Circular

“ Indeed, since circular motion is against the nature of these four elements, there must be some other different body to whose nature it is conformable. There must thus be some simple and primary body, whose nature it is to be carried round in a circle, as earth is carried downwards and fire upwards. ”

“ If circular motion be made about a resting centre, and in that circle there be an epicycle whose revolution is made the contrary way, in such manner that in equal times it make equal angles, every strait line taken in that epicycle will be so carried, that it will always be parallel to the places in which it formerly was. ”

“ A person to whom the double circular motion is familiar in the lathe naturally looks upon one circle moving upon another as in simple motion, if the second circle be fixed to the revolving radius, so that one and the same point of the moving circle travels upon the fixed circle. ”

“ He that understands the natures of the circular pendulum and circular motion, will easily understand the whole ground of this principle, and will know where to find direction in nature for the true stating thereof. ”

“ Wherefore it is not requisite that the natural motions of natural bodies should be onely Circular. Next, I do not understand, why a Circular Motion cannot be gotten naturally without a precedent right motion; for, in my opinion, corporeal motions may be round or circular, without being or moving straight before; and if a straight line doth make a circle, then an imperfect figure makes a perfect ”

“ If we take a watch or other small circular object and place it at A, which we will suppose is a distance of 50 yards, we shall find that it will be only visible as a circular object, and its apparent magnitude or the angle under which it is viewed is then stated to be very small. ”

“ The larger the circle described by b the more is the spring stretched, and the greater is the force with which b is attracted towards the centre. This experiment proves that the force necessary to retain a body in a circular path must be increased when the speed is increased. ”

“ Now, we cannot recommend that the players of a film story should always be shown running around in circles. And yet their separate actions, gestures and bodily movements in general, may often be so composed that they progress in a circular path, each movement tracing an arc of a circle which nowhere touches the frame of the picture. Such circularity of motions would give unity, balance, and repose. ”

“ Suburban residents receive circulars by every other post of every kind and description, and cast them contemptuously aside. In the country the delivery of a circular is not so treated. It is certain to be read. ”

“ Valve circular, sectors, eight, umbilicus circular, without rays; border wide, cellular, with distinct rays. Inserted at a distance within the inner edge of the border are large processes, one on each of four alternate sectors, and two on each of the others. The sectors are cellulate and punctate. ”

“ To return to design in the flat. If we start with a motive of circular masses, we cannot suddenly associate them with sharp angles—I mean in our leading forms. Of course we can make a network or trellis or diaper of the angles, to form a mat, [89] ground, or a framework on which to place our broad masses, as we may see effectively done by the Chinese and Japanese. ”

“ A spiral curve is a [45] harmonious line, says the designer: repeat it, reversed, and you prolong the harmony; repeat it again, with variations, and you complete the harmony. Or, harmonious effect is produced by recurring form and line. Here is a circular form; here is a meandering line: combine and repeat them, and you get a logical and harmonious border motive. ”

“ For the principle of every thing which is moved is a circle, and the circular motion. The mathematical reasons, therefore, which fully consummate the soul, are essential, and self-moving: and the soul, by her cogitative power, diffusing, propagating, and evolving these, from her profound recesses, constitutes all the fair variety of mathematical sciences. ”

“ I have no doubt myself that it found its way into this Appendix in the fifth (? or fourth) century B.C. from a Tâoist source. Kû Hsî, in his 'Lessons on the Yî for the Young,' gives for it the figure of a circle,—thus, ○; observing that he does so from the philosopher Kâu (A.D. 1017–1073) [2] , and cautioning his readers against thinking that such a representation came from Fû-hsî himself. To me the circular symbol appears very unsuccessful. 'The Great Extreme,' it is said, 'divided and produced two lines,—a whole line and a divided line.' But I do not understand how this could be. ”

“ A circle, as the degree of its curvature is every where the same, is of all curve lines the simplest and the most easily conceived. Since it was evident, therefore, that the heavenly bodies did not move in straight lines, the indolent imagination found, that it could most easily attend to their motions if they were supposed to revolve in perfect circles. It had, upon this account, determined that a circular motion was the most perfect of all motions, and that none but the most perfect motion could be worthy of such beautiful and divine objects ”

“ And therefore this endeavour does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect ”

“ For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavour of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. ”

“ The Effects which distinguish absolute from relative motion are, the forces of receding from the axe of circular motion. For there are no such forces in circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then fill'd with water, and held at rest together with the water ”

“ Which motion we may be allowed to call circular, in the same way as Aristotle says that the air and the rain emulate the circular motion of the superior bodies; for the moist earth, warmed by the sun, evaporates ”

“ The astronomy of the ancients admitted none but uniform circular motions, and could therefore be completely cultivated by the aid of their elementary geometry. But the pure science of motion might be extended to all motions, however varied as to the speed or the path of the moving body. ”

“ By taking the circular parallels which we have there appended to the several portions of the earth respectively, and applying them to the countries in question, that are similarly situate, it will be found that the rising of the heavenly bodies will be the same for all parts within those parallels, where the shadows projected are of equal length. ”

“ The head by Van Dyck carries with it the repose which belongs to the completeness of the circle.
Like Saturn and his ring, this sphere within the circle is typical of harmony in unity, and for this reason, though detached as we know it to be, it has a greater completeness than though joined to a body. It is on this general principle that all circular compositions are based—absorption of the attention within the circuit. ”

“ Now the infinite cannot be traversed, and if the body is infinite the interval between the radii is necessarily infinite: circular motion therefore is an impossibility. Yet our eyes tell us that the heavens revolve in a circle, and by argument also we have determined that there is something to which circular movement belongs. ”

“ Every tremulous body in an elastic medium propagates the motion of the pulses on every side right forward; but in a non-elastic medium excites a circular motion. Case. 1. The parts of the tremulous body, alternately going and returning, do in going urge and drive before them those parts of the medium that lie nearest, and by that impulse compress and condense them; and in returning suffer those compressed parts to recede again, and expand themselves. ”

“ So that, if motion first by nature belong to a body first by nature, if circular motion (as being perfect) be prior to rectilinear motion, and if rectilinear motion belong to a first or a simple body, as we see both in fire and in earth, — we may be sure à fortiori that circular motion belongs to a simple body, and that there is, besides the four elements here, prior to them and more divine than them, a different body cf special nature and essence. ”

“ But the circular motion is more proper for a finite, then an infinite, because a circle-figure is perfect and circumscribed, and a straight line is infinite, or at least producible in infinite; and there may be other worlds in infinite Nature, besides these round Globes perceptible by our sight, which may have other figures; for though it be proper for Globes or Spherical bodies to move round, yet that doth not prove, that Infinite Matter moves round, or that all worlds must be of a Globous figure; for there may be as different Worlds, as other Creatures. ”

“ A body moves when it changes its place; but 64 he adds, that if water be in a vessel, the vessel being at rest, the parts of the water may still move, for they are included by each other; so that while the whole does not change its place, the parts may change their places in a circular order. ”

“ The weak point in the system of the Circles—if a humble Square may venture to speak of anything Circular as containing any element of weakness—appears to me to be found in their relations with Women. ”

“ So far as is at present known, these circular graves exist nowhere in such numbers as here, and it can hardly be doubted but that they have some connexion with the great circular rail of the Amravati Tope. That rail is unique in India, whether we consider its extent, the beauty of its sculptures, or the elaborateness of its finish. Other rails exist elsewhere surrounding dagobas or sacred spots, but none where the circle itself is relatively so much greater and more magnificent than the surrounding objects. ”

“ A medium yielding to projectiles does not recede in infinitum, but with a circular motion comes round to the spaces which the body leaves behind it. Therefore as often as a tremulous body tends to any part, the medium yielding to it comes round in a circle to the parts which the body leaves; and as often as the body returns to the first place, the medium will be driven from the place it came round to, and return to its original place. ”

“ I have therefore supposed that there is in the sun for the governing of the primary planets, and in the earth for the governing of the moon, such motion, as being received by the primary planets and by the moon, makes them necessarily appear to us in such manner as we see them. Whereas, that circular motion, which is commonly attributed to them, about a fixed axis, which is called conversion, being a motion of their parts only, and not of their whole bodies, is insufficient to salve their appearances. ”

“ Part 2 The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter for subsequent inquiry. We will now speak of those parts of the whole which are specifically distinct. Let us take this as our starting-point. All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, is their principle of movement. But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two, which are the only simple movements. ”

“ If in a fluid medium, whose parts are stirred by a body moved with simple motion, there float another body, which hath its superficies either 331wholly hard, or wholly fluid, the parts of this body shall approach the centre equally on all sides; that is to say, the motion of the body shall be circular, and concentric with the motion of the movent. But if it have one side hard, and the other side fluid, then both those motions shall not have the same centre, nor shall the floating body be moved in the circumference of a perfect circle. ”

“ If the axes be given, the curve can be approximately constructed by circular arcs in the following manner:—Let AA′, BB′ be the axes; determine D the intersection of lines through B and A parallel to the major and minor axes respectively. Bisect AD at E and join EB. Then the intersection of EB and DB′ determines a point P on the (true) curve. Bisect the chord PB at G, and draw through G a line perpendicular to PB, intersecting BB′ in O. An arc with centre O and radius OB forms part of a curve. ”

“ I say, in the first place, that the whole force and efficacy of all the particles that are situate in AE, the circle of the equator, and disposed uniformly without the globe, encompassing the same after the manner of a ring, to wheel the earth about its centre, is to the whole force and efficacy of as many particles in that point A of the equator which is at the greatest distance from the plane QR, to wheel the earth about its centre with a like circular motion, as 1 to 2. ”