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This webpage reproduces part of the

Claudius Ptolemy

published in the Loeb Classical Library, 1940

The text is in the public domain.

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 p271  Cam.2 p127 Book III

10. Of Length of Life.

The consideration of the length of life takes the leading place among inquiries about events following birth, for, as the ancient​51 says, it is ridiculous to attach particular predictions to one who, by the constitution of the years of his life, will never attain at all to the time of the predicted events. This doctrine is no simple matter, nor unrelated to others, but in complex fashion derived from the domination of the places of greatest authority. The method most pleasing to us and, besides, in harmony with nature is the following. For it depends entirely upon the determination of the prorogative​52 places and the stars that rule the prorogation, and upon the determination of the destructive​53 places or stars.​54 Each of these is determined in the following fashion:

 p273  In the first place we must consider those places prorogative in which by all means the planet must be that is to receive the lordship of the prorogation; 128namely, the twelfth part of the zodiac surrounding the horoscope, from 5° above the actual horizon up to the 25° that remains, which is rising in succession to the horizon; the part sextile dexter to these thirty degrees, called the House of the Good Daemon; the part in quartile, the mid‑heaven; the part in trine, called the House of the God; and the part opposite, the Occident. Among these there are to be preferred, with reference to power of domination, first those​55 which are in the mid‑heaven, then those in the orient, then those in the sign succedent to the mid‑heaven, then those in the occident,​56 then those in the sign rising before mid‑heaven; for the whole region below the earth must, as is reasonable, be disregarded when a domination of such importance is concerned, except only those parts which in the ascendant itself are coming into the light. Of the part above the earth it is not fitting to consider either the sign that  p275 is disjunct from the ascendant,​57 nor that which rose before it, called the House of the Evil Daemon,​58 because it injures the emanation from the stars in it to the earth and is also declining, and the thick, misty exhalation from the moisture of the earth creates such a turbidity and, as it were, obscurity, that the stars do not appear in either their true colours or magnitudes.

After this again we must take as prorogatives the four regions of greatest authority, sun, moon, horoscope, 129the Lot of Fortune, and the rulers of these regions.

Take as the Lot of Fortune​59 always the amount of the number of degrees, both by night and by day, which is the distance from the sun to the moon, and which extends to an equal distance from the horoscope in the order of the following signs,​60 in order that, whatever relation and aspect the sun  p277 bears to the horoscope, the moon also may bear to the Lot of Fortune, and that it may be as it were a lunar horoscope.61

130Of these,​62 by day we must give first place to the sun, if it is in the prorogative places; if not, to the moon; and if the moon is not so placed, to the planet​63 that has most relations of domination to the sun, to the preceding conjunction, and to the horoscope; that is, when, of the five methods of domination​64 that exist, it has three to one, or even more; but if this cannot be, then finally we give preference to the horoscope. By night prefer the moon first,  p279 next the sun, next the planets having the greater number of relations of domination to the moon, to the preceding full moon, and to the Lot of Fortune; otherwise, finally, if the preceding syzygy was a new moon, the horoscope, but if it was a full moon the Lot of Fortune.​65 But if both the luminaries or the ruler of the proper sect​66 should be in the prorogative places, we must take the one of the luminaries that is in the place of greatest authority. And we should prefer the ruling planet to both of the luminaries only when it both occupies a position of greater authority and bears a relation of domination to both the sects.

When the prorogator has been distinguished, we must still further adopt two methods of prorogation.​67 131The one, that which follows the order of the following signs, must be used only in the case of what is called  p281 the projection of rays,​68 when the prorogator is in the orient, that is, between mid‑heaven and the horoscope. We must use not only the method that follows the order of following signs, but also that which follows the order of leading signs, in the so‑called horimaea, when the prorogator is in places that decline from mid‑heaven.69

This being the case, the destructive degrees in the prorogation that follows the order of leading signs are only the degree of the western horizon, because it causes the lord of life​70 to vanish; and the degrees of the planets that thus approach or bear witness​71 merely take away and add years to the sum of those as far as the setting of the prorogator, and they do not destroy because they do not move toward the prorogative place, but it moves toward them.​72 The beneficent stars add and the maleficent subtract. Mercury, again, is reckoned with the group to which he bears an aspect. The number of the addition or subtraction is calculated by means of the location in degrees in each case. For the entire number of years is the same as the number of hourly periods of each  p283 degree, hours of the day​73 when it is day and hours of the night when it is night; this must be our reckoning when they are in the orient, and subtraction must be made in proportion to their departure therefrom, 132until at their setting it becomes zero.

In the prorogation which follows the order of following signs, the places of the maleficent planets, Saturn and Mars, destroy, whether they are approaching bodily, or project their rays from any place whatever in quartile or in opposition, and sometimes too in sextile, upon the signs called "hearing" or "seeing"​74 on grounds of equality of power; and the sign that is quartile to the prorogative sign in the order of following signs likewise destroys. And sometimes, also, among the signs that ascend slowly the sextile aspect destroys, when it is afflicted,​75 and again among the signs that ascend rapidly the trine. When the moon is the prorogator, the place of the sun also destroys. For in a prorogation of this kind the approaches of planets avail both to destroy and to preserve, since these are  p285 in the direction of the prorogative place.​76 However, it must not be thought that these places always inevitably destroy, but only when they are afflicted. For they are prevented both if they fall within the term​77 of a beneficent planet and if one of the beneficent planets projects its ray from quartile, trine, or opposition either upon the destructive degree itself or upon the parts that follow it, in the case of Jupiter not more than 12°, and in that of Venus not over 8°; also if, when both the prorogator and the approaching planet are present bodily, the latitude of both is not the same.​78 133Thus when there are two or more on each side, assisting and, vice versa, destroying, we must consider which of them prevails, both by the number of those that co‑operate and by power; by number when one group is perceptibly more numerous than the other, and with regard to power when some of the assisting or of the destroying planets are in their own proper places, and some are not, and particularly when some are rising and others setting. For in general we must not admit any planet, either to destroy or to aid, that is under the rays of the sun, except that when the moon is prorogator the place of the sun itself is destructive, when it is changed about by the presence  p287 of a maleficent planet​79 and is not released​80 by any of the beneficent ones.

However, the number of years, determined by the distances between the prorogative place and the destructive planet, ought not to be taken simply or offhand, in accordance with the usual traditions, from the times of ascension of each degree, except only when the eastern horizon itself is the prorogator, or some one of the planets that are rising in that region. For one method alone​81 is available for him who is  p289 considering this subject in a natural manner — to calculate after how many equinoctial periods​82 the place 134of the following body or aspect comes to the place of the one preceding at the actual time of birth, because the equinoctial periods pass evenly​83 through both the horizon and the mid‑heaven, to both of which are referred the proportions of spatial distances, and, as is reasonable, each one of the periods has the value of one solar year.​84 Whenever the prorogative and preceding place is actually on the eastern horizon, we should take the times of ascension of the degrees up to the meeting-place; for after this number of equinoctial periods the destructive planet comes to the place of the prorogator, that is, to the eastern horizon. But when it​85 is actually at the mid‑heaven, we should take the ascensions on the right sphere in which the segment​86 in each case passes mid‑heaven; and when it is on  p291 the western horizon, the number in which each of the degrees of the interval descends, that is, the number in which those directly opposite them ascend. But if the precedent place is not on these three limits but in the intervals between them, in that case the times of the aforesaid ascensions, descensions, or culminations will not carry the following places to the places of the preceding, but the periods will be different. For a place is similar and the same if it has the same position​87 in the same direction 135with reference both to the horizon and to the meridian. This is most nearly true of those which lie upon one of those semicircles​88 which are described through the sections of the meridian and the horizon, each of which at the same position makes nearly the same temporal hour. Even as, if the revolution is upon the aforesaid arcs, it reaches the same position with reference to both the meridian and horizon, but makes the periods of the passage of the zodiac unequal with respect to either, in the same way also at the positions of the other distances it makes their  p293 passages in times unequal to the former.​89 We shall therefore adopt one method only, as follows, whereby, whether the preceding place occupies the orient, the mid‑heaven, the occident, or any other position, the proportionate number of equinoctial times that bring the following place to it will be apprehended. For after we have first determined the culminating degree of the zodiac and furthermore the degree of the precedent and that of the subsequent, in the first place we shall investigate the position of the precedent, how many ordinary hours it is removed from the meridian, counting the ascensions that properly intervene up to the very degree of mid‑heaven, whether over or under the earth, on the right sphere, and dividing them by the amount of the horary periods​90 of the precedent degree, 136diurnal if it is  p295 above the earth and nocturnal if it is below. But since the sections of the zodiac which are an equal number of ordinary hours removed from the meridian lie upon one and the same of the aforesaid semicircles, it will also be necessary to find after how many equinoctial periods the subsequent section will be removed from the same meridian by the same number of ordinary hours as the precedent.​91 When we have determined these, we shall inquire how many equinoctial hours at its original position the degree of the subsequent was removed from the degree at mid‑heaven, again by means of ascensions in the right sphere, and how many when it made the same number of ordinary hours as the precedent, multiplying these into the number of the horary periods​92 of the degree of the subsequent; if again the comparison of the ordinary hours relates to the mid‑heaven above the earth, multiplying into the number of diurnal hours, but if it relates to that below the earth, the number of nocturnal hours. And taking the results from the difference of the two distances, we shall have the number of years for which the inquiry was made.

To make this clearer, suppose that the precedent place is the beginning of Aries, for example, and the subsequent the beginning of Gemini, and the latitude that where the longest day is fourteen hours long,​93 137and the horary magnitude of the beginning of Gemini  p297 is approximately 17 equinoctial times.​94 Assume first that the beginning of Aries is rising, so that the beginning of Capricorn is at mid‑heaven, and let the beginning of Gemini be removed from the mid‑heaven above the earth 148 equinoctial times.​95 Now since the beginning of Aries is six ordinary hours​96 removed from the diurnal mid‑heaven, multiplying these into the 17 equinoctial times, which are the times of the horary magnitude of the beginning of Gemini, since the distance of 148 times relates to the mid‑heaven above the earth, we shall have for this interval also 102 times. Hence, after 46 times, which is the difference, the subsequent place will pass to the position of the precedent. These are very nearly the equinoctial times of the ascension of Aries and Taurus, since it is assumed that the prorogative sign is the horoscope.

Similarly, let the beginning of Aries be at mid‑heaven, so that at its original position the beginning of Gemini may be 58 equinoctial times​97 removed from the mid‑heaven above the earth. Therefore, since at its second position the beginning of Gemini should be at mid‑heaven, we shall have for the difference of the distances precisely this amount of 58 times,  p299 in which again, because the prorogative sign is at mid‑heaven, Aries and Taurus​98 pass through the meridian.

138In the same way let the beginning of Aries be setting, so that the beginning of Cancer may be at mid‑heaven and the beginning of Gemini may be removed from the mid‑heaven above the earth in the direction of the leading signs​99 by 32 equinoctial periods. Since, then, again the beginning of Aries is six ordinary hours removed from the meridian in the direction of the occident, if we multiply this by 17 we shall have 102 times, which will be the distance of the beginning of Gemini from the meridian when it sets. At its first position also it was distant from the same point 32 times; hence it moved to the occident in the 70 times of the difference, in which period also Aries and Taurus descend and the opposite signs Libra and Scorpio ascend.100

Now let it be assumed that the beginning of Aries is not on any of the angles, but removed, for example, three ordinary hours from the meridian in the direction of the leading signs, so that the 18th degree of Taurus is at mid‑heaven, and in its first position the beginning of Gemini is 13 equinoctial times removed from the mid‑heaven above the earth in the order of  p301 the following signs.​101 If, then, again we multiply 17 equinoctial times into the three hours, the beginning of Gemini will at its second position be distant from mid‑heaven in the direction of the leading signs 51 equinoctial times, 139and it will make in all 64 times.​102 But it made 46 times by the same procedure when the prorogative place was rising, 58 when it was in mid‑heaven, and 70 when it was setting. Hence the number of equinoctial times at the position between mid‑heaven and the occident differs from each of the others. For it is 64, and the difference is proportional to the excess of three hours,​103 since this was 12 equinoctial times in the case of the other quadrants at the centres, but 6 equinoctial times in the case of the distance of three hours. And inasmuch as in all cases approximately the same proportion is observed, it will be possible to use the method in this simpler way. For again, when the precedent degree is at rising, we shall employ the ascensions up to the subsequent; if it is at mid‑heaven, the degrees on the right sphere; and if it is setting, the descensions. But when it is between these points, for example, at the aforesaid interval from Aries, we shall take  p303 first the equinoctial times corresponding to each of the surrounding angles, and we shall find, since the beginning of Aries was assumed to be beyond the mid‑heaven above the earth, between mid‑heaven and the occident, that the corresponding equinoctial times up to the first of Gemini 140from mid‑heaven are 58 and from the occident 70. Next let us ascertain, as was set forth above,​104 how many ordinary hours the precedent section is removed from either of the angles, and whatever fraction they may be of the six ordinary hours of the quadrant, that fraction of the difference between both sums we shall add to or subtract from the angle with which comparison is made. For example, since the difference between the above mentioned 70 and 58 is 12 times, and it was assumed that the precedent place was removed by an equal number of ordinary hours, three, from each of the angles, which are one half of the six hours, then taking also one-half of the 12 equinoctial times and either adding them to the 58 or subtracting them from the 70, we shall find the result to be 64 times. But if it was removed two ordinary hours from either one of the angles, which are one-third of the six hours, again we shall take one-third of the 12 times of the excess, that is, 4, and if the removal by two hours had been assumed to be from the mid‑heaven, we would have added  p305 them to the 58 times, but if it was measured from the occident we would have subtracted them from 70.

The method of ascertaining the amount of the temporal intervals ought in this way consistently to be followed. For the rest, we shall determine in each of the aforesaid cases of approach or setting,​105 in the order of those that ascend more rapidly, those which are destructive, 141climacteric, or otherwise transitional,​106 according as the meeting is afflicted or assisted in the way we have already explained,​107 and by means of the particular significance of the predictions made from the temporal ingresses of the meeting.​108 For when at the same time the places are afflicted and the transit of the stars relative to the ingress of the years of life afflicts the governing places, we must understand that death is definitely signified; if one of them is benignant, great and dangerous crises; if both are benignant, only sluggishness, injuries, or transitory disasters. In these matters the special quality is ascertained from the familiarity of the occurrent places with the circumstances of the nativity. Sometimes, when it is doubtful which ought to take over the destroying  p307 power, there is nothing to prevent our calculating the occourses of each and then either following, in predicting the future, the occourses which most agree with past events, or observing them all, as having equal power, determining as before the question of their degree.

The Editor's Notes:

51 Perhaps a reference to Petosiris. The passage is included by E. Riess among the fragments of Nechepso and Petosiris, Philologus, Supplementband 6, p358.

52 Aphetic is also used. Hyleg is the Arabic term.

53 Or anaeretic.

54 Bouché-Leclercq's (p411) summary of Ptolemy's system of prorogations is helpful: "His theory rests essentially upon the likening of the zodiac to a whole upon which the life of the individuals is cast with a greater or less force from a certain place of departure (τόπος ἀφετικός) and finds itself arrested, or in danger of being arrested, by barriers or destructive places (τόποι ἀναιρετικοί), without being able in any case to go beyond a quarter of the circle. The number of degrees traversed, converted into degrees of right ascension, gives the number of the years of life."

55 Sc. degrees.

56 Though he pays little attention to the system of "places" or "houses" so much used by the astrologers in (p273)the actual casting of nativity's, Ptolemy here deals with four besides the horoscope itself. Their usual names are: I, Horoscope, ὡροσκόπος; II, Gate of Hades, Ἅιδου πύλη; III, Goddess, Θεά (i.e. moon); IV, lower mid‑heaven, ὑπογεῖον; V, Good Fortune, ἀγαθὴ τύχη; VI, Bad Fortune, κακὴ τύχη; VII, Occident, δύσις; VIII, Beginning of Death, ἀρχὴ θανάτου; IX, God, Θεός (i.e. sun); X, mid‑heaven, μεσουράνημα; XI, Good Daemon, ἀγαθὸς δαίμων; XII, Bad Daemon, κακὸς δαίμων. Cf. P. Mich. 149, col. ix, 13‑19, where slightly different names are given. In this passage Ptolemy has mentioned numbers I, XI, X, IX, VII.

57 The eighth house. "Sign," of course, in this passage means not the fixed signs of the zodiac, but the places or houses of the nativity. One MS. adds here, "which is (p275)called the Inactive Place," probably a scholion which has entered the text. See the critical note.

The critical note to the Greek text, after τὸ ἀσύνδετον τῷ ἀνατέλλοντι δωδεκατημόριον, reads:

ὃ λέγεται τόπος ἀργός add. mg. N et Cam., om. libri omnes.

58 The twelfth house.

59 The directions given amount to this: Take the angular distance from sun to moon in the order of the following signs, i.e. in the direction in which the zodiac is graduated; then lay out the same distance, in the same sense, from the horoscope. The point reached is the Lot of Fortune, and it will be located with respect to the moon as the horoscope is with respect to the sun; hence it can be called a "lunar horoscope." With the older MSS. and Proclus we read φέροντος instead of ἀφαιροῦντες in this passage. On the various accounts of the Lot of Fortune see Bouché-Leclercq, pp289‑296 (who, however, readsº ἀφαιροῦντες here).

60 Here two MSS. and Camerarius (see the critical note) add: "and wherever the number falls, we may say that the Lot of Fortune falls upon that degree of the sign and occupies that place."

The critical note to the Greek text reads:

Hic add. NACam.: ὃρου δ’ ἂν ἐκπέσῃ ὁ ἀριθμὸς ἐλείνην τὴν μοῖραν τοῦ δωδεκατημορίου καὶ τὸν τόπον φαμὲν ἐπέχειν τὸν κλῆρον τῆς τύχης.

61 Camerarius and certain MSS. add here: "We ought, however, to observe which of the luminaries is found following the other. For if the moon is found following the sun, we must lay out the number which intervenes between the horoscope and the Lot of Fortune in the order of following signs; but if the moon is found preceding the sun, we must set forth this same number from the horoscope in the order of leading signs. Perhaps this is what he means, and the writer's intention is to count from moon to sun in the case of those born at night, and to make the interval in the other direction from the horoscope, that is in the order of leading signs; for thus it will turn out to be the same place for the Lot of Fortune and the same relation of aspect which he mentions." The first part of this passage can hardly be genuine because it is at variance with the general directions just given by Ptolemy; the introductory phrase of the last part clearly shows that it originated as a scholion.

62 I.e. sun, moon, horoscope, Lot of Fortune, and the rulers (see above).

63 In an aphetic (prorogative) place, says Cardanus (p469).

64 See III.2 (p233).

65 "But otherwise finally the horoscope is the prorogator" is added here in certain MSS.

66 I.e. a planet which may be the prorogator. The "proper sect" will be diurnal in diurnal genitures, nocturnal in nocturnal.

67 Bouché-Leclercq's (pp418‑419) exposition may be quoted: "The prorogator once determined . . . it is necessary to determine the sense in which it launches the life from its prorogative place; the direct sense, that is, in accordance with the proper movement of the planets, when it follows the series of [following] signs . . . ; retrograde . . . when it follows the diurnal movement . . . . At all events there is in both cases unity of measurement, the diurnal movement. In the sense here called direct the diurnal movement brings the anaeretic planet or 'following place' to meet the 'preceding place' where the prorogator is lodged. In the contrary sense it is the prorogator which is carried to the anaeretic place, which is always the occident. By either manner the length of life was equal to the number of degrees of right ascension between the prorogative place and the anaeretic place, at the rate of one year to a degree." He proceeds to point out that it therefore becomes necessary to convert degrees of the zodiac into degrees of right ascension measured on the equator.

68 On projection of rays (ἀκτινοβολία) see Bouché-Leclercq, pp247‑250. The planets, by their rotation in their orbits moving, as the astrologers said, "from (p281)right to left," "in the order of the following signs," "regard" those that precede them and "cast rays," like missiles, at those that follow them; always, however, if the action is to be effective, at the angle of one of the recognized aspects (opposition, quartile, etc., these two having the greatest offensive force).

69 That is, in such cases either method may be used.

70 The prorogator, which in this case moves toward the anaeretic place.

71 Planets in aspect to one another are said to "bear witness."

72 In this case the rays of the planets are cast away from the prorogator; Bouché-Leclercq, p420.

73 "Hours" were merely twelfth parts of the day (sunrise to sunset) or of the night, and hence "hours of the day" are not of the same length as "hours of the night" except when day and night are equal.

74 Cf. I.15.

75 See above, p267, concerning "affliction." Aries, Taurus, Gemini, Pisces, Aquarius, and Capricorn were classed as rapidly ascending signs; the others, as slowly ascending signs.

76 In this type of prorogation the diurnal movement of the heavens is carrying the planets toward the prorogative (p285)place; cf. Bouché-Leclercq, pp420‑421 (esp. 421). He points out the complexity of the calculation and the multitude of choices that lay open to an astrologer in his interpretation of a geniture.

77 See I.20‑21.

78 This would be true only in cases of the bodily approach of planets, not in aspect. The notion is that the ray will not hit its mark if the two bodies are not in the same latitude.

79 As the anonymous commentator says (p120, ed. Wolf), the sun is of a "middle temperature" (κρᾶσις), and takes the character, good or bad, of the planet associated with it; cf. I.5 above.

80 Some of the MSS. have βοηθούμενος καὶ (or ) ἀναλελυμένος, "assisted or released"; probably an explanatory gloss which worked its way into the text. The anonymous commentator explains the word to mean that a beneficent planet does not permit the sun to retain the "affliction" attached by the evil planet, but "releases" it.

81 The following general description is intended to apply to Ptolemy's lengthy account of this method. In each prorogation, two points on the ecliptic are concerned, the prorogator or precedent and the subsequent or anaeretic place, which we may call P and S respectively. S may or may not be occupied by a planet, but in this type of prorogation it always follows P, that is, lies east of it and comes to the horizon later. P, as a point on the ecliptic, may (a) lie at the intersection of the ecliptic and the equator or (p287)be (b) north of the equator or (c) south of it. The vernal and autumnal equinoxes, the beginnings of Aries and Libra, are the only points of the ecliptic which can occupy position (a); if, however, P is one of these, since it is also a point on the equator, it will pass, like all points on the equator, from horizon to meridian in 6 hours, at the rate of 15° in 1 hour (this is the hour called "equinoctial hour" by the Greeks). If P is to the north of the equator, in a north latitude, its ascension from horizon to meridian will be along a path parallel to the equator and longer than the distance from horizon to meridian on the equator; hence it takes longer than 6 equinoctial hours. Conversely, points south of the equator take a shorter course and ascend in times correspondingly shorter than 6 equinoctial hours. Nevertheless, since the Greeks defined "day" as the period from sunrise to sunset and divided it into 12 hours, similarly dividing the night, the ascension of P from rising to culmination, wherever it is situated on the ecliptic and whatever the latitude, takes place in 6 hours of the day, that is, ordinary or civil (καιρικαί) hours, which may be longer or shorter than equinoctial hours, and equal to them only when P occupies position (a), described above. The "horary magnitude" or "period" of a point on the ecliptic is the expression in terms of equinoctial times (see p95, n2) of the length of the civil hour when the sun is at that point; in north latitudes, horary magnitudes are greater than 15 for points north of the equator and less (p288)for points south, 15 being the horary magnitude of the two equinoctial points. All that has been said about P applies of course to S, which is another point on the ecliptic. The problem of prorogation is simply to discover after how many equinoctial periods or times S comes to the position originally occupied by P with relation to the meridian (or other centre, such as the western horizon). This position is defined as the one in which S is just as many civil hours removed from the meridian (or the point of reference) as was P in its original position.

82 An "equinoctial period" or "time" is the length of time which it takes one degree on the equator to pass a fixed point, i.e. 1360 of 24 hours. An "equinoctial hour" is 15 "equinoctial times." For the definition cf. Heliodorus (?) in CCAG, VII.122, 20 ff.

83 At the rate of 15 per hour, in contrast to the varying horary periods of degrees on the ecliptic.

84 In predicting the life of the subject of the horoscope. Cf. P. Mich. 149, col. xii. ll. 10‑11.

85 The prorogator.

86 The "segment" is the arc (of the ecliptic) between the two places, but the ascension of the following body is to be measured on the right sphere; that is, it is right ascension, which is measured on the equator.

87 Comes to the meridian in the same time, and is on the same side of the equator ("in the same direction"). Ptolemy introduces this characterization of "same and (p291)similar places" because the whole system of prorogation depends on determining the period after which a subsequent body will come to the same place as, or a similar place to, that occupied by a precedent body. It cannot come to exact the same place, because both bodies are on the ecliptic, oblique to the equator. Hence it is necessary to define "similar places."

88 He refers to the arcs of circles, parallel to the equator, passing through the degree of the eclipse in question, and cutting both horizon and meridian, which are intercepted between the horizon and the meridian.

89 This obscure sentence is thus explained by the anonymous commentator: "If you imagine a star moving either from the horoscope (sc. to mid‑heaven), or from mid‑heaven to the horoscope, you will discover the temporal periods of the distance; in the same way also when they are not upon the degrees of the angles."

90 ὡριαίοι χρόνοι; the expression ὡριαῖον μέγεθος, "horary magnitude," is used further on, when Ptolemy gives examples. In the Almagest, II.8, there is a table which gives the time, in degrees and minutes of the equator (i.e. equinoctial times), in which each arc of 10° of the ecliptic rises above the horizon in each of eleven latitudes beginning with the equator (right sphere); the table also gives the cumulative sums of these ascensions for each arc from the beginning of Aries. In the following chapter Ptolemy tells how the horary magnitude may be determined (p293)by the use of this table. His directions are, in brief, to take the sum of the ascensions for the degree of the sun by day (or the opposite degree by night) both in the right sphere and in the given latitude; to ascertain the difference between the two and take ⅙ of it; and then, if the degree was in the northern hemisphere, to add this fraction to the 15 "times" of one equinoctial hour, or, for a southern position, to subtract it. This will give the length of the ordinary or civil hour for the latitude and time of the year in question, in terms of the ascension of degrees of the equator, or "equinoctial times," or as Ptolemy puts it, "the number of (equinoctial) times of the civil hour under consideration." The civil day-time hour was 112 of the period from sunrise to sunset, or, of course, ⅙ of the time from sunrise to noon. In Almagest, II.9, Ptolemy gives the same directions for reducing periods expressed in equinoctial times to ordinary or civil hours; multiply the given equinoctial hours by 15 (in order to express them in "equinoctial times," as are the ascensions dealt with in the present passage) and divide by the horary period.

91 For it will then have "come to the same place" that the precedent originally occupied.

92 Or, horary magnitude.

93 This is the latitude of lower Egypt; cf. Almagest, II.6, p108, 15 ff. (Heiberg), and the table in II.8, pp134‑141.

Thayer's Note: Although Heiberg's Almagest is online, search engines don't pick up the Greek. So here, by way of helping out a bit, is the first passage (in full):

θ´. ἔνατος ἐστι παράλληλος, καθ’ ὃν ἂν γένοιτο ἡ μεγίστη ἡμέρα ὡρῶν ἰσμερινῶν ιδ. ἀπέχει δ’ οὑτος τοῦ ἰσμερινοῦ μοίρας λ κβ καὶ γράφεται διὰ τῆς κάτω χώρας τῆς Αἰγύπτου. καί ἐστιν ἐνταῦθα, οἵων ὁ γνώμων ξ, τοιούτων ἡ δὲ χειμερινὴ σκιὰ ς∠´ γ́ , ἡ δὲ ἰσμερινὴ λε ιβ´, ἡ δὲ χειμερινὴ πγ ιβ´.

94 The method described in Almagest, II.9, cited above, applied to data from the table in Almagest, II.8, gives 17 times 6 min. 30 sec.

95 This is reckoned on the right sphere. The date from the table in the Almagest will give 147 times 44 min.

96 Likewise 6 equinoctial hours, since it is an equinoctial point.

97 I.e. 148 minus 90.

98 The table of the Almagest gives 45 times 5 min. for the combined ascensions of these two signs in the latitude of lower Egypt.

99 I.e. beyond the meridian and toward Aries.

100 The table of the Almagest gives 70 times 23 min.

101 Thus, the first of Aries is west of the meridian and the first of Gemini east of it.

102 I.e. 13 times to reach the meridian, plus 51 times beyond it.

103 I.e. the centres are 6 hours removed from one another, and a difference of 12 times is observed when the movement of the subsequent place up to one of the centres is compared with its movement to the next centre in order. Hence when the prorogative place does not move between centre and centre, 6 hours, but only half of that time, this differential also will be only ½ of its full amount, 6 times instead of 12 times.

104 See p297.

105 The prorogations, which are determined by the approach of the anaeretic place to that of the prorogator, or the setting of the prorogator.

106 I.e. we shall discover whether the periods determined by such prorogations as have been described are terminated by actual death, some important crisis, or an event of less importance. Cf. Hephaestion ap. CCAG, VIII.2, p81, 1 ff.

Thayer's Note: For a masterly debunking of the whole climacterical scheme, at great length and in the most beautiful English prose, see Sir Thomas Browne's chapter on the subject: Vulgar Errors, IV.12.

107 The reference is to what was said earlier in the chapter about the influence of the various planets; see pp281 ff.

108 Cf. what is said about the chronocrators in the latter part of IV.10.

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