Mathematics and Logic in History and in Contemporary Thought |
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Page 28
... magnitudes , and therefore even less of incommensurable magnitudes . Perhaps just because of this , Plato found the discovery of incommensurable magnitudes very important . In his Theaetetus he writes at length about irrationals ...
... magnitudes , and therefore even less of incommensurable magnitudes . Perhaps just because of this , Plato found the discovery of incommensurable magnitudes very important . In his Theaetetus he writes at length about irrationals ...
Page 98
Ettore Carruccio. the postulate of Archimedes is not valid for this kind of magnitude : given two different magnitudes , there exists a multiple of the lesser which exceeds the greater , and therefore , having admitted the divisibility ...
Ettore Carruccio. the postulate of Archimedes is not valid for this kind of magnitude : given two different magnitudes , there exists a multiple of the lesser which exceeds the greater , and therefore , having admitted the divisibility ...
Page 101
... magnitudes in a similar manner ( which seems simpler and more natural ) . We must remember in the first place that the Greeks generally thought they could reason about a magnitude only when they knew how to construct it . Now it was not ...
... magnitudes in a similar manner ( which seems simpler and more natural ) . We must remember in the first place that the Greeks generally thought they could reason about a magnitude only when they knew how to construct it . Now it was not ...
Contents
The Meaning Purpose and Methods of the History of Mathematics and of Logic page | 9 |
PreHellenic Mathematics | 13 |
Greek Mathematics before Euclid | 20 |
Copyright | |
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Mathematics and Logic in History and in Contemporary Thought Ettore Carruccio,Isabel Quigly Limited preview - 2017 |
Mathematics and Logic in History and in Contemporary Thought Ettore Carruccio,Isabel Quigly Limited preview - 2017 |
Common terms and phrases
according algebraic analysis ancient antinomies Apollonius Archimedes Aristotle arithmetic axioms biunivocal correspondence Bortolotti called Carruccio Cavalieri Chapter circle concept cone conic considered construction cubic equations curve deduce defined definition Democritus demonstrated Descartes Diophantus discovery elements Enriques Enriques-De Santillana equal equation established Euclid Euclid's Elements Euclid's postulate Euclidean geometry exist expressed fact false figure finite formula Frajese function fundamental Galileo Geymonat given Greek Hilbert hypothesis ideas indivisibles infinitesimal infinity instance interpreted Leibniz logic magnitudes mathe mathematical infinite mathematicians matics means method of exhaustion modern Mondolfo non-Euclidean geometry numbers obtain Pappus parallels Parmenides passage Peano philosophical plane Plato polygon possible principle problem Proclus properties Pythagorean rational system real numbers relation right angles Saccheri school of Elea segment sides Slave Socrates solved space spherical square straight line surface symbolism theorem theory thought tion Torricelli triangle trivalent logic true valid