"In general the Greeks looked upon an axiom as something which was so self-evident that no reasonable person would object... while a postulate was a request that something be allowed. Now Euclid's fifth postulate... whatever else this postulate may be, self-evident it is not, and this was early perceived. ... The first line of attack was, naturally, the attempt to prove this postulate by the aid of others, and the axioms. Such, presumably, was Ptolemy's idea. But even if we grant that all of Euclid's axioms are self-evident, it does not... follow that he puts in his list all of the assumptions that he really uses."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/Non-Euclidean_geometry
Revision History
No revisions have been submitted for this quote.
Categories
Non-Euclidean geometry
91 quotes on TrueQuotesView all quotes by Non-Euclidean geometry →
Related Quotes
"The creation of non-Euclidean geometry showed... that mathematics could no longer be regarded as a body of unquestion…"
"Edwin Abbott Abbott"
"In the field of non-Euclidean geometry, Riemann... began by calling attention to a distinction that seems obvious onc…"
"Unlike those of science, the conclusions of mathematics had always regarded as deduced from basic truths. ...the very…"
"What was the effect of non-Euclidean geometry on the future progress of mathematics? ...Mathematics passed from serfd…"
"Even the mathematicians of the late nineteenth century did not take non-Euclidean geometry seriously for physical app…"
"... went considerably beyond Sacherri in deducing propositions under the hypotheses of the acute and obtuse angles. T…"
"It is no wonder that no contradiction was found under the hypothesis of the acute angle, for... the geometry develope…"
"Non-Euclidean geometry was the most weighty intellectual creation of the nineteenth century, or, at worst, might have…"
"Euclid’s Elements"