Van Schooten's Ruler Constructions - 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.

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Solution to Problem X

The other eight problems