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] [167] 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 147° 44′. [168] Or rather, according to the Table, 102° 39′.