Circle

“ In every framework of thought which man had ever devised, the circle was prominent, vital. It played its part in every creed of every race, of every time. It was as essential to the ancient arts of magic as to the current methods of science. It played its part in the movement of planets, the shape of stars, perhaps the essence of the total universe.
Man might be too didactic in requiring that awareness develop a physical science comparable to his own, but surely awareness, whatever form it took, would know the circle. ”

“ 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. ”

“ In any circle, the nearer the points of the circumference are to the centre, the closer they will necessarily be to one another. As we draw nearer, each for himself, to our Centre, we shall feel that we have approximated to all those who stand round the same centre, and draw from it the same life. ”

“ 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 circle, therefore, is the cause of ornament to all things, even to the last participations, and leaves nothing destitute of itself, since it supplies beauty, similitude, formation, and perfection to the universe. ”

“ All things growing out of the ground are round, as the trunk of a tree or the stem of an herb. The edge of the world is a circle, hence the circle is a symbol of the world and of the winds which travel to us from all points on the edge of the world. The sun and the moon which mark the day and the night travel in a circle above the sky; for this reason the circle is a symbol of these divisions of time, and of the year, and so is the symbol for all time. ”

“ Thus, the proposition, “A circle is a plane figure bounded by a line all the points of which are at an equal distance from [pg 170] a given point within it,” was considered by them, not as an assertion that any real circle has that property, (which would not be exactly true,) but that we conceive a circle as having it; that our abstract idea of a circle is an idea of a figure with its radii exactly equal.
Conformably to this it is said, that the subject matter of mathematics, and of every other demonstrative science, is not things as they really exist, but abstractions of the mind. ”

“ Every lesser circle of the sphere, will appear a circle to the eye, placed, as we have supposed all along, in the centre of the sphere. And, on the other hand, every visible circle will appear to coincide with some lesser circle of the sphere. ”

“ It seems to me, sir, if we would invite from the locality in which we want to introduce a circle, one or two persons to visit our own circle and see the work we are doing, we might thus incite and be enabled to form a circle, taking the one or two members whom we have invited as the nucleus. ”

“ A circle has proverbially neither beginning nor end. In what order then are we to consider these signs? In the heavens they form a never-ending circle. Where is the beginning and where is the end of this circle through which the sun is constantly moving? ”

“ 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 ”

“ You must understand what is meant by a great circle: it is a circle dividing the sphere into equal parts. Its plane therefore passes through the centre of the sphere. Now, our use of the celestial globe or sphere is founded on the assumption that it is a representation of the heavens, on the supposition that the eye of the observer is at the centre of the sphere. ”

“ The circle represents the round earth. The lines drawn from the two falling balls to the middle of the circle show how they would come together at the centre of the earth if they could keep on, instead of being stopped when they reach the ground. And all the things that are falling any where on the earth are going toward the same point.
Now why is this? What is it that makes things in the air come to the ground when they are not held up? They do not come down of themselves. They are drawn down. The earth [3161] attracts or draws them. ”

“ DEFINITION XVI. And that Point is called the Centre of the Circle.
A Circle is the first, most simple, and most perfect of figures. For it excels all solids, because it exists in a more simple place; but it is superior to the figures subsisting in planes, on account of its [159] similitude and identity. And it has a corresponding proportion to bound, and unity, and a better co-ordination of being. Hence, in a distribution of mundane and super-mundane figures, you will always find that the circle is of a diviner nature. ”

“ 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. ”

“ Symbol. An enormous circle, or transparent sphere, floats in the air and men are putting their heads into this circle.
Interpretation. In this symbol everything that I was thinking of is expressed. The validity of the transsubjective concerns all men without exception; the circle goes through all the heads. This validity must have its cause in something common to all. The heads all belong to the same apparently homogeneous sphere. Not all judgments are transsubjective; with their bodies and limbs men are outside of and under the sphere and stand on the earth as separate individuals. ”

“ 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. ”

“ The circle was undoubtedly known to the early civilizations, its simplicity specially recommending it as an object for study. Euclid defines it (Book I. def. 15) as a “plane figure enclosed by one line, all the straight lines drawn to which from one point within the figure are equal to one another.” In the succeeding three definitions the centre, diameter and the semicircle are defined, while the third postulate of the same book demands the possibility of describing a circle for every “centre” and “distance.” ”

“ A body of men walking in a circle remain together as a body within the circumference of the circle as it moves with the earth; change their paths to a cycloid directed to a distant point, and the body of men will move away in that direction; change their paths to parallel right lines, and as a body they may soon be a mile away and still in a circle. ”

“ The circle represents the Infinite, without beginning or end; the straight line represents the finite, which has both beginning and end. The sphere represents self-existent and eternal individuality and Mind; the straight line, a belief in a self-existent and temporary material existence. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Describe a circle and mark its centre, (fig. 1.)
By constant practice the pupil will be able to draw a circle, and mark its centre with great exactness. The monitor with a pair of dividers will prove it. ”

“ Instead of two bands meeting each other in lines in opposite directions, and parting, to meet again at the other side of the room, they were formed into a circle, one-half moving in one direction, and one-half moving in the opposite, by which means the circle was never broken. ”

“ If from any point without a circle there he drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained in the whole line which cuts the circle, and the part of it without the circle, be equal to the square on the line which meets the circle, the line which meets the circle shall touch it. ”

“ The value of the circle as a unifying and therefore as a simplifying agent cannot be overestimated, especially in solving the problems which occur in composition where the circle has not been a part of the original scheme, but where, when applied, it seems to bring a relief to confusion and disorder. ”

“ The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end. It is the highest emblem in the cipher of the world. ”

“ All great circles of the sphere cut each other in two points diametrically opposite, and consequently their points of section are one hundred and eighty degrees apart. A great circle, which passes through the pole of another great circle, cuts the latter at right angles. The great circle which passes through the pole of another great circle, and is at right angles to it, is called a secondary to that circle. ”

“ Just as the circle may be defined either as a plane surface or as the bounding line which is the locus of a point in a plane at a given distance from a fixed point, so a sphere may be defined either as a solid or as the bounding surface which is the locus of a point in space at a given distance from a fixed point. In higher mathematics the circle is defined as the bounding line and the sphere as the bounding surface; that is, each is defined as a locus. ”

“ 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. ”

“ The leader of the circle, recognizing the signs of the presence of spirits in the circle, will address them and ask them whether or not there is a spirit present who wishes to convey a message to the circle, or to any one present. ”

“ Through two given points describe a circle whose common chord with another given circle may be parallel to a given line, or pass through a given point.
43. Being given the centre of a circle, describe it so as to cut the legs of a given angle along a chord parallel to a given line.
44. If concurrent lines drawn from the angles of a polygon of an odd number of sides divide the opposite sides each into two segments, the product of one set of alternate segments is equal to the product of the other set. ”

“ A circle may be described with any given point as a center and any given line as a radius. This involves the use of the second of the two geometric instruments, the compasses.
5. Any figure may be moved from one place to another without altering the size or shape. This is the postulate of the homogeneity of space, and asserts that space is such that we may move a figure as we please without deformation of any kind. It is the basis of all cases of superposition. ”

“ When a circle is made, and from its centre a number of lines are drawn to the circumference, all these lines, though ever so distant in the circumference, meet together in the point, which is in the middle. ”

“ 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. ”

“ The point by reason of its indivisibility is immeasurable, and the circle by reason of its arc cannot be exactly squared, and therefore cannot be measured with precision." Notes by Miss Hillard: "This is why the Deity is represented by a point. Paradiso, xxviii. 16: 'A point beheld I,' 'Heaven and all nature, hangs upon that point,'" etc. Bk. IV. xvi. 6, quoting Aristotle's Physics: "The circle can he called perfect when it is a true circle. ”

“ Since the sun revolves round the earth it describes a circle, and every circle must have a centre; that we know already. This centre is invisible, it is in the middle of the earth, but we can mark out two opposite points on the earth’s surface which correspond to it. ”

“ The practical value of the six-inch repeating circle may be estimated, by comparing the differences of the partial results from the mean at each station, with the correspondence of any similar collection of observations made with a circle, on the original construction, and of large dimensions ”