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- with respect to mathematics

The basis of all their conclusions is that the acquisition of knowledge of phenomena is according to a fixed, invariable law,—a law mathematically exact in its operation through the senses.

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The arch is mathematically precise.

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We were absolutely opposed at all points; in thought, in feeling and in sentiment, I could not help remembering the wonderful network of shining lines I had seen in that first dream of mine,- lines which were apparently mathematically designed to meet in reciprocal unity.

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These concepts are basic and impersonal; arrived at mathematically, they are mathematically correct.

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The formula makes mathematically evident the time-binding capacity characteristic of the human class of life.

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This invention was not produced, let us say 6000 years ago, because civilization was not then sufficiently advanced: mathematically considered, the production of this great use-value had to await all the accumulated work of six thousand years of human ingenuity and human labor.

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Of course it does not matter mathematically what name we give to a unit of power; we may call it a Zeus or a Zebra; but there is a very vicious implication in using the name of an animal to denote a purely human product.

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Everybody who wants to think logically must think mathematically or give up any pretense of correct thinking—there is no escape and all who refuse to investigate the justice of this statement put themselves outside the pale of logically thinking people.

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The tremendous practical results of such scientific methods are based upon two principles, namely: that, (1) the scientists must think mathematically, their studies of the phenomena must be in “systems” as a complex whole, and they must not intermix dimensions; (2) they must see the danger and not be afraid of old words with wrong meanings, but must use clear and rigorous thinking to eliminate the prejudices in science—the poison of metaphysical speculating with words, or verbalism.

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In nature there are two types of recurrent motion, somewhat closely connected mathematically, in which repetition of motion occurs at regular intervals.

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Both of these types of motion are representable mathematically by equations involving a sequence of trigonometric functions.

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I found the solution, by applying mathematically rigorous thinking.

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The method we use in studying phenomena is analysis, or speaking mathematically, differentiation.

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The duty of mathematically thinking people is to throw such light on this problem as will stop the stupid, or willfully destructive, and show whether they are working for, or against, mankind.

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He opened the front door for her, and they stood together for a moment on the dustless door-mat, mathematically laid upon verandah boards as white as new-peeled almonds.

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Well, in this number of Bees, collected in the burrow before any have emerged, I perceive none, absolutely none but females; or, to be mathematically accurate, I find just one male, one alone; and he is so small and feeble that he dies without quite succeeding in divesting himself of his nymphal bands.

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Bezenburg has mathematically demonstrated just such an aberration in falling bodies, as is mathematically required by the diurnal motion of the earth.

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It is a proposition, mathematically demonstrable, that it costs the community more to arrest, convict, and confine its tramps in jail, than to send them as guests, for like periods of time, to the best hotel.

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Mathematically that is all the further traffic in rotations that soil can bear.

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Since Einstein has cut loose from the ether, he lacks this canvas, and therewith, at the first glance, also loses the possibility of fixing the positions of the heavenly bodies and mathematically describing their movement-i.e., by giving comparisons that define the positions at every moment.

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Example #1

During my visit to London and Paris last year I had many talks with the materialistic philosophers of Europe.
Example #2

We must not look for truth in the deeds and actions of nations; we must investigate truth at its divine source and summon all mankind to unity in the reality itself.
Example #3

The effect is then very fine.
Example #4

But here they take two hundred thousand tall forest trees and set them in a double row; allow no sign of leaf or branch to grow on the trunk lower down than six feet above the ground; from that point the boughs begin to project, and very gradually they extend outward further and further till they meet overhead, and a faultless tunnel of foliage is formed.
Example #5

The lines on this occasion between us five human beings were an almost visible tangle.
Example #6

Never were five human beings more oddly brought into contact and conversation with each other.