Chapter XIV. Number of the’ Modes of Prorogation（续 1）

+ Literally, and perhaps more properly, “ its meeter.”

{ That is to say, orbs, in contradistinction to prorogations made by aspects or degrees merely.

§ Of the stars aid places brought into configuration.

the sun-beams*. This rule must be particularly attended to, because, even though the Moon be not prorogatory, the — solar place itself becomes anzretic, if shackled by the simultaneaus presence of a malefic, and not restored to freedom of operation by any benefic.

The number of years, depending on the distances between the prorogatory and anaretic places, cannot be always gathered simply and at once from the ascensional timest of _ each respective degree; but only in cases when the ascendant itself, or some other specific degree or body, actually ascending in the oriental horizon, may possess the prorogation. For, if it be desired to calculate agreeably to nature, every process of calculation that can be adopted must be directed to the attainment of one object; that is to say,-to ascertain after, how many equatorial timest the place of the succeeding body, or degree, will arrive at the position preoccupied at the birth by the preceding body, or degree: and, as equatorial time transits equally both the horizon and the meridian, the places in question§ must be considered, in respect of their proportionate distances from both these ; each equatorial degree|| being taken to signify one. jolat year. ‘

In conformity with the foregoing remarks, when it may

* ‘Whalley’s translation of this passage isin direct contradiction to -

the sense: and even that of Allatius, as well as other Latin ones, are (if strictly correct) confused in their meaning. . t “ Ascensional times.” These are, in other words, the number of degrees of the equator, equivalent to a certain number of zodiacal degrees, ascending in any particular latitude. They are also otherwise called the oblique ascension of such zodiacal degrees.

} “ Equatorial times” here signify degrees of the equator, by which all time is measured. . § That is to say, of the preceding and of the succetding pa or

|} Which may be intercepted in the arc Between them.

Chap. XIV.] : proLEMy’s TETRABIBLOS. - «180

happen that the prorogatory.and preceding place may be actually on the oriental horizon, it wil] be proper to reckon, at once, the ascensional times which may intervene until the meeting of the degrees; because, after the same number of . equatorial times, the anzreta will arrive at the prorogatory place ; that is to say, at the oriental horizon. Should the prorogatory place be found on the meridian, the whole number of degrees by right ascension, in which the whole intercepted arc will transit the meridian, must then be taken. . And if the prorogatory place be on the occidental horizon, the number of descensions, in which every degree of the distance will be carried down, (or, in other words, the number of ascensions, in which their opposite degrees will ascend), is in that case to be reckoned*.

When, however, a prorogatory and preceding place may — not be situated on any one of the three aforesaid points, but in some intermediate station, it must be observed that other times{ will then bring the succeeding place to the preceding one; and not the times of ascension or descension, or transit of the mid-heaven, as above spoken of. For any-places whatever, which have one particular position, on the same — degree, in regard to the horizon and meridian, are alike and identical. This is the case, for instance, with all places lying on any one of those semicircles which are drawn through the arcs of the meridian and horizon ; and each of these semicircles (all of which have position at the same equal distance from each other) marks one temporal hour] ;

* This number.is that of the oblique descensional times of the intercepted are, or of the oblique ascensional times of the arc opposite

to it.—The whole of the instructions in this paragraph are es eoxem- - plified in the following Chapter.

t Or, times to be reckoned in another manner.

t On this passage, there has been founded, (to use Whalley’s words) “ what we call Mundane Parallels, or parallels in the world. And, “as zodiacal parallels are equal distances from the tropical or equi-

BO PTOLEMY’S TETRABIBLOS, [Book TiT. and, as the time occupied in proceeding through the places* above described, and arriving at the same position of the horizon and meridian, is rendered unequal to and different from the time of transits in the zodiac ; so, also, the transits of other spaces are made, agreeably to their position, m time | again distinct from this.

There is, however, a method by which the sraneHisd of time, occupied in the progress ef a succeeding place to a prorogatory and preceding place, in whatever position, whether oriental, meridianal, or occidental, or any other, may be easily calculated. It is ag follows :—

When it has been ascertained what degree of the zodiac is on the mid-heaven, as also which are the preceding and

“‘ woctial circles, 30 mundane pataNels are a like equal distance from “the horizontal or meridianal points or circles. And as zodiacal ‘‘ parallels are measured by the zodiacal circle, so those nrundaae pa- “ rallels are measured by the diurnal or nocturnal arcs: and just so “ong as the Sun or any other planet is, in proceeding: from the cusp * ofthe tivelfth Fouse to the cusp of the tenth, the same Sun or other “ planct will be in proceeding ‘from ‘the cusp of the tenth tothe cusp of “the eighth Howse. And ¢he distance between San-risiag and *‘ sotting, is the diarnal arc which the meridian euts in ‘two equal “parts. In directions, these mundane parallels have a twofold cen- “ sideration: first, simple; secondly, according to the rapt me- “tion of the earth, or the primum mobile : all which have been largely ‘“ explained by the learned Monk, Piacidus,” &c. That Author has ‘eentainly ‘stated, m one of his Theses, that “ those seats, or parts of “the cirole, are to be received, in which the stars, having a different ‘declination, effect equal temporal hours,’(p. 22,Cooper’s Translation.) and he has fully exemplified this principle in other parts of his “ Primum Mobile ;” but Ptolemy tere speaks only of one of the semivircles hetwoen the horizon and meriditin, without reference to any other semi-. clrete, correspomling in-distance ‘from the horizon and mid-heaven ; and all that he has said on the subject amounts only to this, that the prorogution is conrpteted ‘when the ‘succeeding place atrives at the peal semicircte on which the preceding place had been posited.

* ‘The ascomtant, mid-heaven, ana western horizon ; as rhentioned - in the precoding ‘paragraph.

" succeeding degrees, the period of whose meeting is to he

calculated, the position of the preceding. degree, and its distance in temporal hours from the meridian, are next to be noted ; because any part of the zodiac, on becoming distant from the meridian in the same temporal hours, must fall on the same individual semicircle*. For ascertaining this distance, the number of ascensions, im a right sphere, found in the intermediate space between the said preceding degree and the mid-heaven, either above or under the earth, is to be divided by the number of the diurnal or nocturnal horary times of the said preceding degree: for instance, if that degree be above the earth, by its diurnal horary times ; and, by. its nocturnal, if it be under the earth. It is then to be discovered in what number of equatorial times‘the succeeding degree will be distant from the same meridian, by as many sifnilar temporal hours as those by which the preceding degree is distant from it. And, to effect this, the hours ° in question must be noted, and it must first be observed, by the right ascensions agai, how many equatorial times the succeeding degree; at ‘its original position, is distant from the degree on the mid-heaven 5 and then it must be seeri how many equatorial times it will be distant, on coming to the preceding degree’s distance in temperal hours from the © said mid-heaven: this will be found, by multiplying those hours by the succeeding degree’s horaty times; diurnal, if