[ 3S ] 



am 



of aX"; that is, y = X " x, by Cas. 5. Lem. 2. B. 2. 



Principia. Now the redlangle sDBb is the redangle under 

 the ordinate and moment of the abfcilTe, that is, "Yx ; and 

 the redangle CDpr is the redangle under the abfciffe and mo- 

 ment of the ordinate, that is, Xy ; therefore bD : Cp :: Yx : Xy 5 

 that is, fubftituting its value for y, 



am ^ 



as Yx : X" x 



n 



Y : X" 



in m^ ^ m 



or as aX" : fH X ° , that is, as i to — . 



By a hke procefs it may be fhewn, that if AB be divided 

 into an indefinite number of parts, and upon each there be 

 conftruded a redangle o b in the fame manner as on bB, 

 and through g there be drawn tq parallel to the bafe ; the red- 

 angle o b will be to the correfponding redlangle r q ultimately 



in the given ratio of i to — . Therefore the fum of all 

 ^ n 



the indefinitely little redangles sB will be to the fum of the 

 correfponding redangles Cp, in the fame ratio ; therefore the 



curve ADB is to the curve ACD as i to — , Cor. Lem. 4. 



n 



B. I. Prin. and the curve ADB to the redangle ACDB, as 



I to—-; but the redangle ACDB = YX = aX— -; there- 

 n ' ^ n 



O 



E 2 fore 



