TO OF UNDISTURBED MOTION. 



Scholium 4. There is some difficulty in imagining a 

 slower motion to contain, as it were, within itself, two more 

 rapid motions opposing each other: but, in fact, we have 

 only to suppose ourselves adding or subtracting mathe- 

 matical quantities, Bnd we must rehnquish the prejudice, 

 derived from our own feelings, which associates the idea of 

 effort with that of motion. When we conceive a state of 

 rest as the result of equal and contrary motions, we use the 

 same mode of representation, as when we say, that a cipher 

 is the sum of two equal quantities with opposite signs ; 

 for instance, plus ten and minus ten make nothing. 



Scholium 5. The law of motion, here established, 

 differs but little, in its enunciation, from the original words 

 of Aristotle, as they stand in his Mechanical Problems. 

 He says, that " if a moving body has two motions, bear- 

 ing a constant proportion to each other, it must necessarily 

 describe the diameter of a parallelogram, of which the 

 sides are in the ratio of the two motions." It is obvious, 

 that this proposition includes the consideration not only of 

 uniform motions, but also of motions which are similarly 

 accelerated or retarded: and we should scarcely have ex- 

 pected, that, from the time at which the subject began to 

 be so clearly understood, an interval of two thousand years 

 would have elapsed, before the 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. 



Scholium 6. In the laws of motion, which are the 

 chief foundation of the Principia, their great author intro- 

 duces 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 



