"Right-angled" Quotes from Famous Books
 ... propositions of Euclid, but especially those which concern the equality of two figures, by cutting the one in pieces, and putting the pieces together again to make the other. In this manner, by cutting carefully in parts the squares on the two sides of the right-angled triangle, and arranging these parts carefully, one makes from them the square on the hypotenuse; that is demonstrating empirically the 47th proposition of the first book of Euclid. Now supposing that some of these pieces taken from ...
— Theodicy - Essays on the Goodness of God, the Freedom of Man and the Origin of Evil • G. W. Leibniz
... 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. Instantly Burke was in the corner. He found the eastern wall quite smooth for a space about a foot wide and extending about two yards from the floor. In this he perceived lines of crevice marking ...
— The Adventures of Captain Horn • Frank Richard Stockton
... this: What is the figure representing the acceleration of the motion of a piston, controlled by a crank which revolves with a uniform velocity? I stated it to be a right-angled triangle, and indicated, as I supposed, clearly enough, a simple method by which this could be shown. Your correspondent claims that the calculation, according to my own rule, gives a figure of a totally different form, and one that shows the acceleration, as well ...
— Scientific American, Volume XXIV., No. 12, March 18, 1871 • Various
... have shown the azimuth of Polaris to be a function of the latitude, and as the latitude is now known, we may proceed to find the required azimuth. For this purpose we have a right-angled spherical triangle, Z S P, Fig. 4, in which Z is the place of observation, P the north pole, and S is Polaris. In this triangle we have given the polar distance, P S 10 19' 13"; the angle at S 90; and the distance Z P, being the complement of the latitude as found above, or 90—L. ...
— Scientific American Supplement No. 360, November 25, 1882 • Various
... worked out the proof of the forty-seventh proposition with Mr. Battersby, a young Cambridge man who was curate to Mr. Philpott and who took us on in mathematics. The realisation of the absolute, unalterable fact that in every right-angled triangle the square of the side subtending it is equal to the squares of the sides containing it, filled me with the kind of joy and glory that one feels on reading for the first time Keats's Ode to a Nightingale or one of the great passages ...
— The Adventure of Living • John St. Loe Strachey
... fire-doors toward the rear wall of the building, and 7 ft. distant from it, and above this fire-room and the boilers there was erected a coal-bin of 500 tons capacity. The rear wall of the compressor-house formed the north wall of the bin, the section of which was an isosceles right-angled triangle. Coal was delivered by dumping wagons into a large vault constructed under the sidewalk on 34th Street, and was taken from there to the bin by a ...
— Transactions of the American Society of Civil Engineers, vol. LXVIII, Sept. 1910 - The Site of the Terminal Station. Paper No. 1157 • George C. Clarke
... said, with an ecstasy as if he announced the world's war suddenly over, all oceans safe, all peoples free. He led the way up the cramped white-shell walk with a ceremonial precision that gave the caller time to notice the garden. It was hardly an empire. It lay on either side in two right-angled figures, each, say, of sixty by fourteen feet, every foot repeating florally the smile of the child. The rigid beds were curbed with brick water-painted as red as Cupid's gums. The three fences were green with vines, and here and there against them bloomed tall evergreen shrubs. At one upper corner ...
— The Flower of the Chapdelaines • George W. Cable
... is four parts, the entablature 3, and the intermediate column 12 (Illustration 74). The affinity between 4 and 7, revealed in the fact that they express (very nearly) the ratio between the base and the altitude of the right-angled triangle which forms half of an equilateral, and the musical interval of the diminished seventh, is architecturally suggested in the Palazzo Giraud, which is four stories in height with seven openings ...
— The Beautiful Necessity • Claude Fayette Bragdon
... different shapes, somewhat in the manner shown in the illustration. The puzzle is to give the three measurements for each of the four districts in the smallest possible numbers—all whole furlongs. In other words, it is required to find (in the smallest possible numbers) four rational right-angled triangles of equal area. ...
— The Canterbury Puzzles - And Other Curious Problems • Henry Ernest Dudeney
... to be used for the binding should be folded through the middle lengthwise; then, a beginning being made at one corner of the padding, the edge should be basted, half on one side and half on the other. Right-angled corners should be formed. When basted all around, the tape should be sewn on each side ...
— Ontario Teachers' Manuals: Household Science in Rural Schools • Ministry of Education Ontario
... 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. ...
— The English Governess At The Siamese Court • Anna Harriette Leonowens
... answered the engineer. "We were doomed to execute a series of right-angled triangles all through our erratic course. From the Alkali Desert—or rather, Three Forks Camp, which was our halting-place—we made for the Rocky Mountains, so as to reach the Yellowstone River on this side. And that was where we had such ...
— Picked up at Sea - The Gold Miners of Minturne Creek • J.C. Hutcheson
... Ainsworth has not attempted to account for this phenomenon, which, however, is quite susceptible of explanation. A line dropped from an elevation of 25,000 feet, perpendicularly to the surface of the earth (or sea), would form the perpendicular of a right-angled triangle, of which the base would extend from the right angle to the horizon, and the hypothenuse from the horizon to the balloon. But the 25,000 feet of altitude is little or nothing, in comparison with the extent of the prospect. In other words, the base and hypothenuse of the supposed triangle ...
— The Works of Edgar Allan Poe - Volume 1 (of 5) of the Raven Edition • Edgar Allan Poe
... a bowery wilderness of flowers which would have delighted Anne's heart at any time less fraught with destiny. It was encircled by huge old willows and tall firs, beneath which flourished flowers that loved the shade. Prim, right-angled paths neatly bordered with clamshells, intersected it like moist red ribbons and in the beds between old-fashioned flowers ran riot. There were rosy bleeding-hearts and great splendid crimson peonies; white, fragrant narcissi and thorny, sweet Scotch ...
— Anne Of Green Gables • Lucy Maud Montgomery
... 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. The Great Year of the Pythagorean Philolaus seems to have been different, and that of the Stoics ...
— The Idea of Progress - An Inquiry Into Its Origin And Growth • J. B. Bury
... 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 ...
— A Voyage to Arcturus • David Lindsay
... breakfast,— i.e., a little after seven,—when as yet in shady parts of the grounds the dazzling jewelry of the early dews had not entirely exhaled. So standing, and so occupied, suddenly we were alarmed by shouts as of some great mob manifestly in rapid motion, and probably, at this instant taking the right-angled turn into the lane connecting Greenhay with the Oxford Road. The shouts indicated hostile and headlong pursuit: within one minute another right-angled turn in the lane itself brought the uproar fully upon the ear; and it became evident ...
— Autobiographic Sketches • Thomas de Quincey
... the instruction they gave was altogether wasted. For instance, I learnt geometry for four or five years without grasping the simplest elements of the science. The principles of it remained so foreign to me that I did not even recognise a right-angled triangle, if the right angle were uppermost. It so happened that the year before I had to sit for my examinations, a young University student in his first year, who had been only one class in front of the rest of us, offered us afternoon instruction in trigonometry ...
— Recollections Of My Childhood And Youth • George Brandes
... shoulders, well-built limbs, firmly knit, and tough as iron. His quiet but resolute look was not willingly cast downwards, his grey hair, brushed up in front, was as abundant as if he were still young. The straight lines of his nose formed a geometrically-drawn right-angled triangle. No moustache; his beard cut in Yankee fashion bedecked his chin, and the two upper points met at the opening of the lips and ran up to the temples in pepper-and-salt whiskers; teeth of snowy whiteness were symmetrically placed on the borders of a clean-cut mouth. The head of one of those ...
— Godfrey Morgan - A Californian Mystery • Jules Verne
... contained within the planes of the crystal. Yet to this line and triangle you deny reality. To mathematical truth, you deny compulsive force. You hold that an equilateral triangle may, to you and all other human individuals, be a right-angled triangle if you choose to imagine it so. Allow me to say, without assuming any claim to superior knowledge, that to me your logic results in a different conclusion. If you are compelled, at one point or another of the chain of being, to deny existence to a substance, surely it should ...
— Mont-Saint-Michel and Chartres • Henry Adams
... will depend the success of your boat. Get a square bar of cast steel, 6 feet long, cut off 22 inches for third runner, and divide the rest in halves, across. Shape two forward runners and one hind one as shown in Fig. 1. The bearing surface is a right-angled edge, as shown in Fig. 3. This sharp edge holds the ice firmly without much friction. Holes are bored two inches up into the cross-bars, near their ends, and the runners driven in and fastened with rivets. After the runners are forged, they should be finished with a file and emery paper if not ...
— St. Nicholas Magazine for Boys and Girls, Vol. 5, January 1878, No. 3 • Various
... which festooned it in all quarters, and gave it an appearance of unutterable desolation. The now familiar feeling, that I had seen the place before, filled my mind the first moment, and passed away the next. A broad, right-angled staircase, with massive banisters, rose from the middle of the hall. This staircase could not have originally belonged to the ancient wing which I had observed on my first approach, being much more modern; but ...
— The Portent & Other Stories • George MacDonald
... unlearned and ignorant, I will first state that a cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which remains fixed. The fixed side is called the axis of the cone. Conic sections are obtained by cutting the cone by planes. It may easily be proved that if the angle between the cutting plane and the axis be equal to the angle between ...
— The Romance of Mathematics • P. Hampson
... drearily, make abundance of wry faces, and thought himself but indifferently paid for his attention, when he shared the vast discovery of Pythagoras, and understood that the square of the hypotenuse was equal to the squares of the other two sides of a right-angled triangle. He was ashamed, however, to fail in his undertaking, and persevered with great industry, until he had finished the first four books, acquired plane trigonometry, with the method of algebraical calculation, and made himself ...
— The Adventures of Peregrine Pickle, Volume I • Tobias Smollett
... They are so afraid to do anything that isn't laid out in a right-angled triangle. Every path must be graded and turfed before they dare set their scrupulous feet in it. I like conscience, but, like corn and potatoes, carried too far, it becomes a vice. I think I could commit a murder with less hesitation than some people buy a ninepenny calico. And to see that man ...
— Atlantic Monthly, Vol. 9, No. 55, May, 1862 • Various
... universal to represent to our mind all other figures of three sides. But when we remark more particularly that of figures of three sides, some have a right angle and others not, we form the universal idea of a right-angled triangle, which being related to the preceding as more general, may be called species; and the right angle the universal difference by which right-angled triangles are distinguished from all others; and farther, because the square of the side which sustains the ...
— The Principles of Philosophy • Rene Descartes
... convenience of observers in the slippery and difficult floor of this gallery, we find that upon the top of these benches or ramps, near the angle where they meet the wall, "there are little spaces cut in right-angled parallel figures, set on each side opposite one another, intended no question for ...
— The Contemporary Review, Volume 36, September 1879 • Various
... years of her time and a great deal of her parents' money in equipping herself for a career that she is never going to have, the wretched creature goes and gets married, and in a few years she has forgotten which is the hypotenuse of a right-angled triangle, and she doesn't care. She has much better ...
— My Discovery of England • Stephen Leacock
... 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. The knowledge that 'the whole is equal to all its parts,' and 'if you take equals from equals, the remainder will be equal,' &c., helped him not, I presume, to this demonstration: and a man may, I think, pore ...
— An Essay Concerning Humane Understanding, Volume II. - MDCXC, Based on the 2nd Edition, Books III. and IV. (of 4) • John Locke
... went through the proposition about the hypothenuse of a right-angled triangle, and appended the words of ...
— The Dodge Club - or, Italy in 1859 • James De Mille
... skipper, and probably for his wives and children, as well as his passengers and the whole of his crew. She has a heavy, rough spar for a mast, tapering towards the head and raking forward. The sail which they are now just hoisting is, in shape, like a right-angled triangle, with a parallelogram below its base; the hypothenuse or head of the sail is secured to a yard, like an enormous fishing-rod; the halyards are secured to it about a third of the way from the butt-end, and it is hoisted close up to the head of the mast. ...
— The Three Commanders • W.H.G. Kingston
... 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. The three Henrys and their partizans divided the realm into three hostile camps—threatening each other in simulated peace since the treaty of Fleig (1580), which had put an end to the "lover's war" of the preceding year,—Henry of ...
— The Rise of the Dutch Republic, 1555-1566 • John Lothrop Motley
... triangles, they must know something about mathematics and geometry. Suppose we draw for them that problem in geometry which states that the sums of the squares constructed on the base and altitude of a right-angled triangle is equal to the square constructed on the hypotenuse? If he knows that, maybe we can get to ...
— Through Space to Mars • Roy Rockwood
... metaphysical opinion that everything divine is formed of three parts; and accordingly, on the Theban monuments we often see the gods in groups of three. They worshipped Osiris, Isis, and Horus under the form of a right-angled triangle, in which Horus was the side opposite to the right angle. The favourite part of their mythology was the lamentation of Isis for the death of her husband Osiris. By another change the god Horus, who used to be ...
— History Of Egypt From 330 B.C. To The Present Time, Volume 11 (of 12) • S. Rappoport
... this airy, fantastic idea of irregular grace and bewildered melancholy any one can play Hamlet, as we have seen it played, with strut, and stare, and antic right-angled sharp-pointed gestures, it is difficult to say, unless it be that Hamlet is not bound, by the prompter's cue, to study the part of Ophelia. The account of ...
— Lectures on the English Poets - Delivered at the Surrey Institution • William Hazlitt
... right-angled bend in the road, disclosing a straggling hamlet in a hollow below, and, farther away in the distance, a ...
— The Miracle Man • Frank L. Packard
... (c. ὑπο {hypo} and acc. or simple acc.), to stretch under, or, in its Latin form, to subtend, which term is used quite generally for 'to be opposite to'; in our phraseology the word hypotenuse is restricted to that side of a right-angled triangle which is opposite to the right angle, being short for the expression used in Eucl. i. 47, ἡ την ορθην γωνιαν ὑποτεινουσα πλευρα {hê tên orthên gônian hypoteinousa pleura}, 'the side subtending the right angle', which accounts for the feminine participial ...
— The Legacy of Greece • Various
... not always stand for ideas. The definition of the word triangle as a three-sided figure bounded by straight lines, makes demands upon us which our faculties of imagination are never fully able to meet; for the triangle that we represent to ourselves is always either right-angled or oblique-angled, and not—as we must demand from the abstract conception of the figure—both and neither at once. The name "man" includes men and women, children and the aged, but we are never able to represent a man except as an individual of a definite age and sex. Nevertheless we are in a ...
— History Of Modern Philosophy - From Nicolas of Cusa to the Present Time • Richard Falckenberg
... 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 ...
— The Boy Ranchers on the Trail • Willard F. Baker
... of the finite and infinite, and place ourselves in the conception of order. Can God make a round circle, a right-angled square? Certainly. ...
— The Philosophy of Misery • Joseph-Pierre Proudhon |
