MATHEMATICS, &c. 



THE science which contemplates whatever is 

 capable of being numbered or measured. 



Nature of Mathematics. 



Mathematics does not depend on the quality or 

 existence of bodies, and the truths it teaches are 

 naturally such. They are intrinsical truths, and 

 wholly independent of facts or experiments. They 

 wholly depend on reasoning, and it is impossible 

 they should be otherwise than true, as is the case 

 with all the properties that belong to number and 

 figure. Two and two must inevitably and necessa- 

 rily, and through all time and space be equal to 

 four; the mind has no power of fancying how it 

 should be otherwise. 



Attraction. 



The power of attraction at double the distance is 

 4 times less, at triple the distance 9 times less, at 

 quadruple the distance 16 times less, and so on, ac- 

 cording to the squares of the distance. 



The Circle. 



Kepler thought that a circle was composed of an 

 infinite number of triangles, having their common 

 vertex in the centre of the circle, and their infinitely 

 small bases in the circumference. 



By inscribing a rectilinear figure with a curve, and 

 circumscribing another round it, two limits are at- 



