Theories of the Medicean Planets Deduced from Physical Causes

From the different positions of the Sun, two other anomalies, or inequalities, arise in the Moon's path, which happen in this way: in that month where the syzygies Syzygies: the alignment of the Earth, Sun, and Moon in a straight line, occurring at New Moon and Full Moon, that is the new moons and full moons, occur very close to the line of apsides A P Apsides: the line connecting the highest and lowest points of an orbit, where the planet is closest to and farthest from the center of motion, then another inequality is added to the Moon's course besides the aforementioned one. Because of this, the Moon itself travels with a slower course through the arc A B than matches its standard anomaly, but on the other hand progresses faster through the arc B P. Consequently, near the end of the semicircle and in the following new moon, these inequalities are balanced out so that the half-period is completed in the same time as before. Therefore, the angle of prosthaphaeresis Prosthaphaeresis: the mathematical correction added or subtracted to find the true position of a planet from its average position, namely C B T, is increased this month by 2 degrees 30 minutes, becoming 7 degrees 30 minutes. The same thing happens between new moon and full moon, but in the reverse order.

Next, let the Sun be understood to be at E, so that the line of apsides of the eccentric orbit A P forms right angles with the line of syzygies B T Q. Namely, given that the new moons and full moons are celebrated at B and D, while the lunar quadratures Quadrature: the points in the Moon's cycle, like the first and last quarter, where it is at a ninety degree angle from the Sun occur at the Apogee Apogee: the point in the orbit farthest from the Earth and the Perigee Perigee: the point in the orbit closest to the Earth of the eccentric at A and P, then during that entire month, the Moon's own anomaly will suffer no alteration at all. The proper prosthaphaeresis will not be increased at all, specifically the angle CBT, which does not exceed five degrees.

Finally, conceive of the solar line L T, that is the line of the new and full moon, falling between the line of the eccentric apsis A P and the mean distances. Let the silent moon original: "Luna silens" refers to the New Moon, when it is invisible from Earth. be at O and the full moon at E. Then, from full moon E to O, a second monthly anomaly is observed. It is smaller than the maximum one we discussed at the beginning, but it is nevertheless distributed by the same rule. That is, from the monthly Apogee E (which is always very close to the Apogee of the eccentric), the Moon is affected by a new synodic slowing down until the quadrature. From this point until the monthly Perigee O, the lunar motion is increased with a new speed. Here it must be noted that, although some part of the eccentric orbit, to which slowing naturally belongs, might coincide with some part of the monthly anomaly to which speed of motion belongs, nevertheless that motion which ought to have been slowed down receives an increase of velocity as much as