A Short Account of the History of MathematicsMacmillan and Company, limited, 1908 - 522 σελίδες |
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Σελίδα vi
... use of modern notation ; the reader must therefore recollect that , while the matter is the same as that of any writer to whom allusion is made , his proof is sometimes translated into a more convenient and familiar language . vi PREFACE.
... use of modern notation ; the reader must therefore recollect that , while the matter is the same as that of any writer to whom allusion is made , his proof is sometimes translated into a more convenient and familiar language . vi PREFACE.
Σελίδα 13
... proof used by the early Greek geometricians are compared with those current at a later date . In addition to these general statements we have biographies of a few of the 1 The history of these schools has been discussed by G. Loria in ...
... proof used by the early Greek geometricians are compared with those current at a later date . In addition to these general statements we have biographies of a few of the 1 The history of these schools has been discussed by G. Loria in ...
Σελίδα 15
... proofs were deductive , so that the theorems were not a mere statement of an induction from a large number of special instances ... proof of it . ( iii ) A triangle is determined if its base and base angles be given ( cf. Euc . 1 , 26 ) ...
... proofs were deductive , so that the theorems were not a mere statement of an induction from a large number of special instances ... proof of it . ( iii ) A triangle is determined if its base and base angles be given ( cf. Euc . 1 , 26 ) ...
Σελίδα 16
... proof , he must have been aware that the sum of the angles of a right - angled triangle is equal to two Xright angles . It has been ingeniously suggested that the shape of the tiles used in paving floors may have afforded an ...
... proof , he must have been aware that the sum of the angles of a right - angled triangle is equal to two Xright angles . It has been ingeniously suggested that the shape of the tiles used in paving floors may have afforded an ...
Σελίδα 17
... proof was given at first only in the case of isosceles right - angled triangles , but probably it was extended later ... proofs is evidently included in the last , but there is nothing improbable in the suggestion that the early Greek ...
... proof was given at first only in the case of isosceles right - angled triangles , but probably it was extended later ... proofs is evidently included in the last , but there is nothing improbable in the suggestion that the early Greek ...
Άλλες εκδόσεις - Προβολή όλων
A Short Account of the History of Mathematics Walter William Rouse Ball Περιορισμένη προεπισκόπηση - 1960 |
Συχνά εμφανιζόμενοι όροι και φράσεις
algebra analysis analytical geometry angle Apollonius Arab Archimedes arithmetic astronomy Athenian school Berlin Bernoulli born Brahmagupta Cambridge Cantor centre century chapter circle conic contains cube curve denote Descartes determined died differential calculus Diophantus discoveries discussed earliest edition enunciated equal Euclid Euclid's Elements Euler Fermat fluxions functions Gauss gave geometricians given gives Greek Greek mathematics Hipparchus history of mathematics infinitesimal calculus integral introduced invention investigations John Bernoulli known Lagrange Laplace later lectures Leibnitz Leipzig London mathe mathematicians mechanics memoirs mentioned method modern motion Newton notation obtained papers Paris philosophy plane Principia principles probably problem proof propositions published Pythagoras quadratic quadrature quantity ratio Regiomontanus roots shewed solution solved square straight line subsequently symbols tangent text-books theorem theory of numbers tion treatise triangle trigonometry Vieta volumes W. W. ROUSE BALL writers written wrote
Δημοφιλή αποσπάσματα
Σελίδα 323 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Σελίδα 349 - I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
Σελίδα 256 - The squares of the periodic times of the planets are proportional to the cubes of their mean distances from the Sun.
Σελίδα 335 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Σελίδα 10 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 334 - had Newton proved this superb theorem — and we know from his own words that he had no expectation of so beautiful a result till it emerged from his mathematical investigation — than all the mechanism of the universe at once lay spread before him.
Σελίδα 326 - I was so persecuted with discussions arising out of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet, to run after a shadow.
Σελίδα 45 - If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length to become greater than AB.
Σελίδα 486 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 41 - Philoponus,t it is asserted that the Athenians in 430 BC when suffering from the plague of eruptive typhoid fever, consulted the oracle at Delos as to how they could stop it. Apollo replied that they must double the size of his altar, which was in the form of a cube. To the unlearned suppliants nothing seemed more easy, and a new altar was constructed...