Euclid axiom in a sentence
1) Leibniz's improvement of Euclid's axiom contains the same concept.
2) Euclid's fifth axiom 6 of geometry is illustrated in the diagram below.
axiom collocations
3) In Euclid's original approach, the Pythagorean theorem follows from Euclid's axioms.
4) To Euclid axioms were unshakeable truths (e.g. every two distinct points uniquely determine a line).
Euclid axiom example sentences
5) The independence of the parallel postulate from Euclid's other axioms was finally demonstrated by Eugenio Beltrami in 1868.6) It was shown that Euclid's axioms for geometry, which had been taught for centuries as an example of the axiomatic method, were incomplete.
7) In the mid-19th century, flaws in Euclid's axioms for geometry became known (Katz 1998, p. 774).
8) In "Euclidis Prota"..., which is an attempt to tighten Euclid's axioms, he states...: 'I have diverse definitions for the straight line.
9) Some other complete sets of axioms had been given a few years earlier, but did not match Hilbert's in economy, elegance, and similarity to Euclid's axioms.
10) Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense.
11) This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory.
12) In particular, the monumental work of Isaac Newton is essentially based on Euclid's axioms, augmented by a postulate on the non-relation of spacetime and the physics taking place in it at any moment.
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