Solution to Problem IX

Problem IX:   Given a straight line AB, to extend it to G so that the total AG to the extreme GB has a given ratio C to D.

Construction:  Draw from A a line AE making any angle with AB, and put on it AF equal to C and EF equal to D.  Join FB.  I say that if a parallel EG is drawn to that, intersecting AB extended at G, then AG is to GB as AE is to EF, that is, C to D.

Branch point:  

         The other eight problems