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Let a man of good parts know all the maxims generally made use of in mathematics ever so perfectly, and contemplate their extent and consequences as much as he pleases, he will, by their assistance, I suppose, scarce ever come to know that the square of the hypothenuse in a right-angled triangle is equal to the squares of the two other sides.
Let us change the scene to a classic concert of quite another kind. In a quiet West-end street, we are in a room of singular construction. It is in the form of a right-angled triangle; and at the right angle, upon a small dais, is placed the pianoforte and the desks, and so forth, for the performers.
"And what for?" Bud wanted to know, "He got out this way!" said Old Billee quietly, as he leaned over the cot and pushed with his hand against the side of the tent. A right-angled opening was disclosed, cut with a sharp knife. The loose point was at the bottom, and once Four Eyes had slipped out, the cut flap hung down in place, not disclosing, in the dim light, that the canvas had been cut.
In connection with the idea that God was a Geometer, must be taken the contention held by the Egyptians, and after them the Greeks and Arabs, that the Right-Angled Triangle symbolised the nature of the Universe; it was called the law of the three squares, because in every Right-Angled Triangle, as expounded by the Pythagorean Theorem, the squares, formed on the two sides containing the Right Angle, must together be exactly equal to the square on the third side, whatever the shape of the triangle may be.
WHAT IS IT? "We come into the world," said Epictetus, "with no natural notion of a right-angled triangle, or of a quarter-tone, or of a half-tone; but we learn each of these things by a certain transmission according to art; and for this reason those who do not know them do not think that they know them.
The teaching of drawing was also very incomplete, especially in its first commencement; but drawing from right-angled prisms with equal sides, in various lengths, which was one of the exercises required at a later stage, and drawing other mathematical figures by means of which the comprehension of the forms of actual objects of every-day life might be facilitated were much more to my mind.
The centre of the P'hra-mene is a lofty octagon; and directly under the great spire is a gorgeous eight-sided pyramid, diminishing by right-angled gradations to a truncated top, its base being fifty or sixty feet in circumference, and higher by twenty feet than the surrounding buildings. On this pyramid stood the urn of gold containing the remains of the royal child.
There were patios and pergolas in proportion, and all the walls, with their many right-angled juts and recessions, arose out of a bed of greenery and bloom.
"Guess we'll have to resort to first principles, and draw pictures for them," said Mark. Just then Jack uttered an exclamation, and pointed to the head of the leader. "What's he doing? Making faces at you?" asked Mark. "No; but look at that triangle!" exclaimed Jack. "It's a right-angled one." "Well, what of it?"
Thus they crawled along until they reached the turn-bridge, where the right-angled change in direction gave them relief. The river was full of choppy waves, considerable in size. As they crossed, the SPRITE darted beneath them, lowering her smokestack as she went under the bridge. They entered Main Street, where was a great banging and clanging of swinging signs and a few loose shutters.
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