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42 unduly favoured. His genius, in his case certainly "an infinite capacity for taking pains," enabled him out of his medley of hypotheses, mainly unsound, by dint of enormous labour and patience, to arrive thus at the first two of the laws which established his title of "Legislator of the Heavens".



1.—In Ptolemy's excentric theory, A may be taken to represent the earth, C the centre of a planet's orbit, and E the equant, P (perigee) and Q (apogee) being the apses of the orbit. Ptolemy's idea was that uniform motion in a circle must be provided, and since the motion was not uniform about the earth, A could not coincide with C; and since the motion still failed to be uniform about A or C, some point E must be found about which the motion should be uniform.

2.—This is not drawn to scale, but is intended to illustrate Kepler's modification of Ptolemy's excentric. Kepler found velocities at P and Q proportional not to AP and AQ but to AQ and AP, or to EP and EQ if EC = CA (bisection of the excentricity). The velocity at M was wrong, and AM appeared too great. Kepler's first ellipse had M moved too near C. The distance AC is much exaggerated in the figure, as also is MN. AN = CP, the radius of the circle. MN should be