## The Works of John Playfair ...: With a Memoir of the Author ...A. Constable & Company, 1822 |

### From inside the book

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**Porisms**of Euclid . These last formed the most intricate and paradoxical subject in the history of the ancient mathematics . Every thing concerning them , but the name , had perished . Pappus Alex- andrinus has made mention of three ... Page 6

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**Porisms**, to which more genius was perhaps required than to the first discovery of them , employed Dr Simson , Mr Stewart pursued the same subject in a different , and new direction . In doing so , he was led to the discovery of those ... Page 7

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**porisms**; for a**porism**is nothing else than that particular case , when the data of a problem are so related to one another , as to render it indefinite , or capable of innumerable solutions . These cases , which rarely occur , except ... Page 11

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**porisms**, and one of them forms the 91st of Dr Simson's Restor- ation . They are besides very beautiful proposi- tions , and are demonstrated with all the elegance and simplicity of the ancient analysis . It has been already mentioned ... Page 25

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**Porisms**, after pointing out many propo- sitions that had been suggested by Pappus , and a few that had been adopted from Fermat , he adds , " Alia quædam adjecta sunt quorum præcipua mihi proposuit , et aliquorum constructionem dedit ...### Common terms and phrases

accuracy accurate afford ancient angles appear arch ascertained astronomical Board of Longitude bodies calculation cause circumstances computation considerable considered deduced degree Delambre determined discoveries distance Dr Black Dr Hutton Dr Simson Dr Stewart Dunkirk earth Edinburgh effect employed England equal equator error experiments extremely fathoms force France French geometer geometry give given gravity heat inequalities instrument investigation irregularities Jupiter known Laplace latitude length less longitude mathematical mathematicians matter means measured ment mentioned meridian method mixed mathematics moon moon's motion mountain Mudge nature nearly never Newton object observations orbit pendulum perpendicular philosophers planets Porisms principle probably problem produced Punnae quantity remark repeating circle revolution Robison Royal schistus seems side spherical excess stations supposed surface theodolite theorem theory thing tion toises trigono trigonometrical survey truth University of Edinburgh vibrations whole zenith

### 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.