if a hole of the inflated bladder is opened but air stays in the ball without force (i.e., without compressed air), the bladder retains the same weight. But when the air is compressed into the bladder by force, the air in the bladder becomes heavier than free and diffused air. Galileo also argues that the elements, when in their proper place, are neither heavy nor light, for we do not feel the weight of water when we swim, and that it was previously shown that bodies lighter than water rise up, bodies heavier than water sink down, and bodies the same weight as water go neither up nor down.