"How can any prediction of the return of a comet be made? and, supposing such a prediction to be possible, How can it thence be shown that this comet of 1835, is the same with those seen in 1682, in 1607, in 1531, and in 1456? Before the first of these questions is answered, the reader must be made acquainted with the nature and properties of a certain curve, called by geometers an ellipse."