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The most learned Galileo was the first of all to publish in his Starry Messenger original: "nuncio syderio" that four planets are driven in a circle around Jupiter. He himself named them the Medicean stars. Just as the Moon orbits the Earth, these stars orbit the body of Jupiter. In relation to that planet, they show all the phases that the Moon shows to us: namely full, silent The "silent moon" refers to the new moon, when it is not visible from Earth., crescent, half, and gibbous. They also display all the wonderful phenomena of eclipses that happen to the Moon itself in relation to us. Galileo also discovered the order and size of the orbits of those planets, along with their revolutions and the periods of those revolutions. However, although that most wise mind recognized that there must be various and many irregularities anomalias: deviations from a perfectly circular or uniform motion in these small planets, which are also observed in other wandering stars, he was unable to find them in the short time of his life. After he passed away, although many have toiled over this, they have been unable to acquire even the slightest knowledge beyond what Galileo himself passed down to us. Because the investigation of these eccentricities eccentricitatum: the degree to which an orbit is elongated or off-center and periods seems to me as difficult and arduous as it is long and laborious, I have approached the contemplative part of the study. I noticed that quite a few people have appeared who, although they contributed much study and effort to this matter, not only failed to find anything new, but were even ignorant of what they ought to have been searching for.