f 160 ] 
Geometry informs us, that in fimilar figures the 
furfaces are as the fquares of their fimilar tides; of 
confequence the quantity of cloth will be as the 
fquare of the radius : alfo in fimilar figures and por- 
tions, the impulfe of the wind, upon every fimilar 
fedtion of the cloth, will be in proportion to the fur- 
face of that fedtion; and confequently, the impulfe 
of the wind upon the whole, will be as the furface of 
the whole : but as the diftance of every fimilar fec- 
tion, from the center of motion,, will be as the ra- 
dius ; the diftance of the center of power of the 
whole, from the center of motion, will be as the ra- 
dius alfo ; that is, the lever by which the power adts, 
will be as the radius : as therefore the impulfe -of the 
wind, refpedting the quantity of cloth, is as the 
fquare of the radius, and the lever, by which it adts, 
as the radius limply ; it follows, that the load which 
the fails will overcome, at a given diftance from the 
center, will be as the cube of the radius. 
Maxim 8. fhe ejfeSl of fails of fimilar figure and 
pofition , are as the fquare of the radius. 
By maxim 6 . it is proved, that the number of re- 
volutions made in a given time, are as the radius in- 
verfely. Under maxim 7. it appears, that the length 
of the lever, by which the power adts, is as the radius 
jdiredtly ; therefore thefe equal and oppofite ratios de- 
ftroy one another : but as in fimilar figures the quan- 
tity of cloth is as the fquare of the radius, and the 
adtion of the wind is in proportion to the quantity of 
cloth, as alfo appears under maxim 7 ; it follows that 
•the effedt is as the fquare of the radius. 
Corol^ 
