The Works of John Playfair ...: With a Memoir of the Author ...A. Constable & Company, 1822 |
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Page 7
... problem are so related to one another , as to render it indefinite , or capable of innumerable solutions . These cases , which rarely occur , except in the construction of very general and complicated problems , must always interest a ...
... problem are so related to one another , as to render it indefinite , or capable of innumerable solutions . These cases , which rarely occur , except in the construction of very general and complicated problems , must always interest a ...
Page 9
... problems as the algebraic calculus alone had been thought able to resolve . His solution of Kepler's problem was the first specimen of this kind which he gave to the world ; and it was im- possible to have produced one more to the ...
... problems as the algebraic calculus alone had been thought able to resolve . His solution of Kepler's problem was the first specimen of this kind which he gave to the world ; and it was im- possible to have produced one more to the ...
Page 10
... problem did not admit of an accu- rate solution ; and that no more was to be expected , than an easy and exact approximation . In this , ever since the days of Kepler , the mathematicians of the first name had been engaged , and the ...
... problem did not admit of an accu- rate solution ; and that no more was to be expected , than an easy and exact approximation . In this , ever since the days of Kepler , the mathematicians of the first name had been engaged , and the ...
Page 11
... problem , though the most elementary , may be the least ob- vious , and , though the easiest to be understood , may be the most difficult to be discovered . This solution appeared in the second volume of the Essays of the Philosophical ...
... problem , though the most elementary , may be the least ob- vious , and , though the easiest to be understood , may be the most difficult to be discovered . This solution appeared in the second volume of the Essays of the Philosophical ...
Page 12
... problem of the Three Bodies had been proposed in all its generality , and , in as far as regards the motion of the moon , had been resolved by a direct and accurate approxima- tion . But the intricacy and length of these calcu- lations ...
... problem of the Three Bodies had been proposed in all its generality , and , in as far as regards the motion of the moon , had been resolved by a direct and accurate approxima- tion . But the intricacy and length of these calcu- lations ...
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Popular passages
Page 81 - The mind seemed to grow giddy by looking so far into the abyss of time ; and while we listened with, earnestness and admiration to the philosopher who was now unfolding to us the order and series of these wonderful events, we became sensible how much farther reason may sometimes go than imagination can venture to follow.
Page 335 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 309 - ... that the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, is always equal to two right angles.
Page 125 - The boast of heraldry, the pomp of power, And all that beauty, all that wealth e'er gave, Await alike the inevitable hour — The paths of glory lead but to the grave.
Page 325 - In one of these, where the dictates of Aristotle are still listened to as infallible decrees, and where the infancy of science is mistaken for its maturity, the mathematical sciences have never flourished ; and the scholar has no means of advancing beyond the mere elements of geometry.
Page 522 - An account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London.
Page 55 - It is unreasonable, indeed, to suppose that such marks should any where exist. The Author of nature has not given laws to the universe, which, like the institutions of men, carry in themselves the elements of their own destruction ; he has not permitted in his works any symptom of infancy or of old age, or any sign by which we may estimate either their future or their past duration.
Page 56 - The Author of nature has not given laws to the universe, which, like the institutions of men, carry in themselves the elements of their own destruction. He has not permitted, in his works, any symptom of infancy or of old age, or any sign by which we may estimate either their future or their past duration. He may put an end, as he no doubt gave a beginning, to the present system, at some determinate period; but we may safely conclude, that this great catastrophe will not be brought about by any of...
Page 301 - Between the laws by which the tides diminish from their maximum at the full and change, to their minimum at the first and third quarters, and by which they increase again from the minimum to the maximum, as deduced from the observations at Brest, and as determined by the theory of gravitation, there is an exact coincidence. 2. According to theory, the height of the tides...
Page 439 - ... most general rule that we are enabled to give admits of many exceptions. The violation of the order of events among the phenomena of the former class, the suspension of gravity, for example, the deviation of any of the stars from their places or their courses in the heavens, &c., — these are facts of which the improbability is so strong that no testimony can prevail against it.