A History of Mathematics |
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Page 2
... solved long since ; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure ; it teaches that fortifications can be taken in other ways than by direct attack , that when ...
... solved long since ; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure ; it teaches that fortifications can be taken in other ways than by direct attack , that when ...
Page 14
... solved by aid of a table , given in the papyrus , in which all fractions of the form 2 2n + 1 1 ( where n designates successively all the numbers up to 49 ) are reduced to the sum of unit - fractions . Thus , 7 = 428 ; 35 = 18. When ...
... solved by aid of a table , given in the papyrus , in which all fractions of the form 2 2n + 1 1 ( where n designates successively all the numbers up to 49 ) are reduced to the sum of unit - fractions . Thus , 7 = 428 ; 35 = 18. When ...
Page 19
... solving problems so elementary as these , indi- cates that geometry was still in its infancy , and that the Greeks had not yet gotten far beyond the Egyptian con- structions . The Ionic school lasted over one hundred years . The ...
... solving problems so elementary as these , indi- cates that geometry was still in its infancy , and that the Greeks had not yet gotten far beyond the Egyptian con- structions . The Ionic school lasted over one hundred years . The ...
Page 26
... solving the problem of the quadrature . He did himself credit by remarking that by inscribing in a circle a square , and on its sides erecting isosceles triangles with their vertices in the circumference , and on the sides of these ...
... solving the problem of the quadrature . He did himself credit by remarking that by inscribing in a circle a square , and on its sides erecting isosceles triangles with their vertices in the circumference , and on the sides of these ...
Page 31
... solved the problem of the duplication of the cube . But the solution is open to the very same objec- tion which he made to the solutions by Archytas , Eudoxus , and Menæchmus . He called their solutions not geometrical , but mechanical ...
... solved the problem of the duplication of the cube . But the solution is open to the very same objec- tion which he made to the solutions by Archytas , Eudoxus , and Menæchmus . He called their solutions not geometrical , but mechanical ...
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60 cents abacus Abelian functions algebra Almagest analysis analytical angles Apollonius applied Arabic Archimedes arithmetic astronomical Berlin Bernoulli Boethius calculus Cambridge Cauchy Cayley century circle Clebsch College conic sections contains Crelle's Journal cubic curve degree Descartes determine differential calculus differential equations Diophantus discovery Edition Egyptian elasticity Elementary Treatise elliptic functions Euclid Euclid's Elements Euler expressed Fermat fluxions fractions Gauss gave geometry given gives Greek Hindoo infinite integral invention investigations Jacobi John Bernoulli known Lagrange Laplace Legendre Leibniz linear lines logarithms mathe mathematicians mathematics matical mechanics memoir method motion Newton notation paper Pappus Paris plane polygon principle problem professor progress proof published pupil Pythagoreans quadratic quadrature quantities ratio researches Riemann roots sexagesimal solids solution solved spherical square surface symbol synthetic geometry tangents theorem theory of numbers theta-functions Thomson tion translated triangle trigonometry variable Vieta Wallis writings wrote