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Updated: May 16, 2025
There is abundant evidence in support of the theory that the builders of antiquity, the masonic guilds of the Middle Ages, and the architects of the Italian Renaissance, knew and followed certain rules, but though this theory be denied or even disproved if after all these men obtained their results unconsciously their creations so lend themselves to a geometrical analysis that the claim for the existence of certain canons of proportion, based on geometry, remains unimpeached.
Drawings will also be despatched by telegraph. For such purposes as the transmission of sketches from the scene of any stirring event, the first really practical application of drawing by telegraph will probably depend upon the use of a large number of code words divided into two groups, each of which, on the principles of co-ordinate geometry, will indicate a different degree of distance from the base line and from the side line respectively, so that from any sketch a correct message in code may be made up and the drawing may be reconstructed at the receiving end.
One of the most common cases of difficulty in pursuing mathematical studies, or studies of any kind where the succeeding lessons depend upon those which precede, is the fact that the pupil, though he may understand what precedes, is not familiar with it. This is very strikingly the case with Geometry.
Such rude shocks to mathematical faith have produced that love of formalism which appears, to those who are ignorant of its motive, to be mere outrageous pedantry. The proof that all pure mathematics, including Geometry, is nothing but formal logic, is a fatal blow to the Kantian philosophy.
Since then algebraical truths are true of all things whatever, and not, like those of geometry, true of lines only or angles only, it is no wonder that the symbols should not excite in our minds ideas of any things in particular.
Thus for example, the proper cause by itself of an house or a ship is the art of the mason, the carpenter, or the shipwright; but accidental causes are music, geometry, and whatever else may happen to be joined with the art of building houses or ships, in respect either of the body, the soul, or any exterior thing.
Louis had worked at night, unknown to his mother, and made immense progress between June and September. In algebra he had come as far as equations with two unknown quantities; he had studied descriptive geometry, and drew admirably well; in fact, he was prepared to pass the entrance examination of the Ecole polytechnique. Sometimes of an evening he went down to the bridge of Tours.
Keith writes you the work-a-day news. If so, you know that I have finished all the geometry, and nearly all the Algebra required for the Harvard examinations, and after Christmas I shall begin a very careful review of both subjects. You will be glad to hear that I enjoy Mathematics now. Why, I can do long, complicated quadratic equations in my head quite easily, and it is great fun! I think Mr.
Almost the only incident of his life which is known to us is a conversation between him and that king, who, having asked if there was no easier method of learning the science, is said to have been told by Euclid, that "there was no royal path to geometry."
Of this latter stage the simple figures of Euclidian plane and solid geometry figures which any child can understand are the appropriate symbols, but for that other more developed state of consciousness less apparent but more important these will not do.
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