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Updated: May 18, 2025
By what chains, or indeed infinitely complected tissues, of Meditation this grand Theorem is here unfolded, and innumerable practical Corollaries are drawn therefrom, it were perhaps a mad ambition to attempt exhibiting.
It may be weighty and profound; it may be light, as light as the fall of a leaf or a bird's song on the shore; it may be the thought of Plato when he discourses of the character necessary in a perfect state, or of Socrates, who, out of the theorem of an absolute beauty, goodness, greatness, and the like, deduces the immortality of the soul; or it may be the lovesong of a Scotch plowman: but it has this one quality of answering to a need in human nature higher than a need for facts, for knowledge, for wealth.
A theorem which Max Muller has laid down for our guidance in this kind of investigation furnishes us with an excellent example of the tricks which a superficial analogy may play even with the trained scholar, when temporarily off his guard.
Hope is another pernicious quality leading to all kinds of preposterous expectations which never are, or can be, fulfilled; and as to faith, it is simply a vice. So far from taking anything on trust, you must refuse to accept any statement whatsoever till it is proved so plainly you can't help believing it whether you like it or not; just as a theorem in "
Why should it not be making itself valid like everything else? That some parts of it may be already valid or verified beyond dispute; the empirical philosopher, of course, like any one else, may always hope. Humanism is a ferment that has 'come to stay. It is not a single hypothesis or theorem, and it dwells on no new facts.
Let geography be taught as Fraser teaches it in his "Real Siberia" or Savage Landor in his "In the Forbidden Land" and the map will be studied with interest and the subject never forgotten. Let the notation be dispensed with until the child understands the problem or theorem and Euclid will become fascinating.
When he looked one in the face with intention, and suddenly allowed one to realise, as it were, all the dominating power of his brain, one shrank into insignificance, one felt as an ignorant, intelligent man may feel when confronted with some elaborate theorem of the higher mathematics.
'And ever unsuccessfully: for what theorem of the Infinite can the Finite render complete?... Metaphysical Speculation as it begins in No or Nothingness, so it must needs end in nothingness; circulates and must circulate in endless vortices; creating, swallowing itself. Again, on the other side, he sets his face just as firmly against the excessive pretensions and unwarranted certitudes of the physicist.
Lashmar had seemed to be musing whilst he savoured a slice of pine-apple. At Breakspeare's last remark, he looked up and said: "The world moves, and always has moved, at the impulse of a very small minority." "Philosophically, I am convinced of that," replied the editor, as though he meant to guard himself against too literal or practical an application of the theorem.
11 This follows from the application of Fourier's Theorem, according to which every vibration of any kind is divisible into a sum of periodic partial vibrations, and therefore is regarded as compounded of these. Seeing as 'Deed' I
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