Cassini and Richter had measured the parallax of Mars (and therefore the distance to Mars) a couple of years earlier. Using Kepler's law they could then deduce the distances to the other planets.
Amazing. If you know of a comic (or graphic-heavy article) or a video that can explain to a complete astronomy-noob what parallax is and how it enables one measure the diameter of planetary orbits, please put the link below. (I can only learn science with visual illustrations, and can't mentally process equations.) Thanks!