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8

The answer depends on what "this" means. According to Mancosu's Measuring the Size of Infinite Collections of Natural Numbers (reprinted in his book Abstraction and Infinity): It is actually unclear when the paradox, in the numerical form I just gave, appears. In the Greek tradition we have paradoxes that are related, but are not identical, to it; in this ...


8

Yes, indeed when trying to obtain the law of falling bodies, Galileo's first conjecture was that the speed is proportional to the distance traveled. After some contemplation, Galileo understood that this cannot be the case and eventually came with the correct law. Good source on Galileo: S. Drake, Galileo at work. (There are many editions).


7

There can be no doubt that he has seen them, for the simple reason that he determined their periods and configuration correctly, and published them. Therefore the other things (magnification of his telescope, light pollution etc.) are irrelevant for the answer. You can easily see them yourself using an 8x binocular.


5

The assumption that people believed Aristotle’s law for so long is highly questionable. Aristotle’s law occurs in a philosophical context. He introduces it in order to argue that there can be no such thing as an object of infinite weight. It was not intended as a starting point for quantitative science, nor did many readers take it as such. Insofar as ...


4

Yes, Galileo made that error (and so did Descartes). Only later did he realise that the speed is proportional to the time ellapsed, not to the distance already covered. I suggest that you read The new science of motion: A study of Galileo's De motu locali, by Winifred L. Wisan (Archive for History of Exact Sciences, June 1974, 13, Issue 2–3, pp 103–306).


3

Dialogo sopra i due massimi sistemi del mondo (1632), Day two: SAGR. Tali [facili da intendersi] sono tutte le cose vere, doppo che son trovete; ma il punto sta nel saperle trovare. [Stilmann Drake transl., p.225] So [easy to understand] are all truths, once they are discovered; the point is in being able to discover them. [ Th.Salusbury transl.,...


3

This will answer two out of three parts of the question: (a) 'Why didn't the church go after Isaac Newton?' It was not at all the whole church that was involved in the Galileo affair: it was the establishment of the Roman Catholic church of the time. In much of (mostly northern) Europe, the Roman Catholic church had no authority at all: the reformed ...


3

Not quite. This is what Galileo stated in the Two New Sciences (1638) through his character Sagredo (honest inquirer open to arguments from both sides): "But I, Simplicio, who have made the test can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing ...


2

Galileo's most famous invention was the telescope. Galileo made his first telescope in 1609, modeled after telescopes produced in other parts of Europe that could magnify objects three times and its aperture was 1.5 cm. He made/assembled two telescopes later in 1612/1620 that could finally magnify objects twenty times. With this telescope, he was able ...


1

Why do we need to prove such a thing since the statement of the theorem is the direct consequence of this relation speed = distance/time? This is exactly what he tries to prove here. The difference between you and Galileo is that you were taught some concepts in your childhood, which Galileo was not. For example, the concept of a (real) number. The ancients ...


1

Given that it's reasonably easy to see the 4 major moons with a 6 to 8- power binoculars, (you can find hundreds of discussions of planet-gazing with binocs online) it is quite reasonable to suppose that a patient, skilled observer with a 3 or 4 X telescope could have observed these moons. Keep in mind that Lipperperhey, or users of his 'scope, would have ...


1

This question discusses the common assumption that the only issue of the Galileo trial was heliocentrism. Briefly, some scholars have argued that an additional issue was atomism and its difficult relation with doctrinal issues. Even as far as heliocentrism is concerned, the opposition was not to using it as a technical hypothesis in scientific calculation ...


1

"The church", as you call it, had nothing to say in Protestant England.


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