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Updated: May 10, 2025
I talk of knowing the best which has been thought and uttered in the world; Professor Huxley says this means knowing literature. Literature is a large word; it may mean everything written with letters or printed in a book. Euclid's Elements and Newton's Principia are thus literature. All knowledge that reaches us through books is literature. But by literature Professor Huxley means belles lettres.
Her figure, teeth, voice, hair, manner, hats, clothes, and whole life and conduct were flat as Euclid's plane-surface or yesterday's champagne. To counter-balance the possession, perhaps, of so many virtues, gifts, testimonials, and certificates she had no chin, no eyebrows, and no eyelashes.
The Saracens also gave to trigonometry its modern form, substituting sines for chords, which had been previously used; they elevated it into a separate science. Musa, above mentioned, was the author of a "Treatise on Spherical Trigonometry." Al-Baghadadi left one on land-surveying, so excellent, that by some it has been declared to be a copy of Euclid's lost work on that subject.
The ideal of the school was to fit the children for the struggle into which their lives would thrust them, so that the boy who could spell and read and cipher was supposed to be ready for his life work. Those whose ambition led them into the subtleties of Euclid's problems and theorems were supposed to be in preparation for somewhat higher spheres of life.
Nevertheless, geometry forms the handiest system for applying to experience and calculating shapes and motions. But, ideally, other systems might be used. The 'metageometries' have constructed other ideal 'spaces' out of postulates differing from Euclid's, though when applied to real space their greater complexity destroys their value.
These equations represent, in Cartesian co-ordinates, and with rectangular axes, the conics by the intersection of which two and two Menaechmus solved the problem; in the case of the rectangular hyperbola it was the asymptote-property which he used. We pass to Euclid's times.
Riemann's geometry will be the right thing if the laws of disposition of practically-rigid bodies are transformable into those of the bodies of Euclid's geometry with an exactitude which increases in proportion as the dimensions of the part of space-time under consideration are diminished.
But when we come to the Fourteenth Proposition of Euclid's Data, when I am required to admit, that, "if a magnitude together with a given magnitude has a given ratio to another magnitude, the excess of this other magnitude above a given magnitude has a given ratio to the first magnitude; and if the excess of a magnitude above a given magnitude has a given ratio to another magnitude, this other magnitude together with a given ratio to the first magnitude," I own to a slight confusion of my intellectual faculties, and a perfect contempt for John Buteo and Ptolemy.
I believe in a supreme God and sovereign ruler of the world, by whose wisdom and power all things and beings have been created, and are sustained, and in whose presence I live and enjoy, as implicitly as I believe the fifth proposition of Euclid's first book. I believe in a future life with the like strength.
It paid not the slightest attention to Euclid's definition of a straight line, and in this respect was rather a welcome change from the average American road. Sometimes they passed along avenues of overbranching trees, which were evidently relics of the forest that once covered all the district.
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