[355] 
and that where the Analyfis Compounds, the Synthcds 
Divides, and verfa. 
But to make thofe Rules more ufeful, it won't be amifs 
to fhew the applications he has made of 'em in the folu- 
tion of fome Problems , and becaufe there is a great 
variety oPem in his jBook , we will chufe a few of the 
moft remarkable as Rules in cafes of the like nature* 
PROBLEM. 
H h 
X c 
The Line ac being divided at pleafure in ^ to di- 
vide it again in between b and c fo that^^r xc^ 
be proportional. 
Let therefore xc t : xc^ bx^ 
and Compnendo My : : bc^ hx^ 
and Alternando a€^ be : : xcy bx. 
Let c(i be made , cq_ 
and Comfonendo aq^ : ; be ^ bxn . 
Therefore the Problem is folv'd. 
Let the Conftrudion be made as before. 
Demmftratio99» 
For fince , by the Conftrudion , 4^ is to as be to 
bx. Therefore Dividendo i,e is to that is to bcy as xc to 
bx ^XiA Alter nAnd$ ae is X.0 xe^ as to bx. Therefore 
Dividendo ape^ is to as se tp which was to be done<» 
PROBLEM 
