DISCOVERY OF THE LAWS OF MOTION. 29 



though not much more philosophical than the 

 former, agreed much better with the phenomena. 

 Nicolo Tartalea (Nuova Scienza, Venice, 1550 ; 

 Quesiti et Inventioni Diver si, 1554) and Gualtier 

 Rivius (Architectures, &c., Basil, 1582) represented 

 the path of a cannon-ball as consisting, first of a 

 straight line in the direction of the original projec- 

 tion, then of an arc of a circle in which it went 

 on till its motion became vertical downwards, and 

 then of a vertical line in which it continued to fall. 

 The latter of these writers, however, was aware 

 that the path must, from the first, be a curve; 

 and treated it as a straight line, only because the 

 curvature is very slight. Even Santbach's figure 

 represents the path of the ball as partially descend- 

 ing before its final fall, but then it descends by 

 steps, not in a curve. Santbach, therefore, did not 

 conceive the Composition of the effect of gravity 

 with the existing motion, but supposed them to act 

 alternately ; Rivius, however, understood this Com- 

 position, and saw that gravity must act as a deflect- 

 ing force at every point of the path. Galileo, in his 

 second Diologue'', makes Simplicius come to the 

 same conclusion. " Since," he says, " there is 

 nothing to support the body, when it quits that 

 which projects it, it cannot be but that its proper 

 gravity must operate," and it must immediately 

 begin to decline downwards. 



The Force of Gravity which thus produces de- 

 6 P . 147. 



