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First the chemistry of organic matter was investigated, then the physical attraction of their molecules, and now their geometry is in question. So, says Professor Bateson, the 'geometrical symmetry of living things is the key to a knowledge of their regularity and the forces which cause it. In the symmetry of the dividing cell the basis of that resemblance which we call Heredity is contained'.
I. 47 that the square on the hypotenuse of any right-angled triangle is equal to the sum of the squares on the other two sides. But Proclus also attributes to him, besides the theory of proportionals, the construction of the 'cosmic figures', the five regular solids. This method was fully worked out by the Pythagoreans and proved one of the most powerful in all Greek geometry.
One that loves his credit, not this word reputation; yet can save both without a duel. Whose entertainments to greater men are respectful, not complimentary; and to his friends plain, not rude. A good husband, father, master; that is, without doting, pampering, familiarity. A man well poised in all humours, in whom nature shewed most geometry, and he has not spoiled the work.
These have labored with a godlike energy and skill to trace the interior relationships existing between the recondite revelations of their Geometry, their wonderful laws of mathematical harmonies and unities, and those lines which by common consent are understood to be exponential of certain phases of our own existence.
The germ of algebra may be discerned in the works of Diophantus of Alexandria, who is supposed to have lived in the second century of our era. In that Egyptian school Euclid had formerly collected the great truths of geometry, and arranged them in logical sequence. Archimedes, in Syracuse, had attempted the solution of the higher problems by the method of exhaustions.
By means of what branch of mathematics was that island of our Canadian Crusoe located?" "Geometry," replied Bud confidently. Cub snapped his finger with an impatient jerk of his long right arm. "Of course!" he exclaimed in disgust. "Every branch of mathematics I ever heard of, except geometry, went buzzing through my head. I was trying to recall something in algebra that would fit this case."
Just as a knowledge of the Principles of Geometry enables man to measure distant suns and their movements, while seated in his observatory, so a knowledge of the Principle of Correspondence enables Man to reason intelligently from the Known to the Unknown. Studying the monad, he understands the archangel. The Principle of Vibration "Nothing rests; everything moves; everything vibrates."
Remarking on the plea of the utilitarian, that truth may be justified by the intolerable consequences of its habitual violation, he urges that this is no reason against its being intuitively perceived; just as the axioms of geometry, although intuitively felt, are confirmed by showing the incongruities following on their denial. He repeats the common allegation in favour of
"Do not take what he has just said, madame, for the wanderings of a madman," whispered the doctor; "he handles in this way sometimes the most difficult questions of geometry or astronomy, with an acuteness which would do honor to the most illustrious learned men. His knowledge is great. He speaks all the living languages, but he is, alas! a martyr to his thirst for erudition and pride of learning.
This fundamental law must resemble the truths of geometry in their most remarkable peculiarity, that of never being, in any instance whatever, defeated or suspended by any change of circumstances.
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