# Tag Info

17

Galileo followed a venerable tradition of distinguishing numbers, magnitudes of different kinds (lengths, times, areas, etc.) and ratios. This is somewhat analogous to the strictures of modern dimensional analysis used in physics, but even stricter, and ancient Greeks did not have dimensional constants to bridge the gaps. They did not even have enough ...

15

This morning [13 November 2014] I spent several hours going through many Cantor-related papers and books that I have, and I am now nearly convinced that Galileo probably had no influence on Cantor and Galileo had very little if any influence on other mathematicians. For instance, I believe there was no German translation of Galileo's "Two New Sciences&...

13

See Heytesbury and the Physical Sciences and Nicole Oresme for detailed information about the so-called Oxford Calculators and their contribution (mainly) to mathematics. The issue is not so clearly assessed by modern historiography: There has been some discussion of the meaning of the work of Heytesbury and the other Calculators for the development of the ...

11

By this standard why single out Galileo? Euclid "plagiarized" Elements, there isn't a single theorem in it that can be reliably attributed to him, and there are entire books that can be attributed to early Pythagoreans, Eudoxus or Theaetetus. In the whole 13 books he does not credit a single person by name. Descartes "plagiarized" analytic geometry, after ...

9

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 ...

9

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.

7

Kinematics was distinguished from dynamics by the Merton school (a.k.a. Oxford calculators) of scholastics in 14th century, who worked out kinematics of uniformly accelerated motion. In particular, they formulated the mean speed theorem (a.k.a. Merton rule) (distance traveled is half the sum of the initial and final velocities, times the elapsed time), which ...

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

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 ...

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).

4

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.,209] So are ...

4

You have correctly pointed at Wiki's quotation from Galileo's Dialogo sopra i due massimi sistemi del mondo (The Dialogue Concerning the Two Chief World Systems, 1632) where the thought experiments regarding the "composition of motions" in what we today call "inretial frames" (e.g. the fall of a ball from the mast of a sailing ship) are discussed at lenght (...

3

In this passage Galileo is explaining how a bundle of multiple short fibers twisted into a rope functions. He is analogizing a fiber in the bundle to a fiber held between fingers, and notes that it would sooner break then slip out because the friction is large when the fingers are pressed together hard. Same with the rope, its fibers would sooner break than ...

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 ...

2

Yes, Galileo knowed Kepler's, as well as Tycho's, works. There is an extant copy of Tycho's Progymnasmata with Galileo's annotations, and we have an annotation from Galileo on Kepler's De stella nova: the main interest showed by Galileo's annotations regards novae and comets. Kepler published two booklets in defence of Galileo, after the pubblication in 1610 ...

2

Historian Pietro Redondi wrote a fascinating account of Galileo's tumultuous career in a book entitled Galileo Heretic. There is certainly more detail here than you will need for your lecture but on the other hand it does not contain any technical material in physics except for some very elementary arguments. You can use some of the anecdotes to spice up ...

2

I am not sure how much detail you are looking for. MacTutor has decent short biographies of both Galileo and Newton by O'Connor and Robertson. Einstein wrote a eulogy of Newton in 1927, which also mentions Galileo, but focuses on science rather than personal life. If you want something more detailed and personal there is recent Newton by Iliffe, who is the ...

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 ...

2

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 ...

2

As $BI$ is mean proportional to $BD$ and $BE$. \begin{array}{l} \Rightarrow \frac{B D}{B I}=\frac{B I}{B E} \\ \Rightarrow \frac{B D}{B I} \times B D=\frac{B I}{B E} \times B D \\ \Rightarrow \frac{B D^{2}}{B I}=\frac{B I \times B D}{B E} \\ \Rightarrow \frac{B D^{2}}{B I^{2}}=\frac{B D}{B E} \end{array} $Q.E.D$

1

You don't need calculus to show the relationship that you are pointing out. One only needs to plot distance wrt time. Of course one needs instruments that can accurately measure time which is perhaps where Galileo was helped by his discovery that the pendulum can act as an excellent clock. Calculus is required to demonstrate that relationship follows from ...

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

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

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

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