438 HISTORY OF FORMAL ASTRONOMY. 



which professed to give the true relation of the 

 orbits of the different planets, was thus delivered 3 

 " The orbit of the earth is a circle ; round the 

 sphere to which this circle belong describe a dode- 

 cahedron; the sphere including this will give the 

 orbit of Mars. Round Mars describe a tetrahedron ; 

 the circle including this will be the orbit of Jupiter. 

 Describe a cube round Jupiter's orbit; the circle 

 including this will be the orbit of Saturn. Now 

 inscribe in the Earth's orbit an icosahedron; the 

 circle inscribed in it will be the orbit of Venus. 

 Inscribe an octahedron in the orbit of Venus ; the 

 circle inscribed in it will be Mercury's orbit. This 

 is the reason of the number of the planets." The 

 five kinds of polyhedral bodies here mentioned are 

 the only " regular solids." 



But though this part of the Mysterium Cosmo- 

 grapliicum was a failure, the same researches con- 

 tinued to occupy Kepler's mind; and twenty-two 

 years later led him to one of the important rules 

 known to us as "Kepler's laws;" namely, to the 

 rule connecting the mean distances of the planets 

 from the sun with the times of their revolutions. 

 This rule is expressed in mathematical terms by 

 saying that the squares of the periodic times are in 

 the same proportion as the cubes of the distances ; 

 and was of great importance to Newton in leading 

 him to the law of the sun's attractive force. We 

 may properly consider this discovery as the sequel 

 3 L. TJ.-K. Kepler, 6. 



