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Page 56 - The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed...
Page 138 - A determination of the circumstances under which discontinuity of any kind presents itself in the solution of a problem of Maximum or minimum in the Calculus of Variations, and applications to particular instances. It is expected that the discussion of the instances should be exemplified as far as possible geometrically, and that attention be especially directed to cases of real or supposed failure of the Calculus.
Page 130 - Psychical changes either conform to law or they do not. If they do not conform to law, this work, in common with all works on the subject, is sheer nonsense : no science of Psychology is possible. If they do conform to law, there cannot be any such thing as free will.
Page 39 - It would be harsh, untrue, and odious, to say there is anything like cant in this ; but it is not true to the letter, and tends to mislead. I could point out to you...
Page 68 - As unembodied spirits of direction. And you, ye undevelopable scrolls ! Above the host wave your emblazoned rolls, Ruled for the record of his bright inventions. Ye Cubic surfaces! by threes and nines Draw round his camp your seven-and-twenty lines— The seal of Solomon in three dimensions.
Page 135 - ... sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any olher of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.
Page 112 - is that study which knows nothing of observation, nothing of induction, nothing of experiment, nothing of causation.
Page 95 - More Worlds than One. The Creed of the Philosopher and the Hope of the Christian.
Page 88 - But in the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can ever have passed from one to another, and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth.