( 8i ) 
nation ; fo that I can now add the numera- 
tors 24 and 8 : the fum is 32 for a new nu- 
merator: my fraction therefore thus added 
is 4 equal to one whole, or one hundred : 
for all the parts of any thing muft be equal 
to the whole. This may be made ftill plainer, 
thus. Without any knowledge of Euclid, 
or of Arithmetic, a moment's reflexion con- 
vinces me, that, if I take equal quantities 
from any two numbers, their proportion to 
each other will remain the fame : fo that if 
I take half from the 44 there will remain 
44 If I then take half from each of thefe 
fixteens, there will remain -J-. One ftep far- 
ther brings the fradlion to -; the next ftep 
to ~ and the laft to 4-> which is evidently 
the fame as one a whole numbers for one 
ones is one. 
Let us now confider, whether it be not 
poffible to manage this 25, the quarter, and 
this 75, the three quarters, of a hundred, 
without being troubled with thefe denomU 
nators beneath the line? You know I firft 
wrote them thus -i and ~. But if for the i 
I fubftitute 25, and for the three I take 75, 
I muft then write -j-Vo- and -/A. You re- 
member, that thefe denominators, thefe un- 
der figures, indicate the fpecies of parts: 
F they 
