Squaring the circle

“ Under the flaming yellow stars it stood out luminous, marking the exact center of an enormous circle; a circle roofed by the radiantly flecked heavens, bounded by mountains which rose against the sky-line, abrupt as a wall, black as ink. ”

“ The same old story, the same old vicious circle, the everlastingly recurring mathematical view of things that cannot be treated mathematically; the fruitless attempt to measure the harmonious circle of the soul by the angular square of the book. What poor things our minds are, after all. ”

“ Every ultimate fact is only the first of a new series. Every general law only a particular fact of some more general law presently to disclose itself. There is no outside, no inclosing wall, no circumference to us. The man finishes his story, — how good! how final! how it puts a new face on all things! He fills the sky. Lo! on the other side rises also a man, and draws a circle around the circle we had just pronounced the outline of the sphere. ”

“ I like to think of all the points in a circle really feeling a placid satisfaction in the thought that they are equidistant from the centre! They are infinite in number, and so can well afford to despise the arrogance of a point within, and to ignore the envious murmurs of a point without! ”

“ You should establish the circle:
You should melt the world
In a circle of lovers!
Heart burn, voice lull, raise me, lower me,
With the flame of the flagrant love I awaken:
That red flames stop-flowing through the lands,
Cheeks begin to redden in fraternal receiving,
And brotherly, in a solemn circle, through the world
The wave of the song of Understanding begins to bellow... ”

“ Her brain seemed to her as a pool into which some thoughtless child that did what he liked had flung a stone, starting circle after circle, circles that grew and grew, spreading to the farther edge, and sobbing away into nothing because they could go no farther. ”

“ My neighbour snatched his cap and pulled it down on to his nose.
'What do I find so awful?' he shouted. 'Why, this: the circle is the destruction of all independent development; the circle is a hideous substitute for society, woman, life; the circle... oh, wait a bit, I'll tell you what a circle is! A circle is a slothful, dull living side by side in common, to which is attached a serious significance and a show of rational activity ”

“ Another circle stand outside, and on a given signal try to mount on the backs of the inner circle of boys. If they succeed they remain standing in this way; if not, the boy who failed must take the inside place. ”

“ And consciously or not, something is always being done to guard against a break in the circle. One wave is followed by another and the circling stream is ever flowing between the civilized nations of the world. ”

“ For similarly the uninstructed majority of mankind could not define a circle as a figure bounded by a line of which every point is equidistant from the centre: but nevertheless, when the definition is explained to them, they will accept it as expressing the perfect type of that notion of roundness which they have long had in their minds. ”

“ This chain reaches from Eternity to Eternity, ever in triangles—is not my symbol a triangle?—ever in circles—is not the symbol of the Beloved a circle? Therein is all progress base illusion, for every circle is alike and every triangle alike! ”

“ The inclination of persons in the woods to travel in a circle is unexplained. I suppose it arises from the sympathy of the legs with the brain. Most people reason in a circle: their minds go round and round, always in the same track. ”

“ Ans The investigation of the quadrature of the circle indicates the knowledge of the four vulgar elements, which are themselves composed of elementary spirits or chief principles; as the circle, though round, is composed of lines, which escape the sight, and are seen only by the mind. ”

“ You seem to mark out for yourself a certain sphere, and if you go beyond it, you think you do yourself an injury. Thus, while you have an apparent movement, you are only describing a circle, whose centre and circumference is self. ”

“ I rather gather around myself, link after link, the chains that connected me with the world; I find among my own thoughts that variety and occupation which you only experience in your intercourse with others; and I make, like the Chinese, my map of the universe consist of a circle in a square—the circle is my own empire and of thought and self; and it is to the scanty corners which it leaves without, that I banish whatever belongs to the remainder of mankind. ”

“ A circle ○ bounds the production of all its radii, tends to destroy them, and is in some sort their enemy. How is it possible that things so distinct should not be distinguished in their number as well as in their action? ”

“ There are circles of all sorts, professional, and social, and intellectual, and those who pass from one to another have to undergo mental adjustment before they can understand the language and partake in the momentum of these spheres. Such is the parsonic circle, such the sporting circle, such the circle of politicians, such the legal circle. Let a hunter pitch his rider in pink over a hedge into a ditchful of picnicing clergy and their wives and daughters, and he will be as unable to talk with them as they to entertain him. ”

“ Therefore, sitters at the circle should endeavor to do their part in producing and maintaining such harmony with both the medium, the spirits, and finally with each other—and this last is not the least, by any means. Unless there be at least a very fair degree of harmony between the several members constituting the circle, there will be something important lacking in their harmony of the circle as a whole toward the other two sides of the psychical triangle. ”

“ His work is a pebble thrown into the deep; the stir lasts for a moment, and the wave closes up, to be susceptible no more to the same impression. The circle may widen to other lands and other ages, but around him it is weak and faint. ”

“ As the most uneven shapes, when whirled into rapid and ceaseless motion, will appear a perfect circle, so, once impelled in a career that admits no pause, our life loses its uneven angles, and glides on in smooth and rounded celerity, with false aspects more symmetrical than the truth. ”

“ It is, then, possible to call the circle perfect when it is truly a circle, that is, when it is joined with its own proper or relative virtue, it is then complete in its nature, and it may then be called a noble circle. ”

“ Nature knows nothing of this precious law. Her figure is not the vertical line, nor even the spiral, but the circle—the vicious circle, according to Samuel Butler. 'Men eat birds, birds eat worms, worms eat men again.' Some stars are getting hotter, others cooler. ”

“ The circle, which is self-enclosed and at rest, and, qua substance, holds its own moments, is an immediate relation, the immediate, continuous relation of elements with their unity, and hence arouses no sense of wonderment. But that an accident as such, when out loose from its containing circumference,—that what is bound and held by something else and actual only by being connected with it,—should obtain an existence all its own, gain freedom and independence on its own account—this is the portentous power of the negative; it is the energy of thought, of pure ego. ”

“ A circle is in itself a consummate wonder of geometrical symmetry. It is the line in which the omnipotent energy delights to move. There is no fault in it to be amended. The first drawn circle and the last both embody the same complete fulfillment of a perfect design. Then look at the rays which pass from the inner to the outer circle. How beautifully they bring the greater and lesser circles into connection with each other! ”

“ The world revolves the portion of a circle; yet why that circle of a sun-centre, or that wider circle within which both suns and earths revolve, or what the centre which controls the entire system of immensity may be, he dares not affirm. Our lives are miracles, yet we are habituated to them, and name them chance. ”

“ When you sit in the circle, exerting every faculty of mind and body, with your hands on the table and your feet on the floor, all your brain forces escape through your extremities and are absorbed by the more receptive members of the circle. ”

“ The simplest symbol of it is the circle, the line which returns into itself, not the straight line produced indefinitely; and the readiest way to find it is to consider the satisfaction of desire. There we have myself and its opposite, and the return from the opposite, the finding in the other nothing but self. ”

“ There is something unutterably solemn in watching the shade creep, day by day, round a circle whose diameter man might measure with his grave or even cover with his hand, and contrasting the limits within which it acts with the spaces of time which its stealing tread measures out, and feeling that it is the faithful index of a progress before which the individual being and the universal frame of things are alike hastening to rapid and inevitable decay. ”

“ The bubbles have blended, the circles have come together, and one large circle or other curve is the result. This may be called the Law of Social Attraction. In accordance with the results of one of my previous lectures, I have taken the circle as representing the simplest form of government, which figure, in the case of the elementary settlements, must have been small.
Many of you, most noble professors, are doubtless accustomed to make experiments with the microscope. ”

“ Zan turned over the pages till she found the place indicated and read: “‘Why do we sit in a circle around a fire? That is an old story and a new one.
“‘Then, too, a circle is the best way of seating a group. Each has her place and is so seated as to see everything and be seen by everybody. As a result each feels a very real part in the proceedings as they could not feel if there were corners in which one could hide. The circle is dignified and it is democratic. ”

“ But the pendulum must necessarily move in a ‘great circle,’ and hence to counteract its tendency to deviate into a ‘small circle,’ a correctory movement is constantly going on, to which the lengthening of the period necessary to complete a revolution must be ascribed. ”

“ In short, a child of nature would wonder why people should take the trouble of submitting their feet to [164] a sort of rhythm just enough to shackle their freedom, and prevent the luxury of perfect inanition. Well, thought I to myself, this society is fashionable. These men and women move in what is called the first circle. ”

“ But this idea of the circle—an idea which, in view of all ordinary geometry, is merely the mathematical, as contradistinguished from the practical, idea—is, in sober fact, the practical conception which alone we have any right to entertain in regard to the majestic circle with which we have to deal, at least in fancy, when we suppose our system revolving about a point in the centre of the Galaxy. Let the most vigorous of human imaginations attempt but to take a single step towards the comprehension of a sweep so ineffable! ”

“ SOME PASSAGES IN THE LIFE OF MR. DANIEL WHEELWRIGHT.
CHAPTER I.
A DISQUISITION ON CIRCLES.
"In circle following circle."
The horse at the cider-mill; the mules in the press-room of the American Tract Society; and the watchman who walks his drowsy round until he falls asleep; are not the only beings that spend their lives in traversing a circle. ”

“ We are not going round in circles, we are mounting higher, the circle is a spiral, we have already climbed up many steps.” ”

“ And, moreover, were the circle drawn round each a very contracted one, every man of talent, every genius, in so far as he is in some degree a magician and an enchanter, possesses a secret entirely his own, whereby to perform prodigies within this circle and work wonders there. ”

“ For the first, indeed, and most proximate circle is that which every one describes about his own mind as a centre, in which circle the body, and whatever is assumed for the sake of the body, are comprehended. ”

“ This inward movement of the men is itself balanced by the corresponding outward movement when they go to get more cushions, which is in turn balanced when they come back. Finally this pattern of a circle contracting, expanding, and contracting again, harmonizes perfectly with the fixed circle which is formed when the men seat themselves. ”

“ We are moveless in the centre of the flat, unchanging circle of things. Our magic carpet (or table-cloth) may be taking us on a trip to America or Europe, as the case may be, but so far as our senses are concerned we are standing still for ever and ever. There is nothing that registers progress to the mind. The circle we looked out on last night is indistinguishable from the circle we look out on this morning. Even the sky and cloud effects are lost on this flat contracted stage, with its hard horizon and its thwarted vision. ”

“ I pushed my way through the throng of women and boys, who made up the outer circle of spectators, and soon found myself among the men, who made way for me, until I reached a position from which I could see all that was going on within the circle about which they stood. ”

“ If there are more than fifteen or twenty guests, choose about six men and six girls to form the circle. Even “Mimic” becomes monotonous in a large circle. Those forming the circle are seated, men beside their partners, the leader taking the part of one of the girls. She begins the action by doing something to the man at her right who in turn must mimic her action exactly to the girl to his right, and so the action goes all around the circle till it comes back to the leader who starts a new one. ”

“ By the large, conventional things, or customs, appear to be products of ideation or thinking. Now a band circle is clearly a scheme, a conception, that may well have originated within the mental activities of a single individual, a true psychic accident. ”

“ Every motion is in a circle. If you can take up a stone, and project it into space, and then live long enough, that stone, if it meets with no obstruction, will come back exactly to your hand. A straight line, infinitely projected, must end in a circle. Therefore, this idea that the destiny of man is progressing ever forward and forward, and never stopping, is absurd. ”