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On the port bow arose, standing stark, cut out on the background of mist, a tall, opaque mass, vertical, right-angled, a tower of the abyss. They watched it open-mouthed. The storm was driving them towards it. They knew not what it was. It was the Ortach rock. The reef reappeared. After the Caskets comes Ortach. The storm is no artist; brutal and all-powerful, it never varies its appliances.
He had picked it up from the table and was pointing at a little hole in the side, that had escaped my notice before. "This is what you might call a right-angled camera. I point the glass out of the window and while you think I am looking through it I am really focusing it on you and taking your picture standing there beside me and out of my apparent line of vision. It would deceive the most wary."
The symbol of universal nature among the Egyptians was the right-angled triangle, of which the perpendicular side represented Osiris, or the male principle; the base, Isis, or the female principle; and the hypothenuse, their offspring, Horus, or the world emanating from the union of both principles.
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 would not willingly be rude, but the fact remains a posture in which she would not, I think, have sat for her photograph leaning back in a chintz-covered easy-chair, all the lines of direction about her parallel with the lines of the chair, her arms lying on its arms, and the fingers of each hand folded down over the end of each arm square, straight, right-angled, gazing into the fire, with something of the look of a sage, but one who has made no discovery.
Having continued this examination for about half an hour, we proceeded to enter into particulars respecting triangles; and having discoursed on the difference between isosceles triangles and scalene triangles, I observed that an acute isosceles triangle had all its angles acute, and proceeded to observe that a right-angled scalene triangle had all its angles acute.
As he first solved the problem of inscribing a right-angled triangle in a circle, he is the founder of geometrical science in Greece. He left, however, nothing to writing; hence all accounts of him are confused, some doubting even if he made the discoveries attributed to him.
"Well, my boy, I have just constructed two similar right-angled triangles; the first, the smallest, has for its sides the perpendicular pole, the distance which separates the little stick from the foot of the pole and my visual ray for hypothenuse; the second has for its sides the perpendicular cliff, the height of which we wish to measure, the distance which separates the little stick from the bottom of the cliff, and my visual ray also forms its hypothenuse, which proves to be prolongation of that of the first triangle."
To declare oneself for the opinion of the one or the other is to take sides in a civil war. There are no sects in mathematics, in experimental physics. A man who examines the relations between a cone and a sphere is not of the sect of Archimedes: he who sees that the square of the hypotenuse of a right-angled triangle is equal to the square of the two other sides is not of the sect of Pythagoras.
Heraclitus seems to have accepted it as the duration of the world between his periodic universal conflagrations. Plato derived the number from predecessors, but based it on operations with the numbers 3, 4, 5, the length of the sides of the Pythagorean right-angled triangle.
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