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This seems to be one of the many cases in which the admitted accuracy of mathematical processes is allowed to throw a wholly inadmissible appearance of authority over the results obtained by them. Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff of any degree of fineness; but, nevertheless, what you get out depends on what you put in; and as the grandest mill in the world will not extract wheat flour from peascods, so pages of formulae will not get a definite result out of loose data.
Quarterly Journal of the Geological Society, 25,1869.
Loci: Convergence
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Van Schooten's Ruler Constructions
Second solution to Problem I
Van Schooten offers a second solution to the problem of bisecting an angle. He writes:
Another way: Assuming the point B is in AB, find in CA, produced through A, the segments AD, De, each equal to AB, and draw the straight line through the points D, b, and put on it BF equal to BE, and join AF. I say it bisects that angle BAC.
The proof of correctness of this construction may not be immediately obvious. As a hint, we suggest that a line from B to D might be useful.
Branch point:
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