Epitome Astronomiae Copernicanae: Liber VI, part 7
Part V. Of the Affections Common to the Planets, Either to All or to Several
What do you call the common affections of the planets? Those which befall either all and each, though for different causes, or the six planets separately, not on account of motion but on account of their situation to the Sun, or finally when compared with one another in pairs, any two whatever.
What name has been given to these affections? These, and some of the affections of the motion itself delivered above, come under the name passions of the planets, by which Latin word the Greek pathe is rendered, rather more aptly. For it is an astrological fiction, as if the planets themselves were truly affected by all those things which sight imagines for itself concerning them, which however is true of very few accidents.
What are those which befall all in common, though for different causes? That they become slow or swift, increased or diminished in number.
When is a planet called slow, when swift? These accidents are taken in respect to the mean motion of each, as considered from the equinox, whether the cause of slowness or swiftness be proper to each, from the eccentric, or adventitious, from the great orb. Where retrogradation and stations are also reckoned under the accident of slowness. Although these affections of retrogradation and stations are also separately, by private right, reckoned among the pathe or passions of the planets, yet since they are not of all the planets and are the effect of one planetary orb, called the great one, they have therefore been explained above, in the theories of those to which they belong, as pertaining to the very essence, as it were, of the compound apparent motions.
But when are they said to be increased in number, when diminished? When they are found in more or fewer degrees of the ecliptic than the calculus of the mean motion gives, that is when either both prosthaphaereses, of the eccentric and of the great orb (or in the Moon the simple and the monthly or of the light), or at least the greater of them, are additive in the one case, subtractive in the other, which may happen indifferently to slow or swift planets, or even to stationary and retrograde ones.
What befalls the six planets on account of their situation to the Sun? The planets are with respect to the Sun, 1) either eastern or western, 2) and according to the diversity of these situations they are seen with different aspects, 3) finally on account of all these things they receive different risings and settings and in their appearances are reckoned either increased or diminished in light, or not appearing, hypaugi, under the rays.
When are the planets reckoned eastern to the Sun or western? They are called eastern not because they are distant from the Sun toward the east and the order of the signs, but on the contrary when they precede it in the order of the signs, in Greek therefore called proegoumenoi, because they then have their rising above the horizon by night, or between the setting of the Sun and its rising, but their setting the day covers. For since in the morning, the Sun not yet risen, they can for the most part be seen, they are called in Greek heoioi or eoioi, in Latin matutini, morning planets. So on the contrary those which are distant from the Sun in the order of the signs by less than a semicircle, in Greek hepomenoi, are called western, because they then set by night, while the day hides their rising, and because in the evening, at the setting of the Sun, they are above the horizon and for the most part in view, for that reason they are called in Greek hesperioi, in Latin vespertini, evening planets.
In what order do these affections succeed one another? The three superior planets and the fixed stars at the moment of conjunction with the Sun become eastern from western; the contrary at the moment of opposition. The Moon conversely, conjoined with the Sun, becomes western from eastern, opposed to it holds the contrary. The two inferior planets, Venus and Mercury, associate themselves with the superior when they are themselves conjoined with the Sun below it and retrograde, or with the lowest, the Moon, when they are conjoined with the Sun above it and direct.
II. Of the illumination of the Moon.
What is the cause why the Moon and Venus change their faces? The cause is composed of the illumination of the globes and their situation to the Earth and the Sun.
That I may rightly understand this cause, tell whence the stars have their lights. Of the fixed stars it is hard to answer whether lights are inborn in them; for they stand at so great a degree of height that they enjoy the sight of the Sun under the smallness of the six-hundredth part of one minute; wherefore the Sun appears to them eighteen thousand times smaller than to us here on Earth. Whether, therefore, the Sun nevertheless has such power of illuminating the fixed stars that they in turn can send down to us the light communicated to them by the Sun through the same prolixity of interval, here I see Galileo doubts, nor do I affirm anything. If, however, the stars have lights of their own, this is nothing unusual, because even here on Earth certain parts of certain animals have lights of their own, and by chemical art a light not flickering, like that of lamps and fires, but wholly constant and quiet is procured for some gems. However it may be, whether the fixed stars scatter lights of their own, or reflect the light received from the Sun, they certainly add of their own those various colours and that scintillation. For of a simple cause (as if it were the Sun) the effect is simple and uniform.
But of the planets the matter is certain, that all their light is from the Sun. 1) For the Moon and Venus change their faces in proportion to their configuration with the Sun. 2) The Moon, Earth and Jupiter cast shadows, being set against the Sun, so that certain parts of the Earth are deprived of light by the shadow of the Moon, the whole Moon by that of the Earth, the Jovian planets by the shadows of Jupiter, and become unseen or obscured bodies, which outside the line of opposition were most clearly discerned. 3) Mars, Jupiter and Saturn always appear brighter on that side from which they look nearer to the Sun, darker or coloured on the opposite. Mercury also is seen with a clearer light when it is higher than the Sun and shows the same part of its body which also enjoys the light of the Sun. Nor meanwhile is it to be denied that the surface of the globe of Saturn is ash-coloured in colour, that of Jupiter ruddy or yellow, that of Mars black, as the earthly and perhaps the lunar is yellow, and that the surface of the globe of Venus is most white, that of Mercury blue, notwithstanding that the globes themselves, by reason of their bulk and density, found in book IV above, were not wholly assimilated in colour to fossils.
Whence, then, have the stars that scintillation? Either from some perpetual and continuous alteration of the bodies, as of transparent things, which you might call as it were paroxysms, or from an external turning round of angular or spotted bodies and the unfolding of angles or spots one after another.
How do we know that the Moon wholly lacks light of her own? Because sometimes she is suddenly lost altogether, so that not even a trace of her appears, though fixed stars of the fourth or fifth magnitude can be seen very near her place; wherefore the suspicion of too misty an air has then no place.
Whence, then, has the Moon her own light? From the same place as the surfaces of the Earth, namely from luminous bodies, in whose light she is placed, no opaque body intervening, and chiefly indeed from the Sun, the fountain of all light in the world.
If the light of the Moon were from the Sun, we should see in her, as in a mirror, a little image of the Sun, always round. Provided that the Moon had a polished surface like a mirror; this being denied, the inference does not follow. For we see in the Earth also distant walls entire by the benefit of the light of the Sun, which we do not see when the Sun is covered by clouds, and yet in those walls we do not see the image of the Sun.
What is the figure of the illumination of the Moon by the Sun? Since both are of globular figure, but the Moon of the lesser diameter, as one that, book IV, page 328, occupies only the fifty-ninth part of the diameter of the Sun, a little more than a hemisphere of the lunar body is therefore illuminated by the Sun at any moment; the illumination is bounded by a circle, which is hence called the circle of illumination, and it is distant from the great circle parallel to it, at the apogean new moon, by 15 minutes of one degree of a great circle in the Moon, but at the full moons by hardly half a minute less.
If always a hemisphere, and more, of the globe of the Moon and of any planet is illuminated by the Sun, how then can the Moon change her face? Because, although always about half of the globe is illuminated, yet that half is not always turned wholly to us. But what of it does not look toward us cannot be seen, and lies hid behind the globe in the averted part.
How much, then, of the globe of the Moon or star looks downward to the eye? Again half of the globe, a little less however. And in the apogean Moon, when the diameter of the body appears 30 minutes, if the Sun also is then in apogee, having likewise 30 minutes in visible diameter, then by as much as more than a hemisphere is illuminated, by so much less than a hemisphere is seen, precisely; but the nearer the Moon becomes, the less of her is seen, but she appears larger.
Explain now how the diverse phases of the Moon come about. 1. When the Moon is conjoined with the Sun centrally, as if B be the Earth, A the Sun, and the Moon PO in the line: then the Moon is wholly extinguished, because A the Sun is above PO the Moon: and so the illuminated part LOK of the globe of the Moon is turned precisely upward from the Earth B toward A the Sun and lies wholly hid behind the opaque globe, and so the part NPM, which looks downward to the eye B, is bounded by the same circle of vision NM, which is also the circle of illumination LK: the Moon is called silent, new, empty, in Greek the dark moon, in German the new moon.
2. When the Moon goes out of the line from the Earth to the Sun, as if she be in E, then the circle of vision MN begins to cut the circle of illumination KL, and then some part of the illuminated hemisphere, as LN, is claimed into the visible hemisphere MPN, and that always the greater, the farther the Moon departs from the Sun. This therefore happens in the Moon called nascent and waxing, in Greek the increasing moon, in German the young moon, where she is first horned, sickle-shaped, then halved, at last gibbous or amphikyrtos.
3. When the Moon is distant from the Sun by a whole semicircle, as CEG, so that she has B, the eye on the Earth, and A the Sun beyond her from the same quarter GBA, then the same half LOK of the Moon (not the whole, however) comes into the sight of the Earth B which is also illuminated by the Sun; and the nearer circle of vision NM and the farther circle of illumination LK, drawn back behind the Moon upward from the Earth, are either parallel or touching one another on either side: so that the whole circle of vision is comprised in the illuminated part; and the Moon is called full, the full moon, panselenos.
4. When the Moon has passed the opposite of the Sun, so that in the other semicircle she again approaches the Sun, then for the same causes, in the contrary order however, the same phases arise, gibbous in F, then halved, last sickle-shaped in D. And she is called the waning or decreasing Moon, in Greek the waning, in German the old moon. So also we use the age of the Moon for the number of days from the new moon, in which the Moon is reckoned to be born.
If all phases of the two circles are bounded by two half-circles, one of vision, the other of illumination: what then is the cause that not both boundaries of the phase appear circular, but at times the one line is straight, as if the Moon were bisected? The circle of vision MN always appears as a circle, because it is always presented at right angles to the line drawn from its centre C, E, G, F, D to the eye B, but the circle of illumination LK, with the departure of the Moon from the Sun or its opposite, that is with the angle ABE, ABF, is necessarily inclined and presented obliquely more and more to the sight, until the line from its centre to the eye, as EB, is applied to the plane of that circle KL. Now it is demonstrated in optics that a globe at a distance appears as a plane disc, and in a globe a circle presented obliquely, as at the angle BFL, BDL, does not appear as a circle, but as an ellipse; and if most obliquely and with the angle BEL none, as a straight line.
Where does it become a straight line? In the quadrature of the Sun, or in the waning Moon a little beyond, in the waxing a little before the place of the Sun’s quadrature: namely where the angle between the Sun, Moon and Earth is a right angle at the Moon. Or more geometrically: where the axes of the cones of shadow and of vision make a right angle.
As here ABM is a right angle, and M therefore the place of the Sun’s quadrature. If therefore the Moon be before M, as in E, the angle AEB being right and EBM therefore as great as BAE: then the plane of the circle KL, falling on the line of vision EB, appears as a line. Since therefore the proportion of AB to BE, which is 59 to 1, was established in book IV, the angle EBM will be
How is the breadth of the phase computed at any moment? As the diameter of the circle stands to the versed sine of the angle of the axes, so very nearly is the diameter of the disc of the Moon to the breadth of the phase. For it was said that more than half of the globe is illuminated. Wherefore where the angle is right and the circle of illumination appears as a straight line, there a little more than half the disc is illuminated.
The moment of which phase is more easily discerned, of which with more difficulty? The phase of the halved Moon is discerned within a few hours, in which from hollow she becomes gibbous; but the exact full moon is scarcely seen to change within three days, for equal parts of the additions or subtractions of the illuminated surface are presented to the sight large, like sines, in the middle of the disc, but small, like versed sines, at the margin of the disc, as has been said. And so, although we are so far from the very opposition that the circle of vision cuts the circle of illumination in a very small part, yet it is held to touch it and the phase to be a full moon.
How is the waxing and waning Moon told? The morning or eastern Moon, showing her setting by horns or by the gibbous side, so that in our zones the right hand held up against her appears to be insertable into her: then she wanes. But the evening or western Moon, showing her rising by horns or gibbous side, and when her gibbous side or hollow seems to meet the hollow of the left hand: then she waxes. In Venus the contrary happens.
What else do astronomers gather from the horns of the Moon? 1) The horns always look toward that quarter toward which the zodiac tends. 2) A circle drawn through the extremities of the horns tends toward the pole of the ecliptic. 3) When this circle is erected perpendicular, then the Moon is in the ninetieth degree of the ecliptic from the rising.
What are the spots in the Moon? Although it is impossible to pronounce anything certain about bodies so far removed, yet in three properties the spotted parts of the Moon agree with the seas and lakes which are on the globe of the Earth; but the parts in the Moon that are clear and bright with the mountains, rocks, promontories and shores of our continent. For the spots of the Moon are both deep, like our lakes and seas, and of an equable surface like moisture, and finally dark, as all things moist with us are blacker than themselves when they are dry. But the bright parts in the Moon are high and eminent and rough, like our mountains cut by valleys, and whiter, like dry things.
How do you demonstrate these properties of the diverse parts of the Moon? From the phases of the Moon: for the line which bounds the phase within, if you survey it with the Belgian telescope, is neither a perfect ellipse in the hollow or gibbous Moon nor a perfect straight line in the halved. For through the spotted parts the breadth of the phase is shorter, through the clear parts longer, and the appearance of the whole as it were toothed or serrated. These are arguments of the diverse height of the spotted and the clear parts. So in the part averted from the Sun, in the neighbourhood of the boundary, there are bright points, like the summits of mountains first illuminated by the Sun, which points belong not to the spotted but to the clear parts of the Moon, as appears to one who waits until those parts are wholly illuminated and joined to the breadth of the phase; there are conversely in the brighter illuminated part, again in the confines of the boundary, black points, like shady valleys or caverns. These are arguments of roughness. But the spotted parts lack those bright or notably dark points, which is an argument of an equable surface. Finally, in the bright parts there is a singular boss of immense brightness, like a huge mountain covered with snow: that this may be an argument of whiteness in the high parts, and that blackness and obscurity, the companion of moisture with us, may remain to the deep parts of the Moon and those spread out into plain.
In the horned part of the Moon, turned away from the Sun, a faint light is seen next to the bright horn: I ask whether that is proper to the Moon, or whence it is. The cause must answer to the effect. If that light were proper to the Moon, it would be perpetual. But it is strongest about the new moons, for it overcomes the brightness of twilight, overcomes the density of the horizontal vapours; on the contrary it is weakest in the quadratures, so that it is then noticed only by the keenest sight, and only in deep night, the Moon being high and free from vapours. A cause, therefore, is to be sought which is strongest about the new moons, weak about the quadratures. Such is the face of the Earth, illuminated by the Sun. For at the time when dwellers on Earth have the new moon, the Moon in turn has the full earth (elsewhere I call it the full-earth-moon), because the Moon, placed between the Sun and the Earth, enjoys, with her part which is turned away from the Sun, the sight of the whole hemisphere of the Earth illuminated by the Sun. In the quadratures, however, as the dwellers on Earth see the Moon, so the Moon sees the Earth shining with half a face only. Nor is it absurd that, as the full Moon illuminates our nights and paints with her light the part of the Earth turned away from the Sun, so also the full Earth in turn should illuminate fifteen times more strongly that night which is in the part of the Moon turned away from the Sun; for the apparent disc of the Earth in the Moon is about fifteen times the apparent disc of the Moon on the Earth, as is plain from book IV, page 328, the semidiameters of the bodies of the Earth, 389, and of the Moon, 100, being squared. So also with us, dwellers on Earth, white walls, very strongly illuminated by the Sun, dart light into the darkest caves and prisons and bring day into them.
For what causes do the same phases appear in Venus, since she does not depart from the Sun by a whole semicircle? Whereas the Moon circles the Earth always lower than the Sun, Venus in turn circles the Sun, now lower than it, now higher. When, therefore, she is lower than the Sun and near it, as in the evening occultations and morning appearances, then by the same causes and laws as the Moon she appears horned or sickle-shaped. But when she becomes higher than the Sun, as about the morning occultations and evening emersions, then, presenting the same part or illuminated hemisphere both downward toward the Sun and toward the eye standing still lower in the same quarter, she must appear with a full face, the opposition which the Moon needed for this phase being compensated by the situation above the Sun, which the Moon could not attain. It follows, therefore, that there are also two intermediate places in which the globe of Venus also appears bisected, or dichotomous, like the Moon. This happens at the greatest elongations from the Sun, because it was said above, in part III of this sixth book, that there the orbit of Venus is touched by the line of sight; but the circle of illumination also always applies itself to the orbit, since the illuminating body stands as it were in the centre of the orbit, and in this situation therefore the line of sight and the plane of the circle of illumination coincide; wherefore there a halved phase must exist in Venus also.
Do these phases also have place in the superior planets? Since these are understood by their very name to be above the Sun, they therefore always, whether conjoined with the Sun or opposed to it, turn to the eye or Earth the same part which is turned to the Sun. Conjoined with the Sun, therefore (or near the Sun, as in the evening occultations and morning emersions), they shine with a full face for the same cause as the inferior planets before, as Venus; but opposed to the Sun, for the same cause as the Moon. There remains to them also the gibbous phase, when they are in intermediate places. But bisected or dichotomous they cannot appear, because none of the lines touching their orbits falls into the great orb in which is the Earth. For the tangents fall outside; the orb of the Earth is within.
Mars, however, attains this dichotomous phase very nearly, when in perihelion he falls in the quadrature of the Sun. For then of all the angles between the Sun, Earth and Mars the angle at Mars is the greatest and nearest to a right angle, because the line drawn from Mars touching the great orb is then the shortest, and in the rectitude of the angle at the planet is placed the perfection of the dichotomous phase.
What kinds of risings and settings in respect of the Sun belong to which planets, and in what order, and what names have they thence? The three superior planets, after conjunction with the Sun, rise in the morning heliacally, or emerge from the rays of the Sun; so made eastern and morning planets, at length in the opposition of the Sun they rise and set acronychally, that is they shine all night, or pannychoi; from this they become western and evening planets and at length set heliacally, or are hidden, under the rays of the Sun; evening emersions and morning occultations they do not have, any more than the fixed stars. The Moon in turn, after conjunction with the Sun, emerges in the evening waxing, and proceeding western and evening to the opposition or full moon, becomes all-night and rises and sets acronychally like the superior planets. Thence, made eastern and morning, at length in the morning she sets heliacally, though on the rising horizon, and lacks the morning emersion and the evening occultation. But the inferior planets, Venus and Mercury, since they cannot become all-night, nor have acronychal risings and settings like the superior planets and the Moon, in turn heap up all four kinds of emersions and occultations, whereas the superior planets have had only two of them, and the Moon only two. For the inferior planets, again as before, when they are above the Sun, are first hidden in the morning and rise in the evening, like the Moon, made western from eastern. And then Venus from the Morning Star (Phosphorus) becomes the Evening Star (Hesperus), and keeps this name until, like the superior planets, as also Mercury, she sets in the evening heliacally; thence they rise in the morning heliacally, made eastern in the middle; and so Venus, now conspicuous, becomes Lucifer. Sometimes, however, in Mars and likewise in Venus retrograde, the order of the appearances is changed.
How are the planets said to be hypaugi, or under the rays? In the time intermediate between the occultations and emersions, because then the rays (augai), or the brightness of the air illuminated by the rays of the Sun, though not yet risen, occupy the eyes, so that they do not perceive the stars themselves. So the Moon, so Venus, so Jupiter dazzle the eyes by their presence, so that these do not discern the lesser fixed stars near them.
In what sense are the planets said to be increased or diminished in light? Not by that real light of the phase waxing or waning: for the faces of the planets which stand above the Sun are fully illuminated about their risings and occultations, but by the accidental sight of this illuminated face. For they are said to be increased in light when they become more and more conspicuous, either by the departure of the Sun from them, as happens after the morning appearances of the superior planets and fixed stars, or by their own departure from the Sun, as happens after the evening risings of the Moon and the inferior planets, or by both together, as after the morning risings of the inferior planets; diminished in light, when they return to the Sun, as the Moon and the inferior planets toward the morning occultations, or when the Sun approaches them, as happens toward the evening occultations of the superior planets, or when they meet one another, as the inferior planets toward the same evening occultations, where it happens by accident that the Moon and Venus are said to be diminished in light when truly their faces too are diminished, increased when truly they are increased. Perhaps, therefore, from the Moon this manner of speaking first drew its origin.
How far apart are the emersions above mentioned from the neighbouring occultations, or both from the conjunction of the Sun? There is great variety, and they differ not only between different planets, but also in the different turns of one and the same planet; indeed the very distance of the emersion from the conjunction and the distance of the occultation from it frequently differ among themselves.
Tell the causes of this variety. The causes are chiefly six, of which two, and the chief, belong to book three and the doctrine of the sphere. The first is the obliquity of the zodiac, whence arise the oblique ascensions and descensions, varying for the different signs of the zodiac in which the Sun and planets are. For the same star at an equal remove from the Sun and with equal light, if it rises in the morning before the Sun in signs of right ascension, can stand much higher above the horizon or above the circle of position of the Sun than if this were in oblique signs. The same is to be understood of the evening appearances and right or oblique descensions. Second, all these things are made more evident by the different obliquities of the horizons. For where this obliquity is greater, there the variety of its effect is also greater. And more physical causes come in, namely the different thickness of the air, on which see page 285 and book I, page 146.
The third consists in the diversity of the proper motions in longitude. For the occultations and emersions of the fixed stars, other things equal (on which see page 286), are separated by a shorter time from their conjunction with the Sun than those of the planets; and of these, the lower each is, the longer is the delay of the evening occultation or morning emersion, other things equal. And so Venus, and more Mercury, in the shortness of their delay surpass even the fixed stars in these kinds of appearances. Conversely, from the rays of the Sun in the evening the Moon extricates herself most quickly, after her Mercury, Venus most slowly, and conversely in the morning (other things equal) Venus hides herself first, then Mercury, the Moon most slowly and nearest the moment of conjunction. Nor is the diversity of the motions of one and the same planet of no weight here, especially of Mercury, in the morning appearance and evening occultation; to which add the inequality of the motions of the Sun itself.
The fourth is the different latitude of different planets, and also of one and the same planet. For through it the first and second causes are varied very evidently, since the variety of the declinations is increased.
The fifth consists in the different apparent magnitude of the stars, whence it came about that to the fixed stars, in proportion to the six orders of magnitude, different arcs of emersions and occultations were also attributed (above, book III, page 285). The same therefore holds also in the planets in a certain manner, which, according as they are joined to the Sun in one part or another of their eccentric, appear greater or less, being at different distances from the centre of the Earth, especially Mars, whose eccentricity is the greatest among the superior planets. But this cause has greater force in the inferior planets in the comparison of the evening occultation, when they are near the Earth, with the morning, when they are remote; especially Venus, who becomes here seven times higher from the Earth than there. Add here the different brightness of the lights in different planets, which in the Moon the force of the illumination from the Earth sometimes assists, as was said above.
The sixth cause, finally, consists in the diversity of the face. For the Moon and Venus, if they did not change their faces, supported the one by magnitude, the other by brightness of light, would be seen much longer.
Tell some evident effects of these many causes in the appearances of the planets. 1. Mars sometimes rises twice in the morning from the rays, at an intermediate time, namely after conjunction with the Sun, again hidden for a time. So also he is sometimes twice hidden by the rays before conjunction with the Sun, the rising in the middle time being irregular.
2. Venus, who often lies hid very long, at other times, namely retrograde in Pisces, does not set in the evening until after conjunction with the Sun in longitude, and rises in the morning before the conjunction, and so emerges in the morning before she is hidden in the evening: so that she is conspicuous on the same day in the evening and in the morning, notwithstanding that she is thinned to a horn.
3. Mercury in our hemisphere, as a morning star in Taurus, as an evening star in Scorpio, although advanced very far from the Sun, does not nevertheless emerge from the rays and so comes more rarely into view, though in the southern climates he then rises most clearly.
4. The Moon is sometimes seen on the same day old and new, whence the Greeks gave her the name ene kai nea, old and new, which name passed to the first day of the month, which we call the Calends; at other times conversely she emerges in the evening only on the fourth day from conjunction, when she has already traversed a whole sign from the Sun and besides one decan of the second. Hold the same of occultation conversely.
5. Indeed it is even reported in historical records that the Moon has sometimes been seen standing near the Sun in the very middle of the heaven; this happened at Seville, if I am not mistaken, in the year 1553, in the month of March, on the 13th, the Sun in 3° of Aries, the Moon in 23° (compare vol. II, pp. 84, 699). It is necessary, therefore, that these things concurred: 1) the distance from the Sun in a great circle was 10 or 11 degrees, which distance from the Sun gives an apparent horn 19″ broad, which is the 109th part of the diameter of the Moon; 2) that the substance of the ether about the Sun was pure, as in eclipses of the Sun, in which stars appear; 3) that the Earth in those places where the Sun is vertical (as were then the mountains called of the Moon in Africa) was clothed with snow or at least a hoary mist; 4) that conversely in the place of the spectacle the heaven was very pure and clear and the twilights short. These things being given, the Moon, if not by the very thin line of her horn, yet at least by the light which she had in great measure from the Earth, could shine and move the sight in clear noon.
How do we know how many hours the Moon shines by night? Although this also has great variety on account of the first four of the causes enumerated above, Pliny nevertheless embraces all this variety in a general rule, which holds the mean between extremes. She shines, adding three-quarters and a half-ounce of hours from the second day to the full orb, and subtracting in the decrease. The sense is: as many days as there are in the age of the Moon, so many three-quarters and so many half-ounces of hours (of which any night has twelve) does she shine until she sets, and this indeed from the new to the full, or the age of the Moon of 15 days. Thence, however, as many days as are added to the age of the Moon above 15, just so many three-quarters and so many half-ounces are again to be subtracted from the number of 12 hours collected with the age of 15 days: a three-quarter of an hour is 45 minutes, a half-ounce 2½ minutes, the sum 47½, which taken fifteen times makes nearly 12 hours. (Compare vol. II, 277.)
IV. Of the configurations of the planets among themselves.
What befalls any two planets compared with each other that is worthy of consideration? Two very notable things, one in respect of the rays, the other in respect of the swiftness or slowness of the apparent motions. From the former respect arise aspects, an astrological word, from the latter harmonies.