Mathematics and Logic in History and in Contemporary Thought |
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Page 63
... means of a definition what the word triangle means , but that a triangle exists or that it is possible to con- struct one , and that one may therefore obtain results from the fact of having constructed it , is a truth which is neither ...
... means of a definition what the word triangle means , but that a triangle exists or that it is possible to con- struct one , and that one may therefore obtain results from the fact of having constructed it , is a truth which is neither ...
Page 318
... means : there is no A AB = means : no A is B = AB O means there do not exist members which are A and contemporaneously are not B : that means , every A is B. The following fundamental identities which are obvious in themselves are used ...
... means : there is no A AB = means : no A is B = AB O means there do not exist members which are A and contemporaneously are not B : that means , every A is B. The following fundamental identities which are obvious in themselves are used ...
Page 336
... means for every x there exists a y for which A ( x , y ) is valid . But the parentheses can be omitted when there is ... means of the following rules : ( a ) rule of substitution , ( B ) scheme of deduction , like , ' mutatis mutandis ...
... means for every x there exists a y for which A ( x , y ) is valid . But the parentheses can be omitted when there is ... means of the following rules : ( a ) rule of substitution , ( B ) scheme of deduction , like , ' mutatis mutandis ...
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 | |
17 other sections not shown
Other editions - View all
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