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It would seem as if the analogy were but an artificial play upon words, and that it was only metaphorically that in mathematical demonstration we speak of one thing as following from another. The properties of a curve or a triangle are what they are at all times, and the sequence is merely in the order in which they are successively known to ourselves.
Motley "finds it black and thrusts it farther into the darkness." Every writer carries more or less of his own character into his book, of course. A great professor has told me that there is a personal flavor in the mathematical work of a man of genius like Poisson.
He had with him his clothes and bedding, with a firelock and some powder and bullets, some tobacco, a knife, a kettle, a bible, with some other books, and his mathematical instruments.
Such investigations demand the exercise of the highest mathematical gifts. But not alone is intellectual ability necessary for success in such inquiries. It must be united with a patient capacity for calculations of an arduous type, protracted, as they frequently have to be, through many years of labour.
The book contains a good deal of arithmetical calculation. But he thought meanly of these things, and his real interest was in pure mathematical speculation; he caused to be engraved on his tomb a representation of a cylinder circumscribing a sphere, with the ratio 3/2 which the cylinder bears to the sphere: from which we infer that he regarded this as his greatest discovery.
Of that marvellous endowment which guides the bee to fabricate its cells according to laws of the most rigid mathematical exactness, and guides the swallow in its long flight to its winter home, we agree with Professor Bowen, that there is no trace whatever in human nature.
There has been a great change since that time, a change in which the Johns Hopkins University took the lead, by inviting Sylvester to this country, and starting a mathematical school of the highest grade. Other universities followed its example to such an extent that, to-day, an American student need not leave his own country to hear a master in any branch of mathematics. I believe it was Dr.
The south-western angle of the group formed a long, low point, or cape of rock, making a very tolerable roadstead on its north-western side, or to leeward. This cape was known among the colonists by the name of Rancocus Needle, from the circumstance that it pointed with mathematical precision to the island in question.
"Show why that is so." "It is a self-evident mathematical proposition. The more people a loaf of bread or any given thing is divided among, and the more equally it is divided, the sooner it will be consumed and more bread be called for. To put it in a more formal way, the needs of human beings result from the same natural constitution and are substantially the same.
The questions, what effect will result from the continual addition of a given cause to itself, and what amount of the cause, being continually added to itself, will produce a given amount of the effect, are evidently mathematical questions, and to be treated, therefore, deductively.
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