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If the sides of a polygon are restricted so that they pass through fixed points and all the vertices except one lie on fixed straight lines, the free vertex will describe a conic or a straight line .
This appeared in 1735 and there was then a dispute regarding priority with Maclaurin. Braikenridge claimed to have discovered the theorem and many other results in 1726 when he was living in Edinburgh and told Maclaurin of them. An argument followed and the correspondence is preserved.
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