Questions tagged [euclid]
Euclid of Alexandria was a Greek mathematician and the "father of geometry".
18 questions
1 vote
2 answers
260 views
Why was the Bourbaki group opposed to Euclid and his triangles, as reflected in Jean Dieudonné's rallying cry: "À bas Euclide" (Down with Euclid)?
Why was the Bourbaki group opposed to Euclid and his triangles? As reflected in Jean Dieudonné's rallying cry: À bas Euclide (à bas Euclide)
12 votes
3 answers
1k views
What is the "family tree" of translations of Euclid's Elements?
I once saw a beautiful "family tree" of copies or translations of Euclid's Elements, starting with Greek versions, going on to Arabic translations made in Baghdad and elsewhere, and then ...
- 651
1 vote
0 answers
101 views
Criticisms of the Dedekind's definition of infinite sets for violating Euclid's Common Notion 5
Dedekind's definition of the infinite set says in its essence that part may be equal to the whole contradicting Euclid's Common Notion 5 stating that "the whole is greater than the part." ...
- 503
14 votes
2 answers
1k views
What is the origin of "two straight lines cannot enclose a space" axiom in Euclid's Elements?
This post is prompted by a recent question on MSE asking about "Axiom 10" of Euclid's Elements, as found in editions by Byrne and Casey: "Two right lines cannot enclose a space". ...
- 253
1 vote
1 answer
231 views
Euclid's use of antenaresis and Heath's commentary
In Book 7, Prop. 1. Euclid uses repeated subtraction to prove that two numbers are relatively prime. As explained here the Greek word for repeated subtraction is "antenaresis". There isn't ...
- 503
2 votes
1 answer
392 views
The role of the Elements in the development of mathematics
The Elements are often regarded as the cornerstone of the axiomatic approach to mathematics. However, mathematical textbooks have served as the foundational pillars upon which writing style, language, ...
- 1,329
3 votes
0 answers
305 views
Who came up with the proof of "Bézout's identity" that uses the well-ordering principle?
Let $a$ and $b$ be two integers not both of which are equal to zero. It is an important and well-known fact that $\text{gcd}(a,b)=ax_{0}+by_{0}$ for some integers $x_{0}$ and $y_{0}$. Even though this ...
- 2,034
4 votes
1 answer
384 views
Who first proved necessity of Euclid's formula for pythagorean triples?
The following well-known formula for pythagorean triples is commonly called Euclid's formula: If $a, b, c$ are three natural numbers with $a,c$ odd, $b$ even, $\gcd(a,b,c)=1$ and $a^2+b^2=c^2$, then ...
- 123
10 votes
1 answer
371 views
History of greater-than symbol used in reverse?
I was surprised to find that Oliver Byrne's 1847 marvelous The Elements of Euclid (color version)1 uses $\sqsubset$ to mean "greater than" and $\sqsupset$ to mean "less than," in ...
- 1,467
0 votes
0 answers
46 views
Historicity of Euclid. Looking for the references of Euclid in ancient texts that has survived [duplicate]
The general consensus is that Euclid was a real historical figure. Wikipedia https://en.wikipedia.org/wiki/Euclid concludes on the hypothesis that Euclid was not a real person, "This hypothesis ...
- 1
1 vote
2 answers
1k views
What happened to the original sources of Euclid's Elements?
I am aware of the fact that Euclid's Elements is a compilation of the works of previous Greek mathematicians like Thales, Pythagoras (his school), Eudoxus, Theaetetus, etc. However, I want to know the ...
user14943
17 votes
2 answers
4k views
Did ancient Greek mathematicians consider numbers independently of geometry?
I am currently reading Oliver Bryne's edition of Euclid's Elements, and in The Elements many arithmetic propositions are proved geometrically, and it feels to me that numbers are always treated as ...
- 273
1 vote
1 answer
194 views
Euler's proof of infinite primes first since Euclid?
Q. Is it true that Euler's proof of infinite primes was the first since Euclid's which was from around 300BC? Note: By Euler's proof, I mean the use of his Euler product formula for the zeta function ...
- 425
4 votes
1 answer
497 views
Are Euclid's theorems and proofs due to Euclid?
Some appear to argue that much of the Elements by Euclid is a compilation of knowledge handed down to Euclid from his predecessors. On the other hand, some credit the proof, of the Pythagorean theorem ...
- 205
6 votes
1 answer
507 views
Has Euclid stated Cauchy's theorem?
Cauchy's Rigidity theorem says that if the corresponding faces of two convex polytopes are isometric (congruent) then the polytopes are related by a (proper or improper) motion. Cauchy's biography (...
- 55.8k