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When we demonstrate the forty-seventh proposition of Euclid, it is not necessary that the words should raise in us an image of all right-angled triangles, but only of some one right-angled triangle: so in algebra we need not, under the symbol a, picture to ourselves all things whatever, but only some one thing; why not, then, the letter itself?
In arithmetic, where the sum of the squares of the two sides of a right-angled triangle is illustrated by an example and later on in geometry the same proposition is taken up in a different way and proved as a universal theorem, new and interesting light is thrown upon an old problem of arithmetic.
Jameson was marching. The Boers in the night had been reinforced by men and with artillery and Maxims. Their position was an exceedingly strong one on an open slope, but along a ridge of rocks cropping out of it. It was a right-angled position and Dr. Jameson attacked them in the re-entering angle, thus having fire on his front and flank.
That proposition was the sovereignty of all the Netherlands, save Holland and Zeeland, under a constitution maintaining the reformed religion and the ancient laws and privileges of the respective provinces. But the death of Francis of Anjou had brought about a considerable change in French policy. It was now more sharply defined than ever, a right-angled triangle of almost mathematical precision.
"I don't exactly like to take the responsibility," wavered this modern Faint-Heart. "I don't want you to take the responsibility," I ejaculated, with volcanic vehemence. "I'll take the responsibility. You take the hoe." These duty-people do infuriate me. They are so afraid to do anything that isn't laid out in a right-angled triangle.
Then came in lead-glass screens screens of glass made with a lead percentage. Now, as if science had prepared for this great emergency, operators use gloves saturated with a lead solution, and right-angled instruments, and operate directly in the ray.
"But how in the mischief," thought he, "am I to find anything here?" He held up his lantern and looked about. "I can't move these rocks to see what is under them." As he gazed around, he noticed that the southeast corner seemed to be more regular than the rest of the wall of the cave. In fact, it was almost a right-angled corner, and seemed to have been roughly cut into that shape.
It is characteristic of this type of mind to be interested in the tangibilities of geometry, hence it is not surprising to be told that Pythagoras "carried that science to perfection." The most famous discovery of Pythagoras in this field was that the square of the hypotenuse of a right-angled triangle is equal to the squares of the other sides of the triangle.
At a distance of a couple of miles from the now towering cliffs, the river made a sharp, right-angled turn to the west, and was no longer of use to them on their journey. Maskull stared up doubtfully. "It's a stiff climb for a hot morning." "Let's rest here a little," said she, indicating a smooth flat island of black rock, standing up just out of the water in the middle of the river.
He had no reason to suppose that this day more than another he would find her, but there, half a mile from White Farm, he came upon her, standing, watching a lintwhite's nest. They walked together, and when that little, right-angled, infant fellow of the glen opened to them they turned and followed its bright rivulet to the green hidden hollow. The earth lay warm and dry, clad with short turf.
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