# Questions tagged [euclidean-geometry]

For questions about the mathematical study of shapes and space based on the works of Euclid.

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### Books using the axiomatic method

Apart from works on geometry (such as Euclid's Elements and its various translations) and Spinoza's Ethics, has the axiomatic method been used as a means of exploring a certain field or exposing one's ...
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### Ancient Greek Definition of Area

I am looking for a source that would explain what the ancient Greeks thought the “area” of a polygon was, in a philosophical sense. It’s very easy to find sources about the history of their formulas ...
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### What is Laguerre's definition of the angle via the cross ratio?

I recently read an article which said Cayley showed that affine geometry could be developed from projective geometry after he learnt of Laguerre's definition of the angle using the cross ratio. This ...
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### Who was Burlet, the one from Burlet's theorem?

The Burlet's theorem is a result in Euclidean geometry, which can be formulated as follows: Theorem. Consider triangle $ABC$ with $\angle{C}=\gamma$. Let $P$ be the point where the incircle touches ...
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### DeMorgan's commentary on Euclid's Elements

Augustus DeMorgan wrote comments on Euclid's Elements, which capture many of the most important points. Heath quotes them extensively. I cannot find any source for the original: Where can I see ...
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### History of right hand rule

I am curious to know when the right-hand-rule for vector product was established and used consistently in mathematics. I read here Who gave right hand thumb rule for circular loop of current ...
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### What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

In this quotation from Henri Poincaré's essay "Non-Euclidean Geometry" published in Nature in 1892 (No. 1165, Vol 45, p. 406), he refers to a theorem of Sophus Lie. Does anyone know a source for this ...
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### What's the relationship between Aristotle's theory of elements and motion and geometry?

I'm having a hard time gathering my thoughts about this. I'm trying to find a connection or some sort of relation between the first 3 axioms (postulates) of Euclidean geometry (though around Aristotle'...
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### Euclid’s Proposition I.3 overused?

[ Question copied from https://math.stackexchange.com/questions/2541170/euclid-s-proposition-i-3-overused ] Although the references to postulates, axioms, and previous propositions are not part of ...
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### What geometric results were first proven by assuming all real numbers are rational?

Pythagoras and his followers believed that all magnitudes are commensurable; that is, the ratio of two magnitudes of the same kind, like two lengths or two areas, is equal to the ratio of natural ...
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### What are historical applications of geometry to measuring distances beyond human reach?

I am searching for books and articles about applications of Geometry, in particular to the problem of computing distances and lengths which are apparently beyond human reach. As an example, consider ...
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### What was the old system of using right circular cones to solve problems about circles in the plane?

[I asked this originally at the Math Stack Exchange, and they suggested I also ask about it here.] I heard about this from a college professor but haven't ever been able to find any other mention of ...
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### Does any extant Greek text prove that the area of an inscribed regular polygon increases with the number of sides?

Does any extant Greek text prove that the area of a regular polygon inscribed in a fixed circle increases with the number of sides in the polygon? I can't find such a proposition in Euclid, but the ...
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