Tetrabiblos, or Quadripartite — Ptolemy, trans. J. M. Ashmand (1822)
English·London, 1822·in the original language·355 passages·from a digitised copy at the Internet Archive
The text · part 9 of 9
* Thus (according to the Table inserted at p. 223), in the climate or latitude of Lower 4 gypt, the times of ascension between the first point of Gemini and the first point of Sagittarius, diametrically opposite, are 205° 18’, which, being divided by 15, give 13 hours 41 minutes and a fraction of equatorial time, as the length of the day of the first point of Gemini. And the same number of times of ascension, divided by 12, give 17° 6’ and a fraction of the equator, as the length of the diurnal temporal hour. In the latitude of Southern Britain, the times of ascension between the same points as above-mentioned are 236° 2’, which, divided by 15, give 15 hours 44 minutes and a fraction of equatorial time as the length of the day of the first point of Gemini; and, if divided by 12, they produce 19° 40’ and a fraction of the equator; as the length of the diurnal temporal hour.
p. 219
signs, to the fifteen times of an equatorial hour; but subtracted therefrom, if in the southern signs. The amount thus obtained will be the required number of degrees of the temporal hour in question*. And if it be required to reduce the temporal hours of any given day or night, in a certain climate, into equatorial hours, they must be multiplied by their proper horary times, whether diurnal or nocturnal, as the case may be; the product is then to be divided by fifteen, and the quotient will necessarily be the number of equatorial hours in the climate in question, on the given day or nightt. On the other hand, equatorial hours are also to
* Thus, the aggregate times of ascension, in a right sphere, of the first point of Gemini are 57° 44’; and, in the climate of Lower Aigypt, 45° 5’:the sixth part of the difference between them is 2° 6’ and a fraction, which, added to 15°, again makes the diurnal temporal hour of the first point of Gemini equal to 17° 6’ and a fraction of the equator. In the climate of Southern Britain, the aggregate times of ascension of the first point of Gemini are 29° 43’:the sixth part of the difference between that sum and 57° 44’ of right ascension is 4° 40’ and a fraction, which, added to 15°, makes the diurnal temporal hour of the first point of Gemini, in South Britain, equal to 19° 40’ and a fraction of the equator, as before shewn.
+ For example, Diurnal horaty times of the first point of Gemini, in the latitude of Alexandria - - - - 17° 6’ 30° Number of temporal hours - - - - - 12 15)205 18 0 Diurnal equatorial hours of the first point of Gemini in the latitude of Alexandria - - 13 41 12 Diurnal horary times of the first point of Gemini in the latitude of Southern Britain’ - - - 19° 40’ 10’ Number of temporal hours - - - - - 12 15)2386 2 O
Diurnal equatorial hours of the first point of Gemini in the latitude of Southern Britain - 15 44 8p. 220 be reduced into temporal hours by being multiplied by fifteen, the product of which is to be divided by the horary times proper to the given day or night in the said climate.
The degree ascending in the ecliptic, at any given temponal hour, may also be ascertained by multiplying the number of temporal hours since sunrise, if the given hour be diurnal, but if nocturnal, since sunset, by their proper horary times; and the product is to be added, in the succession of the signs, to the aggregate number (as shewn by the ascensions proper to the climate) of the Sun’s degree, if the given hour be diurnal, but, if nocturnal, to that of the degree diametrically opposite, and that particular degree of the ecliptic which shall correspond with the total number thus found in the ascensions of the climate will be the degree then ascending*.
But, in order to ascertain the degree on the meridian above the earth, the number of temporal hours since the preceding noon are also to be multiplied by their proper honary times, and the product is to be added to the aggregate number of the Sun’s right ascension; and that degree of the ecliptic, with which the total number as found in the aggregate times of right ascension shall correspond, will then be on the meridiant. The degree on the oriental horizon will, however, also shew what degrees occupies the meridian; for, by subtracting 90
* Let the first point of Gemini be on the meridian above the earth; the number of temporal hours since sunrise will then be 6, by which 17° 6’ 30” are to be multiplied. The product will be 102° 39’ : this, added to 45° 5’, the aggregate number of the first point of Gemini in the latitude of Alexandria, will give 147° 44’, which, in the ascensions of the climate in question, will correspond to the 3d degree of Virgo, and shew that to be the degree ascending. In the latitude of Southern Britain the total number would still amount to the same; viz. 147° 44’, but it would shew 7° and about 30’ of Virgo to be ascending.
+ Let the first point of Gemini be three temporal hours past the meridian; these hours reduced to degrees, in the latitude of
APPENDIX. — R21
times (the amount of the quadrant) from the aggregate number ascribed to the said ascending degree in the Table proper to the climate, the number so reduced will be found, in the aggregate times of the Table of Right Ascension, to correspond with the degree on the meridian. And again, on the other hand, by adding 90 to the aggregate times ascribed by right of ascension to the degree on the meridian above the earth, the degree ascending may be obtained, for it will be that degree which corresponds to that total number, as stated in the Table proper to the climate*.
The Sun always preserves an equal distance in equatorial hours from all parts of the same meridian; but his distance in equatorial hours from different meridians varies according to the degrees of distance between meridian and meridian.
Alexandria, will give 51° 19’, which, added to the right ascension of the first point of Gemini, make 109° 3’, shewing the 18th degree of Cancer on the meridian. In the latitude of Southern Britain, these hours would produce 59°, which, added to the right ascension, would make 116° 44’, and shew the 25th degree of Cancer on the meridian.
* Thus, in the latitude of Alexandria, when the first point of Gemini is three temporal hours past the meridian, the 16th degree of Libra will be on the ascendant, and the aggregate times of ascension of that degree in the said latitude are 109° 3’ : by subtracting 90 from this sum, the remainder will be 109° 3’, the right ascension of the mid-heaven answering to the 18th degree of Cancer. In the latitude of Southern Britain, the 18th degree of Libra would be on the ascendant, of which degree the aggregate times of ascension in that latitude are 206° 44’, from which, if 90 be subtracted, the remainder will be 116° 44’, the right ascension of the mid-heaven answering to the 25th degree of Cancer.—The converse of these operations seems too obvious to need explanation.
p. 222
TABLE OF LATITUDES, AS SHEWN BY THE DURATION OF THE LONGEST DAY.
[From the Almagest. ]
LATITUDE.
* Alexandria. + Southern Britain.
p. 223
Extract from the Table of Ascensions (contained in the Alinagest), calculated for every tenth Degree of the Zodiac.
: 3a Climate, | 8th Climate, ee pe thro’? Lower Khro’ Southern the Equator, £eyp ay fat Britain, curnat Are| 30° 22 N. [Lat, 51° 30’ N Diurna Diurnal Arc} Diurnal Are 12 Hours. 14 Hours. {t6 Hs. 30 Mts.
Temes | Aggre-V'limes| Agere4 Times Aggre.
of | gate of gute or gate Ascen.| Times. \Ascen.| Times {Ascen.| Times
z 7 D.M.| D. M.ED. M.! D. M.D. M.I- D. M. ArleS..eseee00{10] 9.10} 9.10] 6.48] 6.481 4. 5 4. 6
20] 9.15/350.50) 6.551353. 12) 4:191355,55) 9.101360. Of 6.48/360. OF 4. 5/360. 0
p. 224
The foregoing extracts have been made to shew the entire agreement between the astronomy of the Tetrabiblos and that of the Almagest. The Tables herein given from the latter work, are, of course, now, 1n some degree, superseded by others of modern calculation, infinitely more complete.
No. III.
The Centiloquy, or Hundred Aphorisms of Claudius Ptolemy*; otherwise called, the Fruit of his Four Books.
I. JvupGMENT must be regulated by thyself, as well as by the science; for it is not possible that particular forms of events should be declared by any person, however scientific; since the understanding conceives only a certain general idea of some sensible event, and not its particular form. It is, therefore, necessary for him who practices herein to adopt inference. They only who are inspired by the deity can predict particulars. II. When an enquirer shall make mature search into an expected event, there will be found no material difference between the event itself and his idea of it. III. Whosoever may be adapted to any particular
* Moxon’s Mathematical Dictionary says, that the ‘‘ Centilo- ‘*quium is a book containing one hundred astrological aphor- ‘isms, commonly ascribed to Ptolemy, as its author, but by ‘some to Hermes Trismegistus.’’ This account, however, seems to be inaccurate; for the Centiloquy attributed to Osiris’s contemporary and counsellor (eulogized by Lilly as having been “one of the wisest of all mortal men, and as ancient as Moses’’), is very different from that known by the name of the Kapros, or ‘Fruit of the Tetrabiblos.’? Whether this latter Centiloquy be really the work of Ptolemy is another question: it has been usually edited as his, but some of the aphorisms seem to relate to horary questions only, which are not adverted to in the Tetrabiblos, and there are others also which do not appear to result from the doctrine of that book.
p. 220
event or pursuit, will assuredly have the star indicative thereof very potent in his nativity. IV. A mind apt in knowledge will discover truth more readily than one practised in the highest branches of science. V. A skilful person, acquainted with the nature of the stars, is enabled to avert many of their effects, and to prepare himself for those effects before they arrive. VI. It is advantageous to make choice of days and hours at a time well constituted by the nativity. Should the time be adverse, the choice will in no respect avail, however favourable an issue it may chance to promise. VII. The mingled influences of the stars can be understood by no one who has not previously acquired knowledge of the combinations and varieties existing in nature. VIII. A sagacious mind improves the operation of the heavens, as a skilful farmer, by cultivation, improves nature. IX. In their generation and corruption forms are influenced by the celestial forms, of which the framers of talismans consequently avail themselves, by observing the ingresses of the stars thereupon. X. In the election of days and hours, make use of the malefics, to the same moderate extent as the skilful physician would use poisons in order to perform cures. XI. A day and hour are not to be elected until the quality of the object proposed shall be known. XII. Love and hatred prohibit the true accomplishment of judgments; and, inasmuch as they lessen the most important, so likewise they magnify the most trivial things. : XIII. In every indication made by the constitution of the heavens, secondary stars, whether auxiliary or injurious thereto, are also to be used. XIV. The astrologer will be entangled in a labyrinth of error, when the seventh house and its lord shall be afflicted.
p. 226
AV. Signs cadent from the ascendant of any kingdom are the ascendants of that kingdom’s enemies. But the angles and succedent houses are the ascendants of its friends. It is the same in all doctrines and institutions. XVI. When the benefics may be controlled in the eighth house, they bring mischief by means of good men: if, on the other hand, they be well affected, they will prevent mischief. XVII. Give no judgment as to the future life of an aged person, until the number of years he may live shall have been reckoned. XVIII. If, while a benefic may ascend, both the luminaries should be in the same minute*, the native will be equally and highly prosperous in all things which ean befall him. So, likewise, if the luminaries be mutually opposed by the east and west. But the contrary effect will be produced, should a malefic be on the ascendant. XIX. The efficacy of purgation is impeded by the Moon’s conjunction with Jupiter. XX. Pierce not with iron that part of the body which may be governed by the sign actually occupied by the Moon. XXI. When the Moon may be in Scorpio or Pisces, purgation may be advantageously used, provided the lord of the ascendant be coupled with some star posited below the earth. If he be coupled with a star placed above the earth, the potion swallowed will be vomited up. XXII. Neither put on nor lay aside any garment for the first time, when the Moon may be located in Leo. And it will be still worse to do so, should she be badly affected. XXIII. Aspects between the Moon and stars give the native much activity; and, if the stars be in power, they indicate an efficient, but if weak an inert, excitation to action.
mn a nr rn a a
* Of the same degree and sign.
APPENDIX. Pn |
XXIV. An eclipse of the luminaries, if in the angles of the nativity, or of an annual revolution, is noxious; and the effects take place according to the space between the ascendant and the place of eclipse. And as, in a solar eclipse, a year is reckoned for an hour, so likewise, in a lunar eclipse, a month is reckoned for an hour.
XXV. The progression of a significator, posited in the mid-heaven, is to be made by right ascension; of another posited in the ascendant, by the oblique ascension of the particular latitude.
XXVI. There is obvious concealment in the case, if the star significative of any particular affair be in conjunction with the Sun, either under the earth or in a place foreign to its own nature. On the other hand, there is manifestation, should the star be raised to elevation out of its depression, and be located in its own place.
XXVII. Venus gives pleasure to the native in that part of the body which may be ruled by the sign she occupies. It is the same with other stars.
XXVIII. When the Moon may not hold a familiarity with two planets, as is desirable, care should be taken to connect her, if possible, with some fixed star combining their qualities. |
XXIX. The fixed stars grant extremely good fortune, unconnected with the understanding; but it is most commonly marked by calamities, unless the planets also agree in the felicity. | XXX. Observe the creation of the first king of any dynasty; for if the ascendant at that creation should agree with the ascendant of the nativity of the king’s gon, he will succeed his father. XXXI. When the star ruling over any kingdom shall enter into a climacterical place, either the king, or some one of the chief men of his kingdom, will die.
XXXII. Concord between two persons is produced by
p. 228
an harmonious figuration of the stars, indicative of the matter whereby good will is constituted, in the nativity of either person.
XXXIII. Love and hatred are discernible, as well from the concord and discord of the luminaries, as from the ascendants of both nativities: but obeying signs increase good will.
XXXIV. If the lord of the place of the new Moon be in an angle, he is indicative of the events liable to happen in that month.
XXXV. When the Sun arrives at the place of any star, he excites the influence of that star in the atmosphere.
XXXVI. In the foundation of cities, consider the fixed stars which may seem to contribute thereto; but in the erection of houses, observe the planets. The kings of every city which has Mars in culmination will most commonly perish by the sword.
XXXVII. If Virgo or Pisces be on the ascendant, the native will create his own dignity; but if Aries or Libra is on the ascendant, he will cause his own death. The other signs are to be contemplated in the same way.
XXXVIII. Mercury, if established in either house of Saturn, and in power, gives the native a speculative and inquisitive intellect: if in a house of Mars, and especially if in Aries, he gives eloquence.
XXXIX. Affliction of the eleventh house, in the creation of a king, indicates damage in his household and his treasury: affliction of the second house denotes the detriment of his subject’s wealth.
XL. When the ascendant is oppressed by the malefics, the native will delight in sordid things, and approve ill-favoured odours.
XLI. Beware the affliction of the eighth house and its lord, at a time of departure; and that of the second house and its lord, at a time of return.
APPENDIX. R29
XLII. Should a disease begin when the Moon may be in a sign occupied at the birth by some malefic, or in quartile or opposition to any such sign, such disease will be most severe; and if the malefic also behold the said sign, it will be dangerous. On the other hand, there will be no danger if the Moon be in a place held at the time of birth by some benefic.
XLIII. The malefic figures of a nation are strengthened by adverse figurations of existing times.
XLIV. It is an evil case if the ascendant of a sick person resist the figuration of his own nativity; and if the time should not bring up any benefic.
XLV. If the ascendant, or principal significators, be not in human signs, the native himself will be also estranged from human nature.
XLVI. In nativities much happiness is conferred by the fixed stars; and also by the angles of the new Moon, and by the place of a kingdom’s Part of Fortune, should the ascendant be found in any of them.
XLVII. Ifa malefic in one nativity fall on the place of a benefic in another nativity, he who has the benefic will suffer damage from him who has the malefic.
XLVIII. If the mid-heaven of a prince be the ascendant of his subject, or if their respective significators be configurated in a benevolent form, they will continue long inseparable. It will be the same, also, should the sixth house of a subject or servant be the ascendant of his prince or master.
XLIX. If the ascendant of a servant be the midheaven in his master’s nativity, the master will place so much confidence in that servant as to be ruled by him.
L. Overlook none of the hundred and nineteen conjunctions; for on them depends the knowledge of worldly operations, whether of generation or of corruption.
LI. Make the sign occupied by the Moon at the time
p. 230
of birth the sign ascénding at the conception; and consider that in which she may be posited at the conception, or the opposite one, as the sign ascending at the birth.
LII. Men of tall stature have their lords of nativity in elevation, and their ascendants in the beginnings of signs; but the lords of men of short stature will be found in declination®. It must also be seen whether the signs be right or oblique.
LITT. The lords of nativity of slight or thin men have no latitude, but those of stout or fat men have; and, if the latitude be south, the native will be active; if north, inactive.
LIV. In the construction of a building, the principal rulers, if coupled with a star below the earth, will impede the erection.
LV. Mars’ evil influence over ships is diminished if he be neither in the mid-heaven nor in the eleventh house; but if in either of those places, he renders the ship liable to be captured by pirates. And if the ascendant be afflicted by any fixed star of the nature of Mars, the ship will be burned. LVI. While the Moon is in her first quarter, withdrawing from her conjunction with the Sun, the bodily humours expand until her second quarter: in her other quarters they decrease. LVII. If, during a sickness, the seventh house and its lord be afflicted, change the physician.
LVIII. Observe the place of an aspect, and its distance from the ascendant of the year; for the event will happen when the profection may arrive thither.
LIX. Before pronouncing that an absent person shall die, observe whether he may not become intoxicated ; before declaring that he shall receive a wound, see
* Or in obscure situations.
APPENDIX. PII
whether he may not be let blood; and before saying that he shall find treasure, examine whether he may not receive his own deposit; for the figures of all these things may be similar. LX. In cases of sickness, observe the critical days, and the Moon’s progress in the angles of a figure of sixteen sides. If those angles be well affected, it is favourable for the invalid; if they be afflicted, unfavourable. LXI. The Moon is significative of bodily matters, which, in respect of motion, resemble her. LXII. By marking exactly the beginning of a conjunction*, judgment may be made of the variation of the weather in the ensuing month. It will depend upon the lord of the angle of every figure, for he controls the nature of the atmosphere; assuming also at these times the quality of the existing weather. LXIII. In the conjunction of Saturn and Jupiter, pronounce according to the nature of that one which may be higher in elevation. Follow the same rule with other stars. | LXIV. After ascertaining the lord of the enquiry, see what power he may have in the annual revolution, or in the ascendant of the new Moon; and _ pronounce accordingly. LXV. In the least conjunction, the difference of the mean conjunction, and in the mean conjunction the difference of the greatest conjunctiont. LXVI. Consider no profection by itself alone, but make reference also to the qualifications and impediments of the stars. 7 LXVIT. Years are diminished by the imbecility of the receiver. LXVIII. A malefic, when matutine, signifies an accident; when vespertine, a disease.
* Of the Sun and Moon. t On this aphorism Partridge has said, ‘‘ how Ptolemy meant ‘¢ it to be understood, I know not; and so I leave it.”’
R32 APPENDIX.
LXIX. The native’s sight will be impaired if the Moon be opposed to the Sun, and joined with nebulous stars; and if the Moon be in the western angle, and both the malefic stars in the eastern angle, the Sun being in an angle also, the native will become blind.
LXX. Insanity is produced if the Moon have no connection with Mercury ;—and, if neither of them be connected with the ascendant, Saturn being in occupation of the angle by night, but Mars by day, especially if in Cancer, Virgo, or Pisces, a demoniac affection will be produced.
LXXI. If both luminaries may be in masculine signs, in the nativities of males, their actions will be consonant with nature; but if so placed in the nativities of females, they increase their action. And Mars and Venus, if matutine, incline to the masculine gender; if vespertine, to the feminine.
LXXII. Matters of education are to be considered by the ascending lords of triplicity; matters of life, by the lords of the conditionary luminary’s triplicity.
LXXIII. If the Sun be found with the Gorgon’s head (Caput Meduse), and not aspected by any benefic star, and if there be no benefic present in the eighth house, and the lord of the conditionary luminary be opposed to Mars, or in quartile to him, the native will be beheaded. If the luminary culminate, his body will be maimed or mangled ; and if the aspect in quartile be from Gemini or Pisces, his hands and feet will be amputated.
LXXIV. Mars, if ascending, uniformly gives a scar in the face. LXXV. If the Sun be in conjunction with the lord of the ascendant, in Leo, and Mars have no prerogative in the ascendant, and if there be no benefic in the eighth house, the native will be burned. LXXVI. If Saturn hold the mid-heaven, and the conditionary luminary be opposed to him, the native will
p. 233
perish in the ruins of buildings, provided the sign on the lower heaven be an earthly sign; if it be a watery sign, he will be drowned or suffocated by water: if a human sign, he will be strangled by men, or will perish by the halter or the scourge. Should there, however, be a benefic in the eighth house, he will not suffer death, although he will be brought near it. LXXVII. Profection of the ascendant is to be made for matters affecting the body; of the Part of Fortune, for extrinsic circumstances; of the Moon, for the connection between the body and the spirit; and of the midheaven, for the employment or profession.
LXXVIII. A star often dispenses influence in a place in which it has no prerogative, thus bringing unexpected advantage to the native. LXXIX. Whoever has Mars in the eleventh house, does not govern his master. LXXX. If Venus be in conjunction with Saturn, and have any lord of house in the seventh house, the native will be of spurious origin. |
LXXXI. Times are reckoned in seven ways; viz. by the space between two significators; by the space between their mutual aspects; by the approach of one to the other; by the space between either of them and the place appropriated to the proposed event; by the descension of a star, with its addition or diminution; by the changing of a significator ; and by the approach of a planet to its place. LXXXII. When a figure may be equipoised, observe the horoscope (or figure) at the new or full moon, and, if that also be equipoised, be not hasty in giving judgment. LXXXIII. The time of obtaining a grant indicates the affection between the applicant and his prince; but the seat* shews the nature of the office ;—
* Or part of heaven indicating the grant.
p. 234
LXXXIV. And if Mars be lord of the ascendant at the time of entering on possession, and posited in the second house, or coupled with the lord of the second, he brings much mischief. LXXXV. Should the lord of the ascendant be configurated with the lord of the second house, the prince will spontaneously create many charges.
LX XXVI.—The Sun is the source of the vital power; the Moon, of the natural power.
LXXXVII. Monthly revolutions are made in twentyeight days, two hours and about eighteen minutes. Judgment is also made by some persons by means of the Sun’s progress; that is to say, by his partia] equations to that degree and minute which he might hold at the beginning. LXXXVIII. In making profection of the part of Fortune for a whole annual revolution, a space equal to that between the Sun and Moon is to be reckoned from the ascendant. LXXXIX. Consider the grandfather’s affairs from the seventh house, and the uncle’s from the sixth.
XC. Should the significator be in aspect to the ascendant, the hidden event or object will correspond in its nature with the ascendant; but if the ascendant be not so aspected, the nature of the event will accord with that of the place in which the significator is posited. The lord of the hour shews its colour; the place of the Moon its time; and, if above the earth, it will be a novel thing; if below, old. The part of Fortune indicates its quantity, whether long or short. The lords of the terms, and of the lower heaven and mid-heaven, and of the Moon, shews its substance or value. XCI. Should the ruler of a sick person be combust, it is an evil portent; and especially if the part of Fortune be afflicted. XCII. Saturn, if oriental, is not so highly noxious to a sick person; nor Mars, if occidental. —
p. 230
XCIII. Judgment is not to be drawn from any figure until the next conjunction shall have been considered : for principles are varied by every conjunction; and therefore, to avoid error, both the last and the next should be combined. XCIV. The place of the more potent significator indicates the thoughts of the inquirer. XCV. The stars rising with the tenth house prove how far the native may be fitted to the occupation which he follows. XCVI. In an eclipse, such significations as are made nearest the angles, shew the events decreed. The nature of the stars in accordance with the eclipse, plants as well as fixed stars, and also the appearances co-ascending, are likewise to be considered, and judgment is to be given accordingly. XCVII. The event inquired about will be speedily accomplished, should the lord of the new or full Moon be in an angle. XCVIII. Shooting stars, and meteors like flowing hair, bear a secondary part in judgements. XCIX. Shooting stars denote the dryness of the air; and, if they are projected to one part only, they indicate wind therefrom: if to various parts, they indicate diminution of waters, a turbulent atmosphere, and incursions of armies. C. If comets, whose distance is eleven signs behind the Sun, appear in angles, the king of some kingdom, or one of the princes or chief men of a kingdom, will die. If in a succedent house, the affairs of the kingdom’s treasury will prosper, but the governor or ruler will be changed. If in a cadent house, there will be diseases and sudden deaths. And if comets be in motion from the west towards the east, a foreign foe will invade the country: if not in motion, the foe will be provincial, or domestic.
END OF THE CENTILOQUY.
p. 236
No. IV.
The Zodiacal Planisphere.
Tue Reader is desired to refer to the annexed Plate, containing diagrams of the Zodiacal Planisphere, which has been spoken of in the Note in p. 146.
Fig. 1 is the Planisphere adjusted for the northern latitude of 80° 22/ (where the longest day consists of fourteen equatorial hours), agreeably to the ‘‘ Exemplification ”’ given by Ptolemy in Chap. 15, Book 3. It represents that portion of the celestial sphere which is contained between the tropics: the central horizontal line is the equator; the curved line extending longitudinally from east to west is the ecliptic; the central perpendicular line is the meridian, or cusp of the 10th house; the other short lines, cutting the equator transversely, are the cusps of the other houses; that of the first house being the eastern horizon; that of the 7th, the western horizon. Hence, the distance from the lst house to the meridian, or from the meridian to the 7th house, shews the semi-diurnal are of any parallel of declination in the ecliptic; and the distance of the 7th house to the 4th, or from the 4th to the lst, shews the semi-nocturnal arc. The distance from the cusp of one house to that of the next, taken on the same parallel, is also equal to two temporal hours; thus, for instance, in the latitude above quoted, the semidiurnal are of 0° Jf is 6 h. 50 m., or 102° 39’ of the equator; consequently the diurnal temporal hour is equal to one equatorial hour and eight minutes, or to 17° 6/ of the equator.
In his first example, Ptolemy directs 0° r to be placed on the ascendant, so that the beginning of YP may be on the mid-heaven: 0° [[ must, therefore, fall on the point A, distant from the mid-heaven 147° 44’ of the equator, as
ae Gare: mcitaes rnp Titer TInt TH eR EET we en. Gr: rare Gru - C2 | Se POON CTA eS EE UE BOBS et 2 eH EH MUAH dit
measured by the line AB; because every point in the sphere always preserves one and the same parallel with the equator; and 0° JJ, in passing to the mid-heaven, must proceed along the line AB. In the present case, however, it is required to know how long 0° JJ will be in coming to the ascendant, the given position of 0° 1: Now 0° [J will be on the ascendant when it arrives at the point G; therefore the distance from A to C is the amount of the prorogation between 0° +r (when posited on the ascendant) and 0° [J], and it is equal to 45° 5/ of the equator. In the second example, 0° rT 1s placed on the mid-heaven, which position must be at D, so that 0° [J must necessarily be at E; and the distance from E to B, equal to 57° 44’ of the equator, is the prorogation between 0° r and 0° JJ, when 0° 7 is on the mid-heaven. In the third example, 0° + is supposed to be on the 7th house, descending, at F, so that = is on the mid-heaven, and 0° [TJ at the point G, in advance of the mid-heaven 32° 16’ of the equator, as shewn by the distance BG. Now it is required to bring 0° JJ to the 7th house (the place of 0° 17), and it will be there on arriving at H, distant from B 102° 39’ of the equator; but as 0° JJ is already at G, the distance from G to H, equal to 70° 23/ of the equator, is the amount of the prorogation between 0° +r and 0° JJ, when 0° 1 is on the 7th house. The fourth example places 0° +r at I, three temporal hours past the meridian ; 0° [J therefore falls on the point K, at the distance of 13 equatorial degrees before the meridian or mid-heaven, and will be three temporal hours past the meridian (the position of 0° rt) on arriving at L, distant 51 equatorial degrees from the mid-heaven: the whole distance from K (the first position of 0° JJ) to L, its second position, equal to 64 degrees of the equator, is therefore the prorogation between 0° 7 and 0° [], when 0° +r is past the meridian at the distance of three temporal hours.—Ptolemy has also instanced two other positions for 0° 1; viz. at two temporal hours past the meridian, and at two temporal hours before the occidental
p. 238
angle; or, in other words, on the cusp of the 9th house, and on that of the 8th. Now, if 0° r be on the cusp of the 9th house, it must be at M, and 0° JJ will be at N, distant 62 equatorial degrees from Q, which is also on the cusp of the 9th. If 0° r be on the cusp of the 8th, it must be at O, and 0° JJ will be at P, distant 66 equatorial degrees from R, which is also on the cusp of the 8th: these two several numbers of degrees will be the respective prorogations between 0° tr and 0° JJ, when 0° 1 is placed on the 9th and 8th houses.
Ptolemy’s ‘‘ Exemplification ’’ has been followed thus minutely in order to shew how perfectly Mr. Ranger’s invention 1s adapted to assist (if not to supersede) arithmetical calculation; for, after the Planisphere has once been accurately laid down, a line drawn parallel to the equator, from the significator to the promittor, or to the promittor’s pole of position, and measured by degrees of the equator, will accomplish the whole operation of ascertaining the amount of prorogation.
Fic. 2 is the Equator extended, zn plano, on a scale proportionate to the planispheres in Frias. 1 and 3: it is divided into 3860 degrees, and into equal time, as measured by the 24 hours of the earth’s daily rotation on its axis, and by smaller portions of four minutes each, corresponding with degrees of the equator.
Fic. 3 ig the Planisphere set for the latitude of Southern Britain, 51° 30’ N., where the longest day is 16 h. 30 m., the semi-diurnal are of 0° [J being consequently 7 h. 52 m., or 118° of the equator, and its diurnal temporal hour equal to one hour and nearly nineteen minutes of equatorial time, or to 19° 40’ of the equator. In applying Ptolemy’s examples, given in Chap. 15, Book 3, to this latitude, it will follow that, when 0° tp. 239 may be on the ascendant, 0° JJ will be at A, and will subsequently arrive at the ascendant at C, after the passage of 29° 43’ of the equator. When 0° rt may be on the mid-heaven at D, 0° JJ will be at E, and will arrive at B, on the mid-heaven, after the passage of 57° 44! of the equator, as in Fic. 1. When 0° 7 may be on the 7th house, at F, 0° J] will be at G, and will come to the 7th house, at H, after the passage of 85° 40/ of the equator. If 0° r be three temporal hours past the meridian, at I, 0° [J would be at K, again 18 equatorial degrees before the meridian, as in Fie. 1, and will be three temporal hours past the meridian, a position similar to that assumed for 0° 1, on arriving at L, distant from the mid-heaven 59 equatorial degrees; thus making the whole distance, from K to L, 17 equatorial degrees.—If 0° +r beon the 9th house, at M, 0° TJ will be at N, distant from Q (also on the 9th house) about 67 equatorial degrees. If 0° r be on the 8th house, at O, 0° [TJ will be at P, distant from R (also on the 8th house) about 76 equatorial degrees.
By taking the trouble to calculate the distances between the several positions given by Ptolemy, the Reader may satisfy himself of the sufficiency of this Planisphere for the purpose for which it was first projected; viz. for the more expeditious measurement of the arcs of direction. The Tables of Ascensions, extracted from the Almagest, in p. 223, will shew that the arcs, as measured in Fras. 1 and 2 of the plate, exactly tally with the amounts of distance obtained by calculating arithmetically, according to the respective latitudes, as quoted in the Tables.
The slight view which has been here given of the Zodiacal Planisphere invented by Mr. Ranger, must not be considered as pretending to offer a complete idea of its powers: they are so manifold and various, thatp. 240 another volume would be required to detail them fully; and it has now been used only in order to give a better illustration of Ptolemy’s examples of the spaces of prorogation than mere words can do. To persons conversant with the mathematical part of astronomy, the facility with which a complete representation of zodiacal latitude, declination, the poles of position, crepusculine circles, and other phenomena, may be made by this Planisphere, will be sufficiently obvious from the accompanying Figures.