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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| De motu antiquiora | 9/12 | https://en.wikipedia.org/wiki/De_motu_antiquiora | reference | science, encyclopedia | 2026-05-05T08:51:23.985272+00:00 | kb-cron |
=== Chapter 15: An argument that rectilinear and circular motions have a ratio to each other === Aristotle asserts that circular motion does not have any ratio to rectilinear motion because a straight line is not in any ratio to or comparable to a curve. Galileo rejects this stating that this would be like saying a triangle and a square are not comparable because the triangle has only three angles while the square has four. Even a circle inscribed in a square has some ratio even though the circle has curved edges while the square has straight edges. He further argues that Aristotle failed to see that the lines have a quantitative relation even if they are qualitatively different. Galileo further claims that Aristotle was reckless in asserting that there is no straight line equal to the circumference of a circle–Archimedes was able to prove this in his work On Spirals, where a straight line is found equal to the circumference of the circle around the spiral of first revolution.
=== Chapter 16: The question of whether circular motion is natural or forced === Galileo offers the question: if the center of a rotating marble sphere (and its center of gravity) were located at the center of the universe, would its rotational motion be forced or not? Galileo argues that since natural motion occurs when bodies move towards their natural place, and forced motion occurs when they recede from their natural place, then it's clear that the sphere rotating about the center of the universe moves with a motion that is neither natural nor forced. This leads him to argue that, if a single star were added to the heaves, the motion of the heavens would not be slowed since the star would only slow the rotational motion when it is moved away from its natural place, but this never happens for rotations about the center of the universe since there is no upward or downward motion. Galileo then recognizes that this view raises another question: since the rotating sphere placed at the center of the universe is neither a natural motion nor a forced motion, would the sphere continue to rotate perpetually or eventually come to rest? For if its motion were natural, then it would seem to move perpetually; but if its motion is forced, then it seems that it would eventually come to rest. Galileo never directly addresses this question, and instead states that the question is better suited for Chapter 17 (where it is also left unanswered). However, Galileo does consider the case of a homogeneous spinning sphere that is outside the center of the universe, concluding that such motion is forced since there is resistance at the axis that supports the sphere. He further argues that if the axis were infinitely small, then no resistance would arise at the axis, and that a rough surface of the sphere would cause air to impede the rotational motion. For a heterogeneous sphere (i.e., where its center of gravity is different from the geometric center), the rotational motion alternates between natural and forced motion since the center of gravity would be rotating about the geometric center.