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).


6

Contrary to what the name suggests, Fourier series were not invented/discovered by Fourier. They were considered by Euler and Bernoullis, in relation to the one dimensional wave equation, not the heat equation. This early story is described for example in the papers by Luzin in Amer. Math. Monthly: Luzin, N. Function. I. Amer. Math. Monthly 105 (1998), no. ...


6

§1.1 (+ supplement) of Bressoud’s A radical approach to real analysis, recommended here just recently, does pretty much exactly what you want.


4

The book Introduction to the Theory of Fourier's Series and Integrals by H. S. Carslaw answers your questions in the first chapter on the History of this subject. Many commonly held false beliefs are debunked in his first chapter, including the idea that Fourier failed to give a rigorous proof of convergence. Another common false belief is that Fourier ...


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

You can download the journal here: https://www.biodiversitylibrary.org/bibliography/5919#/summary There are also Collected works of Schwarz: https://archive.org/details/gesammeltemathem02schwuoft


2

The problem with very old historical stuff including the origins of a certain concepts and giving due credit where it is due is one of the most difficult questions in history. The truth is that we may never know the correct picture behind the question who invented the modern number system? No matter what Wikipedia says. Anyone who is serious scholar of ...


2

Here are plots using Jahrbuch for 1870–1940 and Zentralblatt after that. A glance at their detailed output suggests some unreliability (e.g. Zentralblatt counts a paper twice when both reviewed it), but hopefully not too much overall. Papers and books in other languages (Danish, Dutch, Hungarian, Japanese, Latin, Norwegian, Polish, Portuguese, Spanish, ...


2

The first 3 digits can be easily explained by the rapid tracing of strokes without lifting the writing stylus from the surface of the paper. If you look at the Chinese characters for 1, 2 and 3: 一, 二, 三, you see these represent obvious numbers of strokes. If you write 二 quickly without lifting the pen, this becomes Z, and from there 2. The same goes for 三 to ...


1

You can see the origin of modern numerals and zero from Sanskrit, carved in granite, also at https://youtu.be/pElvQdcaGXE?t=101 in a Temple for zero in a talk by Marcus du Sautoy who looks at the contribution of Ancient Indians like Aryabhata, Brahmagupta, Bhaskara, Madhava, etc Programme: BBC - The Story of Maths Presenter: Marcus du Sautoy


1

MR0106313 Krasovskiĭ, N. N. {\cyr Nekotorye zadachi teorii ustoĭchivosti dvizheniya.} (Russian) [Certain problems in the theory of stability of motion] Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow 1959 211 pp. MR0052616 Barbašin, E. A.; Krasovskiĭ, N. N. On stability of motion in the large. (Russian) Doklady Akad. Nauk SSSR (N.S.) 86, (1952). 453-456.


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