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Updated: May 10, 2025
We may accept Euclid's dictum that a straight line is the shortest road between two points; a wandering line, if longer, is surely as a rule the more interesting.
The farmer took from her hand the well-worn copy of Euclid's Elements, and laying aside his hat with reverence, he read aloud: "The angles at the base of an isoceles triangle are equal, and whosoever shall produce the sides, lo, the same also shall be equal each unto each." The farmer put the book aside. "It's no use, Anna. I can't read the good words to-night."
On our parting, I immediately began to think how there could be any addition to the number of the planets without overturning my 'Cosmographic Mystery, according to which Euclid's five regular solids do not allow more than six planets round the sun.... I am so far from disbelieving the existence of the four circumjovial planets, that I long for a telescope, to anticipate you, if possible, in discovering two round Mars, as the proportion seems to require, six or eight round Saturn, and perhaps one each round Mercury and Venus."
I shall confine myself to one observation on Euclid's genius, and on the immense influence which it exerted on after generations.
It made no part of the learning itself; and was so distinct from it as to make it exceedingly probable that the persons who had studied Greek sufficiently to translate those works, such for instance as Euclid's Elements, did not understand any of the learning the works contained.
Granted his first premiss, his second point followed logically from it, and so he led his hearers on point by point, all closely argued, to an indisputable conclusion. I suppose that the inexorable logic of it all appealed to the Scottish side of me. His preaching had the same fascination for me that Euclid's propositions exercised later, even on my hopelessly unmathematical mind.
In 1525 he published his first book "Instruction in the Measurement with the Compass, and Rules of Lines, Surfaces, and Solid Bodies, drawn up by Albert Duerer, and printed, for the use of all lovers of art, with appropriate diagrams." It contains a course of applied geometry in connection with Euclid's Elements.
I wish to treat you like a gentleman, but I won't be detained. Joe spoke a word to the captain, who kept his back as broad to me as a school-slate for geography and Euclid's propositions. 'Cabin, cabin, the captain repeated.
When 'I will' and 'I choose' coincide, like two of Euclid's triangles atop of one another, line for line and angle for angle, then comes liberty into the life. He that can say, not with a knitted brow and an unwilling ducking of his head to the yoke, 'I must do it, but can say, 'Thy law is within my heart, that is the Christlike, the free, the happy man.
And for this opinion he gives, as far as we have been able to discover, no reason whatever, except that everybody who vigorously and freely exercises his understanding on Euclid's Theorems assents to them. "The activity of private judgment," he truly observes, "and the unity and strength of conviction in mathematics vary directly as each other."
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