DISCOVERY OF THE LAWS OF MOTION. 325 



Causes of change of motion which at each instant operate upon it ; and 

 thus men would have been led to the notion of Accelerating Forces, 

 that is, Forces which act upon bodies already in motion, and accel- 

 erate, retard, or deflect their motions. It was, however, only after 

 many attempts that they reached this point. They began by consid- 

 ering the whole motion with reference to certain ill-defined abstract 

 Notions, instead of considering, with a clear apprehension of the con- 

 ditions of Causation, the successive parts of which the motion consists. 

 Thus, they spoke of the teudency of bodies to the Centre, or to their 

 Own Place ; — of Projecting Force, of Impetus, of Retraction ; — with 

 little or no profit to knowledge. The indistinctness of their notions 

 may, perhaps, be judged of from their speculations concerning projec- 

 tiles. Santbach, 5 in 1561, imagined that a body thrown with great 

 velocity, as, for instance, a ball from a cannon, went in a straight line 

 till all its velocity was exhausted, and then fell directly downwards. 

 He has written a treatise on gunnery, founded on this absurd assump- 

 tion. To this succeeded another doctrine, which, though not much 

 more philosophical than the former, agreed much better with the phe- 

 nomena. Nicolo Tartalea (Nuova Scienza, Venice, 1550 ; Quesiti et 

 Inventioni Diversi, 1554) and Gualtier Rivius {Architectural &c, Basil, 

 1582) represented the path of a cannon-ball as consisting, first of a 

 straight line in the direction of the original projection, then of an arc 

 <>f a circle in which it went on till its motion became vertical down- 

 wards, 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 descending before its final fall, but then it de- 

 ds 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 

 Composition, and saw that gravity must act as a deflecting force at 

 every point of the path. Galileo, in his second Dialogue, 6 makes Sim- 

 plicius come to the same conclusion. " Since," he says, " there is noth- 

 ing 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. 



* PrdbUmatum A&tronomicorum et Geometricorum Sectiones vii. &c. &c. Auetore 

 Daniele Santbach, Noviomago. Easilese, 1561. ° P. 147. 



