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I must first state the cause, why the star Venus never recedes from the sun more than 46 degrees, nor Mercury more than 231, while they frequently return to the sun within this distance2. As they are situated below the sun, they have both of them their apsides turned in the contrary direction; their orbits are as much below the earth as those of the stars above mentioned are above it, and therefore they cannot recede any farther, since the curve of their apsides has no greater longitude3. The extreme parts of their apsides therefore assign the limits to each of them in the same manner, and compensate, as it were, for the small extent of their longitudes, by the great divergence of their latitudes4. It may be asked, why do they not always proceed as far as the 46th and the 23rd degrees respectively? They in reality do so, but the theory fails us here. For it would appear that the apsides are themselves moved, as they never pass over the sun5. When therefore they have arrived at the extremities of their orbits on either side, the stars are then supposed to have proceeded to their greatest distance; when they have been a certain number of degrees within their orbits, they are then supposed to return more rapidly, since the extreme point in each is the same. And on this account it is that the direction of their motion appears to be changed. For the superior planets are carried along the most quickly in their evening setting, while these move the most slowly; the former are at their greatest distance from the earth when they move the most slowly, the latter when they move the most quickly. The former are accelerated when nearest to the earth, the latter when at the extremity of the circle; in the former the rapidity of the motion begins to diminish at their morning risings, in the latter it begins to increase; the former are retrograde from their morning to their evening station, while Venus is retrograde from the evening to the morning station. She begins to increase her latitude from her morning rising, her altitude follows the sun from her morning station, her motion being the quickest and her altitude the greatest in her morning setting. Her latitude decreases and her altitude diminishes from her evening rising, she becomes retrograde, and at the same time decreases in her altitude from her evening station.

Again, the star Mercury, in the same way, mounts up in both directions6 from his morning rising, and having followed the sun through a space of 15 degrees, he becomes almost stationary for four days. Presently he diminishes his altitude, and recedes from his evening setting to his morning rising. Mercury and the Moon are the only planets which descend for the same number of days that they ascend. Venus ascends for fifteen days and somewhat more; Saturn and Jupiter descend in twice that number of days, and Mars in four times. So great is the variety of nature! The reason of it is, however, evident; for those planets which are forced up by the vapour of the sun likewise descend with difficulty.

1 According to Ptolemy, these numbers are respectively 47°51′ and 24°3′; the modern astronomers have ascertained them to be 48°and 29 °. The least elongations of the planets are, according to Ptolemy, 44°7′ and 18°50′, and according to the observations of the moderns, 45°and 16 °; Marcus in Ajasson, ii. 354.

2 I have not translated the clause, "quum sint diversæ stellæ," as, according to Hardouin, it is not found "in probatissimis codd.," and appears to have little connexion with the other parts of the sentence; it is omitted by Valpy and Lemaire, but is retained by Poinsinet and Ajasson.

3 When these inferior planets have arrived at a certain apparent distance from the sun, they are come to the extent of their orbits, as seen from the earth.

4 "Quum ad illam Solis distantiam pervenerunt, ultra procedere non possunt, deficiente circuli longitudine, id est, amplitudine." Alexandre in Lemaire, ii. 277.

5 The transits of the inferior planets had not been observed by the ancients.

6 "utroque modo;" "latitudine et altitudine;" Hardouin in Lemaire, ii. 279.

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