xv j PREFACE. 



degree of generality, simplicity, and elegance, prevented my complying at 

 the time with these friendly solicitations. I was not disappointed in this ex 

 pectation, and have no cause to regret the delay. For, the methods first 

 employed have undergone so many and such great changes, that scarcely 

 any trace of resemblance remains between the method in which the orbit of 

 Ceres was first computed, and the form given in this work. Although it 

 would be foreign to my purpose, to narrate in detail all the steps by 

 which these investigations have been gradually perfected, still, in several 

 instances, particularly when the problem was one of more importance than 

 usual, I have thought that the earlier methods ought not to be wholly sup 

 pressed. But in this work, besides the solutions of the principal problems, 

 I have given many things which, during the long time I have been en 

 gaged upon the motions of the heavenly bodies in conic sections, struck 

 me as worthy of attention, either on account of their analytical elegance, 

 or more especially on account of their practical utility. But in every case 

 I have devoted greater care both to the subjects and methods which are 

 peculiar to myself, touching lightly and so far only as the connection seemed 

 to require, on those previously known. 



The whole work is divided into two parts. In the First Book are de 

 veloped the relations between the quantities on which the motion of the 

 heavenly bodies about the sun, according to the laws of KEPLER, depends ; 

 the two first sections comprise those relations in which one place only is 

 considered, and the third and fourth sections those in which the relations 

 between several places are considered. The two latter contain an explanation 

 of the common methods, and also, and more particularly, of other methods, 

 greatly preferable to them in practice if I am not mistaken, by means of 



