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"Alas, my boy," said he, "human knowledge is confined within very narrow limits; and when I have taught you mathematics, physics, history, and the three or four modern languages with which I am acquainted, you will know as much as I do myself. Now, it will scarcely require two years for me to communicate to you the stock of learning I possess."
The present chapter will in particular serve this purpose. Science, since Galileo, has been rooted in the conviction that the logic of mathematics is a means of expressing the behaviour of natural events. The material for the mathematical treatment of sense data is obtained through measurement.
Their logic is their spontaneous and intelligible side: and while they differ from mathematics and from one another in being directed in the first instance upon various unintelligible existing objects, yet as they advance, they unite: because they are everywhere striving to discover in those miscellaneous objects some intelligible order and method.
Well, as you are too stupid for the law, I suppose I must try you with something easier say mathematics." Tom looked at him aghast. "A nice pleasant subject, full of calculations. But we shall see. I suppose you will not mind helping me?" "I shall be glad to, uncle." "That's right; but you don't know yet what I want you to do.
In the first year in a Realgymnasium: religion, 3 hours; German, 4 hours; Latin, 8 hours; geography, 2 hours; mathematics, 4 hours; natural science, 2 hours; writing, 2 hours.
From what has been said concerning the calculation of the earth's diameter and of the distances of the sun and moon, it may be readily understood that the ancient mathematician had arrived at great proficiency in the geometrical branch of mathematics. This should cause no surprise when we remember what is meant by "Euclid."
His attention was first turned to the study of mathematics by a desire to inquire into the truth of judicial astrology, and he is said to have discovered the folly of that study by erecting a figure with the aid of one or two of the problems in Euclid.
Philippa Yordas went through the whole of her orders again most clearly, and at every one of them the dogman nodded his large head distinctly, and counted the nods on his fingers to make sure; for this part is gifted with high mathematics. And the numbers stick fast like pegs driven into clay. "Poor Jordas! Philippa, you are working him too hard. You have made great wrinkles in his forehead.
On this point we cannot do better than quote some remarks from Kant's preface to the second edition of his Kritik der reinen Vernunft. But it must not be supposed that it was as easy for mathematics as it was for logic, where reason is concerned with itself alone, to find, or rather to build for itself, that royal road.
To remedy these alleged evils, he therefore proposed that there should be established "two Grammar Schools, one at Quebec, and one at Montreal, each under a Rector or Head Master and three Assistants, at which the following branches of education shall be taught: the Greek, Latin, French and English languages, Writing, Arithmetic, Geography, and Practical Mathematics.
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