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And this is the nature and use of geometry, to run us up to such appearances, as, by reason of their simplicity, cannot lead us into any considerable error. I shall here take occasion to propose a second observation concerning our demonstrative reasonings, which is suggested by the same subject of the mathematics.
Hence anything which will curtail our sufferings and add to our pleasures or our powers, should be sought as the highest good. Geometry is desirable, not as a noble intellectual exercise, but as a handmaid to natural philosophy. Astronomy is not to assist the mind to lofty contemplation, but to enable mariners to verify degrees of latitude and regulate clocks.
He could change iron and lead into silver and gold; he discovered the elixir of life, and might have been living even to this day had he thought it worth while to do so. There was a student at the university whose name was Gebhart, who was so well acquainted with algebra and geometry that he could tell at a single glance how many drops of water there were in a bottle of wine.
The geometry of Egypt and the astronomy of Babylon remained where the necessity of the pyramid-builders and the superstition of the astrologers had carried them. Even the art of war was in a rudimental stage. In battle, huge multitudes were precipitated upon one another. There are some evidences of strategy, when we reach the campaigns of Cyrus.
The "Mezzo Cammin" is a line too narrow for their eager steps. Proportion is the one quality in emotional geometry which is left out of their lesson of life. Their grammar deals only with superlatives; and the positive seems to them inelastic, dead and common-place. Imaginative sympathy colours and transforms the whole picture of existence.
His father Fazio was a geometrician of repute and a student of applied mathematics, and, though his first desire was to make his son a jurisconsult, he gave Jerome in early youth a fairly good grounding in arithmetic and geometry, deeming probably that such training would not prove a bad discipline for an intellect destined to attack those formidable tomes within which lurked the mysteries of the Canon and Civil Law.
Drawing, natural science, gymnastics, and manual training are entirely new, while language lessons, history, and music have been expanded to include much that is new for lower grades. Still other studies are even now seeking admission, as modern languages, geometry, and sewing.
"Are you going to try that again?" asked Mark, as he and his chum walked along to their geometry class. "Sure," replied Jack. "I want that to succeed. I know I am on the right track."
Familiarly associated in general apprehension with that inductive triad known as "Kepler's Laws," which form the foundation of Celestial Geometry, it is much less generally known that he was an august and oracular soul, one of those called Mystics and Transcendentalists, perhaps the greatest genius for analogy that ever lived, that he led a truly epic life, a hero and helper of men, a divine martyr of humanity.
But still the effects, whether produced by successive or by simultaneous action, do, wholly or in part, cancel one another: what the one force does, the other, partly, or altogether undoes. There is no similar state of things in geometry. The result which follows from one geometrical principle has nothing that conflicts with the result which follows from another.
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