Mr . glenie’s Method , &c. 451 
a very contracted field of geometrical comparifon; 
whereas the laft extends it indefinitely. Within the 
narrow compafs of the firft, the ancient geometers per- 
formed wonders, and their labours have been pufhed 
Hill farther by the ingenuity and indefatigable induftry 
of the moderns. But no author, that I have been able to 
meet with, gives the leaft hint or information with re- 
gard to any general method of expreffing geometrically, 
when any two magnitudes of the fame kind are given, 
what degree of augmentation or diminution any one of 
thefe magnitudes rauft undergo, in order to have to the 
other any multiplicate or fub-multiplicate ratio of thefe 
magnitudes in their given ftate; or any fuch ratio of 
them as is denoted by fractions or furds ; or (to fpeak ftill 
more generally) a ratio which has, to the ratio of the 
firft-mentioned of thefe magnitudes to the other, the 
ratio of any two magnitudes whatever of the fame but 
of any kind. Neither have I been able to find that any 
author has fliewn geometrically in a general way, when 
any number of ratios are to be compounded or decom- 
pounded with a given ratio, how much either of the 
magnitudes in the given ratio is to be augmented or di- 
minished, in order to have to the other a ratio, which is 
equal to the given ratio , compounded or decompounded 
with the other ratios. To invefcigate all thefe geome- 
N n n 2 trically, 
