274. Theorems and Problems 
on from E to I, as wellas from I toV : Hence 
y and CV are equimultiples of n and CE; 
therefore as n:r:: CE: CV:: rectangle 
Cii: rectangle BV: let g= quantity of re- 
sistance which would penetrate the same me- 
dium through the space CT; and we shall 
have for the same reason, as n:q:: rectangle 
CH: rectangle BT. Now let P be greater 
than p; and AC will be greater than BC. 
In this case, the force required to penetrate 
the medium whose resistance =p, through the 
space CE, will be to that required to penetrate 
that whose resistance =P, through the same 
space, as BC to CA, by def. 5.; that is, the 
quantities of resistance of the two mediums 
will be in the same ratio, by axiom 4. Hence 
by equimultipies g: R:: rectangle BT: rec- 
tangle Ca; but as qg:r:: rectangle BT: rec- 
tangle Cb; consequently as R:r:: rectangle 
Ca: rectangle Cb:: PS: ps. Q.E.D. 
Cor. 1. When FP is constant, R has a con- 
stant ratio to PS; but when p is variable, 
y has a constant ratio to ps, by prime and ulti- 
mate ratios; hence as R:r:: PS: ps. 
Cor. 2. As F': f:: R: r, by axiom 4; hence 
as F': f:: PS: ps, Pand p bemg invariable; 
but if p be variable, we have as F': f:: PS: 
ps; that is, F has a constant ratio to PS; 
