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However, on the side of the way by invisiblechanges to navigate to the most various forms, is a setevidence. Some time ago, talking about the subject withone scientist, a Professor, I explained my position - You areallow no discernible relationship between the circle and the hyperbola. Onezamknutaya curve, the other curve is infinite. One all the parts are similarbetween them, the other - no two pieces are similar (except for partssymmetric). One limit of known space, the other does notlimits of space, though continued indefinitely. Betweenhowever, no matter how opposite these curves in all their properties, theycan be associated next to posledstviya curves, of which none will bedelicately different from the next. Thus, if weto cut a cone by a plane at right angles to its axis we get a circle.If, instead of perfectly right angles, the plane will make with the axis an angle in89o59', we will have an ellipse which no human eye, even whenthe most accurate compass, unable to distinguish from the circle. Slimminggradually the angle of the ellipse will first be made faintly eccentric,then clearly eccentric and soon becomes so elongated shapethat will no longer be any obvious similarities with a circle. Whencontinue this process, the ellipse passes insensibly into a parabola, and finallydue to the further reduction of the angle to the hyperbola. Here we getfour different species of curve - circle, ellipse, parabola and hyperbola, havingtheir specific features and individual equations; but the first and last of them,being completely opposite in nature, connected asthe members of one series, obtained as a result of only one processinsensitive changes.
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