q6 lecture II. 



ly understood, two thousand years would have elapsed, before this law began 

 to be applied to the determination of the velocity of bodies actuated by de- 

 flecting forces, which Newton has so simply and elegantly deduced from it. 



In the laws of motion, which are the chief foundation of the Principia, 

 their great author introduces at once the consideration of forces; and the first 

 corollary stands thus ; " a body describes the diagonal of a parallelogram by 

 two forces acting conjointly, in the same time in which it would describe its 

 sides by the same forces acting separately." It appears, however, to be more 

 natural and perspicuous to defer the consideration of force, until the simpler 

 doctrine of motion has been separately examined. 



We may easily proceed to the composition'of any number of different motions, 

 by combining them successively in pairs. Hence any equable motions, repre- 

 sented by the sides of a polygon, that is, of a figure consisting of any number 

 of straight sides, being supposed to take place in the same moveable body, in 

 directions parallel to those sides, and in the order of going round the figure, 

 destroy each other, and the body remains at rest. We may understand the 

 truth of this proposition by imagining each motion to take place in succession 

 for an equal small interval of time; then the point would describe a small 

 polygon similar to the original one, and would be found, at the end of every 

 such interval, in its original situation. 



When the motions to be combined are numerous and diversified, it is often 

 convenient to resolve each motion into three parts, reduced to the directions 

 of three given lines perpendicular to each other. It is easy to find in this 

 manner by addition and subtraction only, the general result of any number 

 of motions. We may describe the flight of a bird, ascending in an oblique 

 direction, by estimating its progress northwards or southwards, eastwards or 

 westwards, and at the same time upwards, and we may thus determine its 

 place as accurately, as by ascertaining the immediate bearing and angular ele- 

 vation of its path, and its velocity in the direction of its motion. 



