A History of Mathematics |
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Page 22
... quantities by him and his school will be taken up under the head of arithmetic . According to Eudemus , the Pythagoreans invented the prob- lems concerning the application of areas , including the cases of defect and excess , as in ...
... quantities by him and his school will be taken up under the head of arithmetic . According to Eudemus , the Pythagoreans invented the prob- lems concerning the application of areas , including the cases of defect and excess , as in ...
Page 68
... quantities a , b , c , d were said to be in arithmetical proportion when abc - d ; in geometrical proportion , when a : bc : d ; in harmonic proportion , when a b : b c = a : c . It is probable that the Pythagoreans were also familiar ...
... quantities a , b , c , d were said to be in arithmetical proportion when abc - d ; in geometrical proportion , when a : bc : d ; in harmonic proportion , when a b : b c = a : c . It is probable that the Pythagoreans were also familiar ...
Page 69
... quantities , which is attributed by Eudemus to the Pythagoreans . It was indeed a thought of extraordinary boldness , to assume that straight lines could exist , differing from one another not only in length , — that is , in quantity ...
... quantities , which is attributed by Eudemus to the Pythagoreans . It was indeed a thought of extraordinary boldness , to assume that straight lines could exist , differing from one another not only in length , — that is , in quantity ...
Page 70
... quantities at length . He investi- gates every possible variety of lines which can be represented by √ √ã ± √b , a and b representing two commensurable lines , and obtains 25 species . Every individual of every species is ...
... quantities at length . He investi- gates every possible variety of lines which can be represented by √ √ã ± √b , a and b representing two commensurable lines , and obtains 25 species . Every individual of every species is ...
Page 73
... quantities in integral numbers are to be found . It may be stated thus : The sun had a herd of bulls and cows , of different colors . ( 1 ) Of Bulls , the white ( W ) were , in number , ( + ) of the blue ( B ) and yel- low ( Y ) : the B ...
... quantities in integral numbers are to be found . It may be stated thus : The sun had a herd of bulls and cows , of different colors . ( 1 ) Of Bulls , the white ( W ) were , in number , ( + ) of the blue ( B ) and yel- low ( Y ) : the B ...
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Abel Abelian functions algebra Almagest analysis analytical angles Apollonius applied Arabic Archimedes arithmetic astronomical became Berlin Bernoulli born calculus Cauchy Cayley century circle Clebsch coefficients conic contains convergent Crelle's Journal cubic curve degree Descartes determine developed differential equations Diophantus Dirichlet discovery elasticity elliptic functions Euclid Euler Felix Klein Fermat fluxions fractions Gauss gave geometry given Göttingen Greek Hindoo important integrals invention investigated Jacobi John Bernoulli Lagrange Laplace later Legendre Leibniz linear lines logarithms mathe mathematicians mathematics matical mechanics memoir method motion Newton notation paper Paris partial differential equations plane Poincaré Poisson polygon principle problem professor proof published pupil Pythagoreans quadratic quadrature quantities quaternions researches Riemann Riemann's surfaces roots solution solved square surface Sylvester symbols synthetic synthetic geometry tangents theorem theory of functions theory of numbers theta-functions Thomson tion treatise triangle trigonometry University variable velocity Vieta Weierstrass writings wrote