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Van Schooten's Ruler Constructions - Fourth Solution to Problem I

C. Edward Sandifer

We repeat Problem I, trisecting a given angle.

Problem I.  Given a rectilinear angle BAC, to cut it into two equal pieces.

Van Schooten wrote a fourth solution.

Again another way:  Assume in AB the given point G, and from A is located in AC a line AF equal to AB; CA is produced to E so that EA is either larger or smaller than AB.  Then produce BA from the point A and place a straight line AD equal to AE; and make through the points E, B and D, F straight lines EBG and DFG, which intersect at G.  This done, if the straight line is drawn through AG, it will bisect that angle BAC.

Van Schooten gives two diagrams, depending on whether EA is larger or smaller than AB.  We give here the illustration taking EA larger than AB.


Problem II