IN order to exemplify the foregoing instructions, let the first point of Aries be supposed as the preceding place, and the first point in Gemini the succeeding; and let the latitude of the country, to which the operation relates, be such as will cause the longest day to consist of fourteen hours 2; and where the horary magnitude of the beginning of Gemini will be about seventeen equatorial times. 3
Let the first point of Aries be first placed on the ascendant, so that the beginning of Capricorn may be on the mid-heaven above the earth,
In like manner, let the first point of Aries be next placed on the mid-heaven, culminating; so that the first point of Gemini, in its first position, may be distant from the said mid-heaven 58 equatorial times. 4 Now, as it is required to bring the first point of Gemini, in its second position, to the mid-heaven, the whole distance is to be reckoned, viz. 58 times, in which Aries and Taurus pass the mid-heaven; because, again, the prorogatory place was culminating. 5
In the same way, let the first point of Aries be descending 6; so that the beginning of Cancer may occupy the mid-heaven, and the first point of Gemini precede the mid-heaven at the distance of 32 equatorial times. 7 Therefore, as the first point of Aries is on the west, and again distant six temporal hours from the meridian, let these six hours be multiplied by the seventeen times; which will produce 102, making the sum of the distance 8 of the first point of Gemini, at its future descension, from the meridian. 9 But, as the first point of Gemini, at its first position, was already distant from the meridian 32 times which number 102 exceed by 70; it will consequently arrive at its
Again, let the first point of Aries have another position, not in any angle, 2 but, for instance, at the distance of three temporal hours past the meridian; so that the 18th degree of Taurus may be on the mid-heaven, and the first point of Gemini be approaching the mid-heaven, at the distance of thirteen equatorial times. The seventeen times must, therefore, be again multiplied by the three hours, and the first point of Gemini, at its second position, will be found to be past the meridian, at the distance of 51 times. 3 The distance of 13 times of the first position and 51 times of the second position are then both to be taken; and they will produce 64 times. In the former instances the prorogatory place performed in the same succession; viz. occupying 46 times in coming to the ascendant, 58 in coming to the mid-heaven, and 70 in coming to the west; so that the present number of times, depending on the intermediate position between the mid-heaven and the west, and being 64, also differs from each of the other numbers, in proportion to the three hours' difference of position. For, in the other cases which proceeded by quadrants, 4 according to the angles, the times progressively differed by twelve, but, in the present case of a minor distance of three hours, they differ by six. 5
There is, however, another method which may be used, and which is still more simple; for instance, should the preceding degree be on the ascendant, the following intermediate times of ascension, 6 between it and the succeeding degree, may be reckoned; should it be on the mid-heaven, the times of ascension must be reckoned on a right sphere; and, if it be on the west, descending, the intermediate times of descension 7 are to be reckoned. But, should the preceding degree be between any two of these angles, as, for instance, at the distance of Aries, just spoken of, the proper times for each angle must first be considered. And, since the first point of Aries was assigned a position between the two angles of the mid-heaven and the west, the proper times of the distances from
If, however, the preceding place should be distant from either angle two temporal hours, which are the third part of 6, then, in that case, the third part of 12, the amount of the excess, must be taken, viz. 4: and, if the said two hours be the distance, as calculated from the mid-heaven, the said 4 times are to be added to the 58 times; but, if it be the distance from the occidental angle, the 4 times are to be subtracted from the 70.
In conformity with these rules now laid down, the amount of the times must necessarily be obtained. 2
In order to obviate the doubts which frequently arise, as to the particular star or place to which the anæretic dominion ought to be assigned, all the meetings should be duly contemplated and considered, each by each; and thus, after considering those chiefly corresponding with the events already past, and with the future events about to follow, or with the whole altogether, it will be practicable to found an observation on the equality or inequality of their influence.
96:2 This, in the Northern Hemisphere, would be the latitude of Alexandria (where Ptolemy flourished), or, in his own words, that of the 3rd Climate, passing through Lower Egypt, numbered 30° 22'.--Vide extracts from the Tables of the Almagest, inserted in the Appendix.
96:3 This is the magnitude of the diurnal temporal hour of the first point of Gemini in the latitude prescribed.
97:1 By right ascension, as shown by the Extract, inserted in the Appendix, from the Tables of Ascensions in the Almagest. The exact distance, however, according to that Table, is 47° 44'.
97:2 Or rather, according to the Table, 102° 39'.
97:3 That is to say, of the oblique ascension, which is here required to be reckoned; because the prorogatory and preceding place is in the ascendant. Vide p. 95, and Note 2 in p. 94. And the first point of Gemini, on arriving at the ascendant, will be distant from the mid-heaven 102° 39' by right ascension; the 13th degree of Aquarius being then in culmination in the prescribed latitude. The oblique ascensions in the latitude 30° 22' N. are also shown in the extract referred to in the preceding note: and it thereby appears, that Aries and Taurus ascend in 45° 5', instead of 46°.
97:4 Or, rather, 57° 44'--by right ascension.--Vide extract above referred to.
97:6 Or on the cusp of the 7th House.
97:7 Or, rather, 32° 16'--by right ascension again.--Vide extract as before.
97:8 By right ascension. The amount according to the Table is, however, 102° 39', as before stated.
97:9 On which the 10th degree of Virgo will then be posited.
98:1 By oblique descension and ascension: Vide p. 95.--The Table shows the amount to be 70° 23'.
98:2 In reference to p. 95, and Note 1 in the same page.
98:3 The 18th degree of Cancer being then in culmination.
98:4 Or semi-diurnal arcs, each equal to six temporal hours.
98:5 The amount of the progressive difference of the times of prorogation, as here mentioned, is of course only applicable to the parallel of declination of the first point of Gemini, in the latitude before quoted. It must necessarily vary in all other parallels of declination, and also in all other latitudes.
98:6 Oblique ascension.
98:7 The times of oblique descension of any arc of the zodiac are equal to the times of oblique ascension of its opposite arc; as before explained.
99:1 That is to say, at the time of the 1st point of Aries transiting the cusp of each angle respectively.
99:2 The calculation of time may be greatly facilitated by the use of a zodiacal planisphere, said to have been invented about thirty years ago by Mr. Ranger, who died without making his invention public. The invention consists of a set of instruments perfectly adapted, as far as relates to the zodiac, for astronomical, as well as astrological, purposes; and the completeness with which it solves, in the most intelligible and expeditious manner, all the astronomical problems of the zodiac, deserves attention. Whether a similar plansiphere was known in the days of Placidus, I am not aware; but it is worthy of remark that the following words occur in his "Primum Mobile," and seem almost to have been predicted of Mr. Ranger's planisphere:--"If any one would provide himself with a Ptolemic planisphere, with the horary circles, crepuscules, the zodiac's latitude, and all other things requisite, it would be of very great service towards foreseeing the aspects." (Cooper's Translation, p. 87.) In the Appendix will be found a plate, containing diagrams drawn by the instruments in question, which, though not completely filled up, will show how easily, and, at the same time, how accurately, the measure of time in directions may be ascertained. The said diagrams have been adapted to the "exemplification" here given by Ptolemy; one of them being laid down for the latitude of Alexandria, and the other for the latitude of southern Britain (51° 30' N.), with similar positions of the preceding and succeeding places adverted to in the text.
100:1 These meetings and descensions are technically termed "directions."
100:2 On these words Placidus has the following remark: "The revolutions may possess some virtue, but only according to the constitution of the stars to the places of the prorogators of the nativity, and their places of direction, but no farther; as Ptolemy was of opinion, and briefly expresses himself in his Chapter of Life. 'Those who are afflicted, both in the places and conclusions of the years, by the revolution of the stars infecting the principal places, have reason to expect certain death.'" (Cooper's Translation, p. 127.)
100:3 Of the significators before mentioned.