Ptolemy's Tetrabiblos · Ptolemy
EXEMPLIFICATION
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[165]; and where the horary magnitude of the beginning of Gemini will be about seventeen equatorial times.[166] [165] 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. [166] This is the magnitude of the diurnal temporal hour of the first point of Gemini in the latitude prescribed. 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, and the first point of Gemini be distant from the said mid-heaven 140 equatorial times.[167] Now, since the first point of Aries is distant six temporal hours from the mid-heaven above the earth, the times of that distance will be found, by multiplying the said six hours by the seventeen equatorial times of the horary magnitude of the first point of Gemini, to be 102.[168] The whole sum of the distance to the mid-heaven above the earth, is 148 times; and as 148 times exceed 102 by 46, the succeeding place will consequently devolve into the preceding place after 46 times (being the amount of the times of ascension of Aries and Taurus[169]); since, in this instance, the prorogatory place is established in the ascendant.
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.[170] 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.[171] In the same way, let the first point of Aries be descending[172]; 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.[173] 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[174] of the first point of Gemini, at its future descension, from the meridian.[175] 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 descension after 70 times, the amount of the excess; in which space Aries and Taurus will have descended, and their opposite signs Libra and Scorpio arisen.[176]
Again, let the first point of Aries have another position, not in any angle,[177] 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.[178] 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,[179] 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.[180]
The anæretic and critical influences of all meetings or descensions of prorogators[185] remain to be determined; beginning, in due order, with such as are accomplished in the shortest time. And whatever else may happen, by means of any affliction or assistance offered (in the manner heretofore prescribed) during the actual transit of the meeting, is also to be decided on, as well as whatever may occur through other circumstances, arising out of the ingresses taking place at the time: because, should the places of both the significators be afflicted, and should the transit of the stars, at the then existing ingress, operate injuriously on the chief ruling places, it is then altogether probable that death will ensue;[186] and, even though one of the places[187] may be disposed favourably to human nature, the crisis will still be important and perilous; but, if both the places be so disposed favourably, some debility only, or transient malady, or hurt, will then happen. It is, however, necessary in these cases, to consider also what familiarity, or analogy, the peculiar properties of the places, thus meeting, may bear to the circumstances of the nativity. 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.
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