A Note on Hariot's Method of Obtaining Meridional Parts

Extract

In an article in this Journal some years ago, the late Professor E. G. R. Taylor and Dr. D. H. Sadler drew attention to and discussed Hariot's calculation of meridonal parts. The question was raised but not answered as to ‘how Hariot discovered the extremely complex and far from obvious method’ that he used. This note draws attention to a possible, and indeed a very likely, way in which the method may have been discovered.

The conformal property of the stereographic projection of the surface of a globe from a pole on to its equatorial plane has been known since antiquity. It is used in the design of the astronomer's astrolabe. Hariot's manuscripts contain in more than one place a diagram for a proof of the property. One of these is reproduced in a recent article on Hariot. Halley, in an article on meridional parts, says of the conformal property, ‘But this not being vulgarly known, must not be assumed without a Demonstration’. From this result he obtains the formula for meridional parts, unaware that the same proof may have been used almost exactly a hundred years previously. In fact, he says, ‘I hope I may be entituled to a share in the emprovements of this useful part of Geometry’ on the basis of ‘having attained … a very facile and natural demonstration of the said Analogy’.