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Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
In H. Eves, Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
Loci: Convergence
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Van Schooten's Ruler Constructions
Problem II
Problem II: Given a straight line with endpoints A, B, to bisect it.
Construction: Take any point C at random away from the line AB, and from A through C draw the indefinitely long line ACD, and locate on that line CD equal to the double of AC, and from D through B make a straight line. In that line, put BE equal to BD, and, joining C, D, I say it bisects AB at F.
Branch point