"A... fallacy is contained in all proofs [of the Parallel Postulate] based upon the idea of direction. ... Another class of demonstrations is based upon considerations of infinite areas. [In] Bertrand's Proof... The fallacy... consists in applying the principle of superposition to infinite areas as if they were finite magnitudes."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Chapter 1. Historical, pp. 6-8.
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"