FIRST BOOK. 



GENERAL RELATIONS BETWEEN THOSE QUANTITIES BY WHICH THE 

 MOTIONS OF HEAVENLY BODIES ABOUT THE SUN ARE DEFINED. 



FIEST SECTION. 



RELATIONS PERTAINING SIMPLY TO POSITION IN THE ORBIT. 



1. 



IN this work we shall consider the motions of the heavenly bodies so far only 

 as they are controlled by the attractive force of the sun. All the secondary 

 planets are therefore excluded from our plan, the perturbations which the 

 primary planets exert upon each other are excluded, as is also all motion of 

 rotation. We regard the moving bodies themselves as mathematical p6ints, and 

 we assume that all motions are performed in obedience to the following laws, 

 which are to be received as the basis of all discussion in this work. 



I. The motion of every heavenly body takes place in the same fixed 

 plane in which the centre of the sun is situated. 



II. The path described by a body is a conic section having its focus in the 

 centre of the sun. 



III. The motion in this path is such that the areas of the spaces described 

 about the sun in different intervals of time are proportional to those intervals. 

 Accordingly, if the times and spaces are expressed in numbers, any space what 

 ever divided by the time in which it is described gives a constant quotient. 



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