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A REMARK ON THE CONSTRUCTION OF THE CENTRE OF A CIRCLE BY MEANS OF THE RULER

CHRISTIAN GRAM
Mathematica Scandinavica
Vol. 4, No. 1 (September 18, 1956), pp. 157-160
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24490022
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A REMARK ON THE CONSTRUCTION OF THE CENTRE OF A CIRCLE BY MEANS OF THE RULER
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Abstract

In the plane, let there be given two non-intersecting and non-concentric circles with unknown centres. Then it is impossible to construct the centres by means of the ruler alone. This was proved by D. Cauer by an argument which applies also if, in addition, the line joining the centres is given. In this note it is pointed out that Cauer's argument fails if it is permitted, under the construction, either to distinguish between pairs of intersecting lines and pairs of parallel lines or to recognize the Euclidean order of points, given or constructed, on a line. This is demonstrated by giving a construction of the centres of the circles by means of the ruler if the two circles and a point of the line joining their centres are given.

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