On the Latitude
Don't let the pedestrian title fool you into thinking that Part V is not profound!
Kepler is able to reapproach latitudes with a firm sense of rigor now that he has discovered and communicated the principles of planetary motion. He takes up the location of the nodes in chapter 61. Inclination is his subject in chapter 62, where he confirms his theory of latitude with observations, and demands the physical cause for the location of the limits/nodes and apsides. Physical causes are the subject of chapter 63: if a magnetic power causes the eccentricity of the orbit and the closeness at perihelion, couldn't this same power cause the planet to move above and below the ecliptic? If the same power causes both motions, then the nodes would be located at the apsides, which he finds not to be the case, but then he poses something remarkable:
We shall also see whether, if some mean ecliptic be proposed for the six planets, that which we were requiring a little earlier is accomplished, namely, that the nodes of each of the planets correspond to the apsides. (p.617)
More on this in chapter 68. Before that, Kepler again confirms in chapter 64 that there is very little, if any perceptible parallax of Mars, and finds the maximum latitudes at syzygy, pondering what would happen if the “apsides and limits were to coincide at some time, but whether this is going to happen before the whole fabric comes to ruin is uncertain.” In chapter 66, he is able to take a last swing at the complete foolishness of Ptolemy, and he amazing superiority of his method. That oppositions do not always coincide with greatest latitudes was an insoluble conundrum for Tycho, and the theory of latitudes for Ptolemy introduced “inclination, deviation, and reflection,” on top of all his other absurdities. In 67 comes a resounding and indubitable proof that the actual sun must be taken as the center of the world, rather than mathematical fictions.
Chapter 68 offers a profound hypothesis: that a “royal road”, or “mean ecliptic” exists, determined by the physical equator of the power of the sun's revolution, rather than the path of the earth effected by this power, and that the ecliptic is inclined to this royal road just as other planets' eccentrics are considered as inclined to the eccliptic. If this be true and demonstrable, it will revolutionize astronomy yet again. If its orientation can be known, then the trouble in chapter 63 of the non-alignment of nodes and apsides could actually be found to coincide, since the nodes would be redefined as nodes with the royal road, rather than the earth's ecliptic.
To test this breathtaking hypothesis, Kepler uses all the ancient and Ptolemaic observations he can get his hands on, but finds them inadequate to the task he has set himself:
Thererfore, as long as we are wanting suitable observations from antiquity, circumstances compel us to leave this discussion of the motion of the nodes, along with many other matters, to posterity, if, indeed, it should please God to vouchsafe the human race a length of time in this world sufficient to work through such remaining questions thoroughly. (p.640)As for Kepler, so for us.