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algebra analysis analytical angle applied Arab arithmetic astronomy attention attraction born calculus Cambridge century chapter circle collected complete connected considerable considered contains curve denote described determined died differential discussed divided earliest edition educated equal equation Euclid expressed fact figure four functions gave geometry given gives Greek idea illustration important interest introduced invention issued Italy knowledge known later lectures London mathematicians mathematics means mechanics memoirs mentioned method motion nature Newton notation obtained original Paris particular period position principles printed probably problem produced proof properties propositions proved published quantities questions ratio represented researches roots rule seems shewed side similar solution solved square subsequently symbols taken theorem theory tion treated treatise triangle various volumes writers written wrote
Page 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.
Page 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.
Page 256 - The squares of the periodic times of the planets are proportional to the cubes of their mean distances from the Sun.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...