Mathematics and Logic in History and in Contemporary Thought

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