The Works of John Playfair ...: With a Memoir of the Author ... |
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Page 7
With this view , he , no doubt , thought of extending the hypotheses of that problem to their utmost generality ; that is , to any number of perpendiculars drawn to an equal number of lines , and to any power whatever of these ...
With this view , he , no doubt , thought of extending the hypotheses of that problem to their utmost generality ; that is , to any number of perpendiculars drawn to an equal number of lines , and to any power whatever of these ...
Page 9
In doing this , he was pursuing the object which , of all others , he most ardently wished to attain , viz . the application of geometry to such problems as the algebraic calculus alone had been thought able to resolve .
In doing this , he was pursuing the object which , of all others , he most ardently wished to attain , viz . the application of geometry to such problems as the algebraic calculus alone had been thought able to resolve .
Page 10
problem , of computing the place of a planet for a given time , to that of drawing a line through the focus of an ellipse , that should divide the area of the semi - ellipse in a given ratio . It was soon found , that this problem did ...
problem , of computing the place of a planet for a given time , to that of drawing a line through the focus of an ellipse , that should divide the area of the semi - ellipse in a given ratio . It was soon found , that this problem did ...
Page 11
will be convinced , that the solution of a problem , though the most elementary , may be the least obvious , and , though the easiest to be understood , may be the most difficult to be discovered . This solution appeared in the second ...
will be convinced , that the solution of a problem , though the most elementary , may be the least obvious , and , though the easiest to be understood , may be the most difficult to be discovered . This solution appeared in the second ...
Page 12
Succeeding mathematicians had been employed about the same subject ; the 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 ...
Succeeding mathematicians had been employed about the same subject ; the 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 ...
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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.
Bibliographic information
| Title | The Works of John Playfair ...: With a Memoir of the Author ... Volume 4 of The Works of John Playfair ...: With a Memoir of the Author, James George Playfair |
| Author | John Playfair |
| Publisher | A. Constable & Company, 1822 |
| Original from | the New York Public Library |
| Digitized | 2 May 2006 |
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