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But a presentation of its principles thus clarified makes it also evident that mathematics as such cannot predicate anything about perceptual objects or real objects. In axiomatic geometry the words "point," "straight line," etc., stand only for empty conceptual schemata. That which gives them substance is not relevant to mathematics.
Why is the equivalence of the practically-rigid body and the body of geometry which suggests itself so readily denied by Poincare and other investigators? Simply because under closer inspection the real solid bodies in nature are not rigid, because their geometrical behaviour, that is, their possibilities of relative disposition, depend upon temperature, external forces, etc.
In the latter epoch, beings descended from demons built Nineveh and Babylon; organized human existence; invented arithmetic, geometry, astronomy and the calendar; counted the planets; numbered the days of the year, divided them into months and weeks; established the Sabbath; decorated the skies with the signs of the zodiac, instituting, in the interim, colleges of savants and priests.
If when classes assembled she found herself in the same geometry section with her chum she would make an excuse and change to another period of recitation. The frown deepened on her smooth forehead as she jotted down her subjects on the sheet of paper before her. Suddenly conscious of the intent regard of someone, she raised her head.
The average distance between the coils, even in the structures of the young Epeirae, is one centimetre. Let us not be misled by the word 'spiral, which conveys the notion of a curved line. All curves are banished from the Spiders' work; nothing is used but the straight line and its combinations. All that is aimed at is a polygonal line drawn in a curve as geometry understands it.
"Certainly, if it can be received; but therein consists the difficulty. I am afraid it is as reasonable to expect a savage to apprehend the exalted truths of Christianity, as one unaquainted with geometry, the forty-ninth proposition of the first book of Euclid." "The comparison is not just. Science demands pure intellect; but religion, both intellect and feeling, perhaps most of the latter.
Rousseau once wrote, in a letter about Rivière's book, that the great problem in politics, which might be compared with the quadrature of the circle in geometry, is to find a form of government which shall place law above man.
Thus Rhetoric and Cicero, Civil Law and Justinian, Speculative Theology and the Areopagite, Practical Theology and Peter Lombard, Geometry and Euclid, Arithmetic and Abraham, are grouped together. It will be seen that the whole learning of the Middle Age its philosophy as well as its divinity is here combined as in a figured abstract, for the wise to comment on and for the simple to peruse.
He dabbled in geometry, mechanics, and botany. He paid some attention to antiquities and works of art, and was considered in his own circle as a judge of painting, architecture, and poetry. It is said that his spelling was incorrect.
Being well grounded in arithmetic and geometry, he had no difficulty in making himself master of the geometrical and astronomical theorems which occurred in the course of his studies.
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