A History of Mathematics by Carl B. Boyer & Carl B. Boyer

Author:Carl B. Boyer & Carl B. Boyer
Language: eng
Format: epub
Publisher: John Wiley & Sons, Ltd.
Published: 2010-12-24T16:00:00+00:00

Georg Mohr

Lahire was not the only geometer of the time to be unappreciated. In 1672, the Danish mathematician Georg Mohr (1640–1697) published an unusual book titled Euclides danicus, in which he showed that any pointwise construction that can be performed with compasses and straightedge (i.e., any “plane” problem) can be carried out with compasses alone. Despite all of the insistence by Pappus, Descartes, and others on the principle of parsimony, many of the classical constructions were shown by Mohr to have violated this principle through the use of two instruments where one would suffice! Obviously, one cannot draw a straight line with compasses, but if one regards the line as known whenever two distinct points on it are known, then the use of a straightedge in Euclidean geometry is superfluous. So little attention did mathematicians of the time pay to this amazing discovery that geometry using compasses only, without the straightedge, bears the name not of Mohr but of Lorenzo Mascheroni, who rediscovered the principle 125 years later. Mohr’s book disappeared so thoroughly that not until 1928, when a copy was accidentally found by a mathematician browsing in a Copenhagen bookstore, did it become known that Mascheroni had been anticipated in proving the supererogation of the straightedge.

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