  In the first edition the method was applied only to the comet of 1680-81. The results are presented in a one-foot long diagram on the only fold-out page in the edition. Nothing like this diagram, shown in Figure 3, had ever appeared in print before. The diagram continued to appear in the next two editions, though in reduced form not requiring a fold-out in the third. In the second edition the method was refined and applied as well to the comets of 1664-65, 1683, and 1682 reflecting research Halley had carried out and published in his Astronomiae Cometicae Synopsis of 1705. The comet of 1682, now known as Halley's comet, was singled out as being sufficiently similar in trajectory to the comet of 1607 to warrant the proposal that it returns every 75 years.