Ptolemy - Ptolemy's Tetrabiblos - Book 3: Ch. 15 lyrics

CHAPTER XV 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; and where the horary magnitude of the beginning of Gemini will be about seventeen equatorial times. 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. 1 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. 2 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 3); 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. 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 pa** the mid-heaven; because, again, the prorogatory place was culminating. 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 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 1. 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 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 a**igned a position between the two angles of the mid-heaven and the west, the proper times of the distances from these angles to the first point of Gemini 1 would be found to be 58 from the mid-heaven, and 70 from the west. The distances, in temporal hours, of the preceding degree from each of these angles, are then to be ascertained; and whatever proportion these same temporal hours, contained in such distances between the said preceding degree and each angle, may bear to the temporal hours of the whole quadrant, the same proportion, out of the excess of the times of distance of one angle over those off the other, is either to be added to, or deducted from, the actual number of times of the respective angles. For instance, in the example before set forth, 70 times exceed 58 times by 12; and the preceding place was distant from the angles three equal temporal hours, which are the half of six, the number belonging to the whole quadrant. Now, three being the half of six, and 12 being the amount of the excess, the half of 12 is therefore to be taken, giving 6 to be either added to the 58 times, or subtracted from the 70: thus, in either way, producing 64, the required number of times. 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. The anæretic and critical influences of all meetings or descensions of prorogators 1 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 a**istance 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 d**h will ensue; and, even though one of the places 3 may be disposed favour-ably 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 an*logy, 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 a**igned, 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.