ASTRONOMY. 173 



These two propositions, which have already been 

 shewn to hold of the Earth's motion, are there- 

 fore common to the motions of all the planets. 

 They were discovered by KEPLER, and were first 

 found out by him, with infinite ingenuity and la- 

 bour, when he was endeavouring to determine 

 the orbit of Mars. 



171. When the focus of an ellipse, and three 

 points in its circumference, are given, the el- 

 lipse may be described ; and hence the plane- 

 tary orbits may be determined, that is, the axis, 

 the eccentricities, and thence the equations to 

 the centres, &c. 



The application of this to find the three Elements 

 of an orbit, the Eccentricity, the place of the 

 Aphelion, and the Epoch, or radical mean place, 

 for a given time, is in LA LANDE, 1288, &c. Also 

 VIUCE'S Astronomy > vol. i. 257. See also NEU- 

 TONII Prin. Math. lib. Inius^ prop. 21. Schol. 



172. When the mean distances of the planets 

 are compared, and also their periodical times, it 

 is found that the squares of the periodical times 

 are as the cubes of the distances. 



This great general fact was also discovered by KEP- 

 LER, and is the third of the laws that bear the 

 name of that astronomer. 



173. When 



