340 On the Fundamental Principles of Mathematics. 



intervening portion of duration thus transferred must be regarded 

 as nothing in comparison with either Eternity. 



We may thus in some very humble measure learn how it is, 

 that, in the view of the infinite mind, "a thousand years" should 

 be "as one day, and one day as a thousand years." 



(23.) A finite quantity in comparison with others of the same 

 species, which are in some respect boundless, has, (22.), been 

 found to be as nothing. We shall therefore designate it in this 

 comparison as a relativ3 zero ; it being zero by comparison, in a 

 more intense sense, than the quantities described in (19.) were 

 relatively infinite, in comparison with others beneath them ; and 

 also a more intense sense than the same quantities were infinitesi- 

 mal, in comparison with those above them. 



1 : 



Character of the Symbols jl and ^ 



_ht line described in (22.), as interminable in 

 one direction, be assumed as a measuring unit, then any finite 

 straight line being, (23.), a relative zero, we shall have for the 

 symbol of the ratio of the greater of these quantities to the less 



1 







q ; and for that of the less to the greater, j-. # 



Since, moreover, the finite straight line is a relative zero, (the 

 line interminable in one direction being the standard); if p de- 

 note the length of one finite straight line, and q that of another, 

 we shall have in mariner as before, 



p represented by or as-?; and q represented by or =j', whence, 



p 



Or more directly still ; p being relatively represented by zero, and 

 q by the same, 



as before. 



From this equation, however, neither^ nor q can be determin- 

 ed ; nor even the actual ratio, of the one to the other. 



•The line interminable in one direction is, moreover, either the secant of the tan- 

 gent of 90° ; or, i hen taken negatively, it is either the secant or the tangent of 



270°; and radius of the circle being i we have tan. 90° — 8 ^-^==^ ! md sec> 



° cos. 90° 



9 °°~co7~90° = 6' re3ults agreeing with the preceding determinations, when the 

 greater line was regarded as the unit, and the less became a relative zero. 



