73

The other answer is correct. In addition, there is significant evidence that Fermat did not have a proof of the theorem now known as Fermat's Last Theorem. First, we should note that Fermat was not a professional mathematician, only an amateur. He never published any mathematics himself. With just that, it would not seem strange that he did not publish his ...


33

Yes, it is true. Fermat's own copy was used in the publication of Diophantus by Fermat's son Samuel, and he included Fermat's notes. The original with Fermat's handwriting is lost. https://www.joh.cam.ac.uk/library/special_collections/early_books/fermat.htm#:~:text=When%20reviewing%20his%20copy%20of,to%20fit%20in%20the%20margin. (The page with his most ...


29

There is no way that Fermat could have had anything approaching the now commonly-accepted proof. Almost none of the concepts in that proof were known in any form in Fermat's time. Further, Fermat is known for publishing very few of his proofs; almost none survive today, and even in the 1800s there was significant doubt in the mathematical community that he ...


14

You can read Kepler's Harmonia Mundi (there is an abbreviated English translation, but it includes that part.) Kepler was looking for all kinds of numerical relations for many years (most of his life). Most of the relations he found in Harmonia Mundi are accidental and are of no value for modern science. I agree with your friend, that given 6 pairs of ...


12

Today, sky coordinates are measured as "Right Ascension" (RA) and declination. These are similar to the angular coordinates we use for the Earth's surface but are measured on the celestial sphere relative to the celestial equator and pole. By using the current sidereal time, it is possible to map the local sky coordinates (ie. a horizontal bearing relative ...


11

The interaction of physics and artillery begins with Galileo (there was no physics to talk about before that time except the statics). There are pictures in the books before Galileo which show completely unrealistic trajectories of projectiles. Galileo developed a computational device which he called the Geometric and Military Compass, which he produced and ...


11

I agree that it is amazing and a credit to Kepler's insight into numerical patterns, which is reminiscent of Euler's. It took Kepler extra 12 years to discover the third law after discovering the first two, perhaps exactly because of the comparative scarcity of data points. According to Kepler, after years of searching for additional patterns on March 8 of ...


10

At the time of Brahe and Kepler they did not use the right ascention and declination to record the movement of planets. These coordinates are related to the Earth, and it is known since the times of Hipparchus and Ptolemy that one has to use the ecliptic coordinates, that is a system related to the Sun motion. (Ecliptic is the large circle in the sky on ...


10

Looking at a brief history of communication and your post it seems that there were disputes because who originally published the discovery was easily disputable. The fact that there was a steady decline in such disputes was due to improving communication technology AND standard publishing practices. As to the point of using an anagram while publishing. ...


6

I think that the authoritative Introduction by Edward Rosen to his translation with commentary of : Johannes Kepler, Kepler's Somnium The Dream, or Posthumous Work on Lunar Astronomy (1967 - Dover reprint) can give us the necessary informations. It seems quite clear that the booklet was not intended to be a sci-fi novel at all. The origin is in the draft ...


6

If you can read Italian, here you can find full biographic details of his life. What follows is a short summary. As was customary in Italy (and not only in Italy) until at least the 18th century, his name was written in many different ways, like Urbano (Giovan Francesco) Davisi, or D'Aviso, Avvisi, De Aviso, De Avisus and in the Latinized form Avisius, and ...


6

Wells misspelled him a little. Urbano d'Aviso (1618-1685) was a little known student of Cavalieri. Aside from the pentagon folding and disputed authorship of Trattato della Sfera, originally published in 1656 under a pseudonym, he is sometimes mentioned as a Catholic cleric who suggested that water vapor consisted of miniscule bubbles of water filled with ...


5

Kepler never supported Brahe's system in print. In his first book (1596) he proposes his own version of heliocentric system. Collaboration with Brahe is 1600-1612. During this period he wrote Astronomia Nova (1609) based on heliocentric system. And all his later books are based on heliocentric system as well.


5

I don't know, but Images of earth from outside had been made for more than 500 years. A globe of the Earth would seem to count as a "depiction of any kind". The sphericity of the Earth was established by Greek astronomy in the 3rd century BC, and the earliest terrestrial globe appeared from that period. The earliest known example is the one ...


4

Kepler's third law was discovered on the basis of comparison of periods and distances of the planets. This was in 1619. Only in 1621 Kepler noticed that Galileo moons of Jupiter also satisfy this law. This fact was later used by Galileo as an argument in favor of Copernican system. By the way, Kepler was one of the first astronomers who used logarithms. (...


4

The Wikipedia article on Harmonices Mundi states that Kepler gave only the conclusion. Since he had taken all of Brahe's observations, the presumption is that he used this data, for he was very familiar with it, and it was more than adequate for the task. His published result describes the relationship in terms of the sun and planets, but not planets and ...


4

From the evidence that we have, it is most likely that Fermat never even claimed to have a proof of the FLT, see the extensive discussion at Mathoverflow here. Quoting from the accepted answer: Not only do we not know the date, we don't even know whether he wrote the remark at all. For all we know it might have been invented by his son Samuel, who published ...


4

Maybe some of Newton's prisms were preserved. An article by A.A. Mills (1981) shows images. He writes: Newton appears to have purchased all his prisms: there is no intimation that he made any of them, although he was obviously skilled at grinding lenses and mirrors. This availability of ready-made glass prisms is rather puzzling, for the period in question ...


3

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 ...


3

At the time of Kepler distances were not measured or observed directly. Or if measured, the results were completely wrong. All his laws are stated in terms of RATIOS of distances, and these ratios can be in principle measured from the geometry of the situation. When you describe everything as seen from the Earth (as the ancients did), distances are ...


2

Kepler's 3rd law could have been deduced based on the orbital parameters mentioned in Ptolemy's Almagest (of the 2nd century CE). It was not important for this that Kepler had more modern observations of higher accuracy available to him, nor that he had discovered that the orbits were ellipses instead of circles. The following chart shows the orbital sizes ...


2

The question of Kepler's possible influence on Fermat is a subject of scholarly controversy, exhaustively analyzed by Cifoletti in her book on Fermat. For details see this 2018 publication in Foundations of Science.


2

The short answer is yes. Under the following conditions: Let me state the problem more exactly: suppose that a solar eclipse of at least 40% WILL occur within a year from now. Could some person in the second half of 17th century make this prediction with 100% probability? a) prediction for short period (few months, perhaps up to a year). b) possession of a ...


1

Galileo did not publish any opinion on Kepler's work, though they corresponded with Kepler. Why this is so, subject to speculation. See, for example Koestler, Sleepwalkers (this author is unfriendly to Galileo). One possible reason was that Galileo simply did not appreciate enough Kepler's contributions, which was mostly mathematical, and very different in ...


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