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Van Schooten's Ruler Constructions - Verbatim first solution to Problem I

C. Edward Sandifer

In the detailed version of the solution to Problem I, we slightly misrepresented the given data.  In fact, when he gives us the angle BAC, he seems to be assuming that AB is a segment, and that C is a segment with A as one of its endpoints.  It could also be that B and C are both line segments, sharing A as an endpoint, and that the symbol B is also used to denote a point on the segment B.  This seems to have no real consequence, but it is curious.  Van Schooten’s words translate as follows.

Suppose that in the line AB points B and D are placed. and are placed on line AC so that AE equals AD, and E is a point further along AC so that EF equals DB; And draw straight lines BE, DF, which intersect at G.  I say that the line AG cuts the angle BAC into two equal pieces.

                  Van Schooten also includes a proof of the correctness of each of his constructions, but we will generally leave those to the reader.

Branch point :

     Second solution to problem I.

     Problem II.