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the phenomena, I conceived that I also might take the liberty of trying whether, on the supposition of the earth's motion, it were possible to find better explanations of the revolutions of the celestial orbs than those of ancient times. Having then assumed the motions of the earth that are hereafter explained, by long and laborious observation I found at length that if the motions of the other planets be likened to the revolution of the earth, not only their observed phenomena follow from the suppositions, but also that the several orbs, and the whole system, are so connected in order and magnitude that no one part can be transposed without disturbing the rest and introducing confusion into the whole universe." He looked, he here says, for a new theory because the old one was unsymmetric; and his new theory satisfies because it consistently explains the facts of observation and because it was symmetric. Symmetry of the kind referred to is not essential to a true theory. If any theory explains every fact of observation quantitatively as well as qualitatively, it is to be accepted. Copernicus was not free from hampering presuppositions any more than his predecessors.

"We must admit," he says, "that the celestial motions are circular, or else compounded of several circles, since their inequalities observe a fixed law, and recur in value at certain intervals, which could not be unless they were circular; for the circle alone can make that which has been recur again." In writing this passage his mind was closed to every idea but one. Copernicus knew, far better than most of us, that ovals and ellipses might also serve to represent recurring values, but the thought did not even cross his mind in connection with celestial motions. He was committed to circular motions exclusively, from the outset.

"We are therefore not ashamed to confess," he says, "that the whole of the space within the orbit of the moon, along with the center of the earth, moves around the sun in a year among the other planets; the magnitude of the world (solar system) being so great that the distance of the earth from the sun has no apparent magnitude (is indefinitely small) when compared with the sphere of the fixed stars. . . . All which things, though they be difficult and almost inconceivable, and against the opinion of the majority, we, in the sequel, by God's favor, will make clearer than the sun, at least to those who are not ignorant of mathematics."

The system of Copernicus required thirty-four circles and epicycles—four for the moon, three for the earth, seven for the planet Mercury and five for each of the other planets. Cumbrous as this apparatus appears to us, it was a distinct simplification of the Ptolemaic system as taught in the sixteenth century. Fracastor, writing in 1538, employed sixty-three spheres to explain the celestial motions.

One word must be said of the theory of trepidation which Coper-