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Updated: May 4, 2025
Looking over the expanse of the ages, we think more earnestly and lovingly of Cadmus, who gave us the alphabet; of Archimedes, who invented the lever; of Euclid, with his demonstrations in geometry; of Faust, who taught us how to print; of Watt, with his development of steam, than of the resonant orators who inflamed the passions of mankind, and the gallant chieftains who led mankind to war.
Thales the Milesian was the author of several of the geometrical theorems and demonstrations now included in the Elements of Euclid. The celebrated fifth proposition of the first book, so famous among all the modern nations of Europe as the great stumbling block in the way of beginners in the study of geometry, was his.
That things which are equal to the same thing are equal to one another, is as obvious in any particular case as it is in the general statement: and if no such general maxim had ever been laid down, the demonstrations in Euclid would never have halted for any difficulty in stepping across the gap which this axiom at present serves to bridge over.
Lancelot ruefully recognised the truth of the chalk-line story. Comus drew the desired line with an anxious exactitude which he would have scorned to apply to a diagram of Euclid or a map of the Russo-Persian frontier. "Bend a little more forward," he said to the victim, "and much tighter. Don't trouble to look pleasant, because I can't see your face anyway.
Even when we have general propositions we need not use them. Thus Dugald Stewart showed that the axioms need not be expressly adverted to in order to make good the demonstrations in Euclid; though he held, inconsistently, that the definitions must be.
Among the contents of that curious almanac are Latin and French enigmas, mathematical questions and paradoxes. The concluding paragraph for the dedication of that day is entitled "Truth's Moral Euclid"; the proposition given being: "Virtue promotes happiness, private and public. Vice is destructive of happiness, private and public. Honour is the reward of virtue."
"Being the teacher to whom reference is made, I am now quite willing to confess that for the remainder of that afternoon, less than a problem in Euclid would have been sufficient to disqualify me for the remaining scholastic duties of the hour. I felt it, of course, to be no small honor for a humble teacher to be called to the sanctum of Thomas A. Edison.
On the morrow he had to meet Nellie at Euston, and he had shrunk from meeting her, with her terrible remorseless, provincial, untheatrical common sense; but now, in another magic flash, he envisaged the meeting with a cock-a-doodle-doo of hope. Strange! He admitted it was strange. And then he failed to hear several words spoken by Rose Euclid. And then a few more.
If he wishes his works to live with those of the poet and orator, he must, like them, cultivate those beauties of style which are fitted to his matter. Euclid did so; and his Elements have been for more than two thousand years the model for all writers on geometry.
We may say with confidence, then, that we are placed here to increase in knowledge and in virtue." "This is the core of all religion, and this much needs no faith in the acceptance. It is as true and as capable of proof as one of those exercises of Euclid which we have gone over together. On this common ground men have raised many different buildings.
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