38 HISTORY OF MECHANICS. 



To see that a transverse force would produce a 

 curve, was one step ; to determine what the curve 

 is, was another step, which involved the discovery 

 of the Second Law of Motion. This step was made 

 by Galileo. In his Dialogues on Motion, he asserts 

 that a body projected horizontally will retain a uni- 

 form motion in the horizontal direction, and will 

 have, compounded with this, a uniformly accele- 

 rated motion downwards, that is, the motion of a 

 body falling vertically from rest ; and will thus 

 describe the curve called a parabola. 



The Second Law of Motion consists of this 

 assertion in a general form; namely, that in all 

 cases the motion which the force would produce is 

 compounded with the motion which the body pre- 

 viously has. This was not obvious; for Cardan 

 had maintained 11 , that "if a body is moved by two 

 motions at once, it will come to the place resulting 

 from their composition slower than by either of 

 them." The proof of the truth of the law to 

 Galileo's mind was, so far as we collect from the 

 Dialogue itself, the simplicity of the supposition, 

 and his clear perception of the causes which, in 

 some cases, produced an obvious deviation in prac- 

 tice from this theoretical result. For it may be 

 observed, that the curvilinear paths ascribed to 

 military projectiles by Rivius and Tartalea, and by 

 other writers who followed them, as Digges and 

 Norton in our own country, though utterly different 

 11 Op. vol. iv. p. 490. 



