OF UNDISTURBED MOTION. 63 



tion, by supposing a right line to be drawn through two 

 successive points in which it is found; and then if these 

 points be conceived to approach each other witliout limit, 

 we shall have tlie line of its direction. Now, such a line 

 is called in geometry a tangent, for it meets the curve, but 

 does not cut it, provided that the curvature be continued 

 without contrary flexure (126). 



221. Theorem. A moving point never 

 quits the line of its direction without a new 

 disturbing cause. 



A right line being the same with respect 

 to all sides, since it must remain wholly at 

 rest if it be supposed to turn round any two 

 of its points (60), there can be no imaginable 

 reason why the point should incline to one 

 side more than to another. Let AB be the direction of the 

 motion of A in the plane ABC, and let CB and DB be equal 

 and perpendicular to AB, then the triangles ABC and ABD 

 are equal (86), and A is similarly related to C and D. But 

 if A depart from AB, and be found in any point out of it, 

 as E, ED will be greater than EC (103), and A will be no 

 longer similarly related to C and D, contrarily to the ge- 

 neral law of induction (217). 



Scholium. This argument appears to be sufficiently 

 satisfactory to give us ground for asserting, that the law 

 of motion, here laid down, may be considered as inde- 

 pendent of experimental proof. It was once proposed as 

 a prize question by the Academy of Sciences at Berlin, to 

 determine whether the laws of motion were necessary or 

 accidental; that is, whether they were to be considered as 

 mathematical or as physical truths. Maupertuis, then 

 president of the academy, endeavoured to deduce them 



