25
votes
Accepted
Did ancient Greek mathematicians consider numbers independently of geometry?
The answer is yes. There was a split. First of all, for the Greek mathematics (and very long after them)
"numbers" were integers. "Rational numbers" were called fractions, and no ...
- 46.4k
8
votes
Is there any historical "evidence" maintaining that Euclid is a single person?
There's little question that some parts of "The Elements" were added by later authors. Heath's English translation gives a lengthy commentary on what is likely in the original work and what is known ...
- 544
8
votes
Has Euclid stated Cauchy's theorem?
I found it. It is Definition 10 in Book XI.
https://mathcs.clarku.edu/~djoyce/elements/bookXI/defXI9.html
Euclid takes the assumption of Cauchy's theorem as the definition of equality of
polytopes! ...
- 46.4k
6
votes
Accepted
Greater-than symbol in Byrne's *The Elements of Euclid*
Byrne's symbols are variations of Oughtred's, contamporaneous with Harriot's, see Cajori, History Of Mathematical Notations, vol. I, p.192. They were adopted by Barrow, Newton's teacher, in his ...
- 70.9k
6
votes
What happened to the original sources of Euclid's Elements?
Multiple copies of the works of Euclid's predecessors probably existed. Including similar compilations called Elements. On the opinion of people who did mathematics at the time and after Euclid, his ...
- 46.4k
6
votes
Accepted
Euler's proof of infinite primes first since Euclid?
There is a proof by Goldbach, which appears in a letter he wrote to Euler in 1730 (a few years before Euler published his product formula for the zeta function). It is as follows: if $F_n=2^{2^n}+1$ (...
- 5,678
6
votes
Accepted
Are Euclid's theorems and proofs due to Euclid?
We do not know for sure, but most of them probably not, the proof of the Pythagorean theorem included. The current consensus on the priority of the results in Euclid's Elements is summarized by Lambek ...
- 70.9k
5
votes
Accepted
Is there any historical "evidence" maintaining that Euclid is a single person?
I too do not see any reason to doubt that the works of Euclid were written by one person, apart, naturally, from some interpolations. However, I must disagree with Konstantinos when he writes that “...
- 3,415
5
votes
Did ancient Greek mathematicians consider numbers independently of geometry?
If you consider Diophantus "ancient" then the answer is "no". In his "Arithmetic" numbers are not necessarily related to geometry or physics. For Pythagoras, indeed, ...
- 880
3
votes
Accepted
Who first proved necessity of Euclid's formula for pythagorean triples?
Nobody. This happens quite often, one author does something that does not measure up to modern specifications of "proving X", but, after a succession of such authors, the result is trivial ...
- 70.9k
3
votes
How did Aristotle influence Euclid?
As Simpson clearly states in the section "Aristotelian logic" of his article, principle 3 is the law of excluded middle: $P \vee \neg P$ is true. Euclid's Elements indeed rely on classical logic ...
- 3,759
3
votes
How did Aristotle influence Euclid?
You are right: syllogisms are not used by Euclid. More generally: “Although Aristotle emphasized the use of syllogisms as the building blocks of logical arguments, Greek mathematitians apparently ...
- 5,678
2
votes
How did Aristotle influence Euclid?
Heath, the famous translator of the Elements, concludes in his introduction to vol. 1 of his translation of the Elements, §"3. First Principles: Definitions, Postulates, and Axioms", that ...
- 5,211
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