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4. Number of the Modes of Prorogation

J. Dusky Major Considerations:

From our advantage point, it may seem the Sun simple follows up a daily path (the Ecliptic), accompained by the planets which follow/twitt the Sun. Such position & Ecliptical behavior happens due to the Earth’s inclination rotating on its own axis while revolving the Sun, making us observe/believe the Sun as an encompassing body in a certain permanent direction, while forming the entire Solar Arc followed up by the planets and stars, each in their own upbeat and semi-arcs. 

Such rotational phenomenon is known as the primary motion, and is the base of the technique of Primary Directions, where the “wheel of life” is turned and planets and points advance to different and sometimes major areas of the radix which weren’t when the native was born. 

Thus, a native may not be born with Sun in the 10th place but in the 11th place let’s say it, signifying things that a Sun in the 10th wouldn’t, but the Direction of the Sun Direct to the corresponding Mc semi-arc will indicate not only objective events related to the culmination of major Sun’ stuff but also the 10th house things (culmination) related to the natal Sun in the 11th house. Such results will depend on Direct/Converse Motions, where the passive and active sources change. In my thinking, either the native attracts/conceives the event or the event attracts/pulls the person.

The Base: Each degree as a point of reference in the 360° degrees Zodiac Wheel will take certain (4′) minutes to fully move on to the degree experienced by the antecedent degree already moving foward simultaneously. For example, let the significator Asc be Leo and the promissor Moon in Cancer when an individual is born, then soon after birth, the Moon will reach Direct the same position held by the Asc rising in the Sign of Leo, but it will only have effect in life about years later. 

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Ptolemy now briefly explores(d) the motions of Directions. When to use Direct or Converse Directions (concerning hyleg, in this case) in the Primum Mobile ?

Note: For the sake of simplicity, I will adopt such terms (Direct/Converse – and not “projecting rays” or “Horimaea”) in the discussion ahead for better vizualization, these topics get complicated to get intellectually dissimulated – I confess this chapter made my soul twist into wierd shapes, there were days I suggested myself I wasn’t capable of fully-truly understanding this chapter, but with the help of other sources/authors, I think now I did put to rest such debilitating thought while satiating out my curiosity by focus-reading and research, however, interrogation points here and there still run my mind no matter the source I get/got back to.

Second Note: Also, it is worthy remebering the reader that Ptolemy in this particular chapter, writes more about the interaction in the Primum Mobile among the Hyleg (if any) and the Anaereta, and here he does not point to particular cases of Directions of any other planet in a sense that Ptolemy does not point to others major events while the native is alive; I had to keep my mind open and understand them as Primary source of the expiriation of one’s body (death – lenght of life). For example, he won’t allow directions of “lenght of life” to happen below the Horizon axis – thus the body’s expiration of a nativity on Earth shall be investigated at the Solar Arc (where life thrives) and not through Nocturnal Arc (underground where the dead is buried). However, authors foward in time began adding more hylegical places to the wheel (ex. Hyleg rejoicing Moon in 3rd house etc.) which won’t be disucssed here.

Projection of Rays & Horimaea [Horary Proportion]: “When the Prorogator [moderator of life] has been distinguished, we must still further adopt two [2] methods of prorogation:

Ptolemy just pointed out to the only 2 (two) possible modes of Primary Directions at the Primum Mobile, the Direct & Converse Directions but terming them as the “following sign” [projection of rays] or the “leading sign” [horimaea]. In other cases, astrologers may know as Dexter (“upper/superior”) & Sinister (“under/inferior”), which are not terms I employ.

In Primary Directions there will always fundamentally exist 2 (two) interests you will want to know about, the one that is moving (active) and the other which stands still (passive). Although Ptolemy only writes about those in the middle of the chapter, I think it would be wise to know the difference right away:

From our perspective the Sun is born in the East and travels uninterrupted crossing the skies until reaching the opposite & Western horizon angle while vanishing without a trace but imaginary (the ‘Diurnal’ Arc) – As we experience things in this planet from East to West, we could easily assume the Direct/Right Direction/motion as clockwise to the turning of the Zodiac Wheel. *₁ And if we put this idea on a Map/Chart/Radix, from the perspective of the Significator, it will be seen the Direct Motion as the Zodiac signs are being carried to it. In such Mode of Direction, the Promissor is the active point that is ‘brought’ towards Significator.

Such perspective change when we “bring” Significator to Promissor instead, then it is termed a Converse Direction and it will appear the opposite is happening in the 2D projection – where from the perspective of the Significator, it will seem like the Zodiac signs are borne backwards. *₂ Martin Gansten reminds us the fact never in history authors imagined the planets being carried by opposite (from west-to-east) direction. Instead, the same motion is still applied from east-to-west but the movable & passive sources change.

Note: And this is exactly how we view whatever astrological maps – when we view transits for example, we observe these in the Radix as being bodies/points virtually moving anti-clock the Wheel, yet following up the next Zodiac Signs and not back. But their movement is experienced clockwise if we face the spinning planet Earth relative to the Universe from the Ascendant as Eastern Horizon. From this point we can begin to name directions followed by the Mc. Astrologers reading general natal charts face the world from geocentric and not heliocentric view, and if you observe it in virtual 3D room you will want to move the scene/percursor where South is above and North is below while the Eastern Horizon becomes the primary point and the West where points/bodies die out, picturing the skies and Earth from a different perspective as opposed seen in geographical maps of the world, for the sake of astrological systematization and simplicity I supposed.

Additional Note: Authors in time changed or reverted the mode of the Promissor vs. Significator’s  meanings in natural motion state and let the Significator be the one as the active (moving) element instead of the Promissor in a Direct Direction, which can be quite confusing! I still must find examples to prove such claim.

The antagonist claimed one should only use Direct Direction when the (Promissor?) Hyleg is in the orient (lex. et Hyleg be in the 11th place, then Direct Direct  to its own culmination [conjunct Mc] foward in time), but when (Promissor Hyleg?) is between the 10th and the 7th houses, one should use both Direct & Converse Directions (where you can indeed direct Hyleg to both (Direct to) 7th and (Converse to) 10th houses’ cusp). 

Retrograde: Authors foward in time would say to use Converse Directions only when planets are Retrograde in the radix, which is not an idea I’d consider consistent, meaning that retrograde or not, planets may do find their paths also Converse and that will echo in real life objectively, be it for a long period of time or a single event distributed in a specific time frame. In such case I think the part “affected” then would act as the active agent instead.

Note: I think one should consider observe both modes in the whole chart, but as long as “lenght of life” is concerned, these rules seem to be well studied and applied throughout time even before Ptolemy’s period (otherwise it wouldn’t had been in the treatise?). When death is not on the menu for the time being, if you do have planets in the 12th or even in the 11th place, it is definitly worthy observing Directions to both major points as Significators: the Ascendant & Midheaven’s cusp, as major events in life shall be developed from such Directions. 

Note II: However, these are my observations, what about yours? Do you use Converse (significator carried to promissor) directions? Or, even concerning the modern ‘Secondary Progressions’, have you ever done/used/seen the Converse motion? You may actually be surprised, they are the days/months/years before you were born, the final expectancy, which when read in the future, you will notice similar pattern taking place simultaneously in real life. 

The Anaeretic/Anaereta West(ern) Angle – The 7^th Place & Murdereous Degrees: In my own investigations on Primary Directions, many were the cases that this was true, where the Western Horizon “obscures the lord of life”, however I never noticed if all of them were exclusively Converse:

“This being the case, the destructive degrees in the prorogation that follows the [Converse] order of leading signs [Hyleg can’t be found under earth but if rising, yet what Ptolemy is saying is to Direct Converse which doesn’t make sense if not but by configuring the 7th cusp as Promissor (the caused part but the passive element in this case); one shall direct Converse the Promissor 7th cusp to Significator Hyleg in the 9th? Because if you Direct Converse Hyleg as Promissor from the 9th then the mode would make Hyleg conjunct the 10th cusp instead!] are only the degree of the western horizon, because it causes the lord of life to vanish; and the degrees of the planets that thus approach or bear witness merely take away and add years to the sum of those as far as the setting of the Prorogator, and they do not destroy because they do not move toward the prorogative place, but it moves toward them.”  – I think what happens in here is that, when it involves the western angle, Hyleg can easily become Significator in the Direction Converse, and thus the moving part. You will also notice that planets considered Anaereta (in murderous degrees) will act as Promissors while Hyleg will act as Significators in Directions both Direct or Converse.

Placidus (1603-1688) later on commented:“[…] How largely and differently authors have spoken of this direction of the significator to the west, putting various constructions on the words of Ptolemy, is known to everyone. See Cardan in his Commentaries, Maginus in “Primum Mobible and the Use of Legal Astrology in Physic (c. viii)”, where he delivers the sentiments of Naibod. Argol censures wholly this doctrine of Ptolemy’s, of directing the moderator of life to the west, as vain and useless; but I say it is worthy of remark, and altogether conformable to truth; because then the rays and intermediate stars of the malign only lessen the arc of direction to the west, and do not destroy life, when, by a right direction, the moderator of life [Hyleg] does not remain at the same time with the malignant planet: for, should this happen, they kill, without any manner of doubt.” (Cooper’s translation, pp. 106 and 108.) – [or, let Hyleg be conjunct Mars in the Radix and during the Direction to the Promissor West’s cusp Converse let also square Saturn at the same time – but for this to occur then Saturn must be square the 7th cusp in the Radix?].

Add or Subtraction of Years/Months: “…The beneficent stars add [increases the prorogation’s Arc & Years in/of Life] and the maleficent subtract [diminishes the prorogation’s Arc & Years in/of Life]. Mercury, again, is reckoned with the group to which he bears an aspect. The number of the addition or subtraction is calculated by means of the location in degrees in each case. For the entire number of years is the same as the number of hourly periods of each degree, hours of the day when it is day and hours of the night when it is night; this must be our reckoning when they are in the orient, and subtraction must be made in proportion to their departure therefrom, until at their setting it becomes zero.” – Mercury then shall be observed what planets it is configured to, malefics or benefics in order to know its binary inclination. Thus, one should be aware if the degrees between the Hyleg and the said planet, for its degrees/orbs will indicate the amount of adding or diminishing in life. 

→ I don’t think there are any software avaliable where this can be done BUT the Direction/Arc alone, thus the astrologer must do it by hand (add or eliminate years to the Arc by the interruption of planets “in the way”). 

Ptolemy continues on the Numbers of Years: “The amount of the increase or diminution is indicated by the degree, in which each star, so operating, is exactly situated; for the number of years will depend upon, and correspond with, the “horary times” (the number of equatorial degrees in a certain latitude on the Earth, to transit in an equatorial hour) proper to each degree; and if the birth be by day, care must be taken to calculate the diurnal horary times; if by night, the nocturnal. These directions are to be understood as applicable to instances wherein the degrees in question may be in the ascendant; if farther advanced, a deduction proportionate to the distance is to be made, unless they should be on the occidental horizon, in which case there can be no remainder.” 

The Cutter/Killers Anaeretic Mars & Saturn: “In the prorogation which follows the order of following signs [Direct], the places of the maleficent planets, Saturn and Mars [the Main Anaereta(s)], destroy, whether they are approaching bodily [Conjunction Direction], or project their rays from any place whatever in quartile [square] or in opposition, and sometimes too in sextile, upon the signs called “hearing” or “seeing” on grounds of equality of power [read the chapter: Commanding and Obeying; Of Beholding & of Equal Power];”  – Ex. Supposed Promissor Anaeretic be Saturn yet still at 0° degrees Taurus while Significator Hyleg is the Sun in Pisces at 29° degrees, but because it is a Zodiac sign following the Aversion Aries (they are/were still agreeing (or fighting for) in power), Ptolemy said it would kill if/when configured to. Here is a good example of the figuring out the Aspects of the Zodiac and how the ancients viewed Degree-to-degree Aspects + (vs.) + Sign by Sign relationship/dynamics. Taurus & Pisces are sextile by Zodiac sign, but their degrees in the wheel as the example I provided, are almost in exact Aversion.

Note: Now, would that mean that Ptolemy understood that Saturn and Mars could only truly “kill” if they were/are Promissor & Direct in Direction to Significator Hyleg? And that in respect to Converse directions could only “murder” if Anaereta then is Significator and Hyleg is Promissor? This is something I actually never noticed, I shall from now on and let’s see if this was exactly what the author meant. Probably Ptolemy meant the Western horizon could kill if progammed as Promissor, or he simple inverted the meanings of them. 

Well, either way, if Anaereta is Significator, it could only be interpteted as one thing: Hyleg is then visited by Significator (Converse) instead of otherwise, the event which shall occur, and thus the Significator as Anaereta provides information not only of the qualitative level but also quantitative, that is, the data or Arc such event will lead to the end of life by the meeting of the Hyleg. Or synthethized: the “End” (Anaereta) is taken (Converse) to the body (Hyleg) that contains/pulsates “Life”.

Promissor Square (of Anaereta) that Destroys: “…and the sign that is quartile  to the prorogative sign in the order of following signs [Direct – first square of the Sign] likewise destroys.” – Supposed Anaereta Saturn in Taurus is in terms with Mars and is Direct Direct to Hyleg Moon is Leo which square Mars in Aquarius in terms with Saturn in the radix etc. However… (see note ahead – ѱ₁)

The Fast Trine & The Slow Sextile (of Anaereta) that Can Destroy: “…And sometimes, also, among the signs that ascend slowly [Cancer, Leo, Virgo, Libra, Scorpio and Sagittarius in Northern Hemisphere – while in the South Hemisphere the Signs are their opposites] the sextile aspect destroys, when it is afflicted, and again among the signs that ascend rapidly the trine.” [Signs of Long/Short Ascension go to Book I; Chapters 14-15] + [Abù Ma’shar version on Agreements click here] – Ex. In the radix, let natal Significator Hyleg Moon be in Cancer and sextile Promissor Anaereta Mars in Virgo which square Saturn in Sagittarius etc., or; let Significator Hyleg Lot of Fortune be in Scorpio at 1° degree while Anaereta Saturn in Pisces at 20° degrees and square Mars in Gemini etc. 

Notes: but I also think, Ptolemy meant not only in the radix, but when the said sextile perfects in the Primum Mobile even when Aanaereta doesn’t exactly sextile in the radix. For example, let the Hyleg be the Moon in Cancer but Promissor Anaereta Saturn in the radix is in Libra, but once the Anaereta directs Direct in the Primum Mobile (first movable) it would eventually hit the same spot hold by the degree (Virgo) in the wheel/radix which sextile Hyleg Moon. ѱ₁ – Would be the same principle  applied to the square that destroys?

When the Moon is Hyleg, the Sun can Kill: “…When the Moon is the Prorogator [Hyleg] the place of the Sun also destroys. For in a prorogation of this kind the approaches of planets avail both to destroy and to preserve, since these are in the direction of the prorogative place.” [ex. in the radix, let the Sun be in the 12th place while the Moon in Cancer conjunct cusp of the Mc etc.]

Be Aware of the Afflicted Places in the Wheel that Destroy: “…However, it must not be thought that these places always inevitably destroy, but only when they are afflicted.” [many were the examples I gave along the way]

Prevention/Impediment by Venus/Jupiter: “…For they are prevented both if they fall within the term of a beneficent planet [ex. let Mars be in terms with Jupiter or/and Trine the planet which is from Angular position] and if one of the beneficent planets projects its ray from quartile [square], trine, or opposition [he omits sextile? – did he considered it too capricious to imped?] either upon the destructive [Aanaeretic-Killer] degree itself or upon the parts that follow it;

Jupiter: in the case of Jupiter not more than 12° degrees [of Orbs – not only from conjunction/joint but also the 4 classical aspects],

Venus: and in that of Venus not over 8° degrees [of Orbs – not only from conjunction/joint but also the 4 classical aspects];

Latitude Matters: …also if, when both the Prorogator and the approaching planet are present bodily, the latitude of both is not the same [ex. let Venus not be the same latitude of Saturn when both are square then when the cutter reaches Hyleg by Primary Direction it won’t destroy “that much”, where such evilness of the Anaereta will be impeded – now, we can only guess when they have the same latitude? Would then the benefic planet had been “evenomed” by the Malefic’s Latitude’s path?].” – 

→ Basically you could easily tell all astrologers agreed that Directing In Zodiaco you are actually directing a body’s or point’s Ecliptical Longitude. If you read well enough Ptolemy’s words, notice the calculation and timming of a Direction would not alter by Latitude, in a sense he wouldn’t consider Directions In Mundo (actual body North/South of the Ecliptic), but in Ptolemy’s hypotetical scenario, not only the interpretation is added a bit more chill, but the result in the native’s life could be potentilly and objectically fatal or at least quite destructive, as the Benefic could be corrupted by Malefic of the same Latitude and thus not being able to impede further Anareta’s intention in ending it up or hurting. Either way, I think the differentiation in Latitude in Directions in interpretation for Ptolemy seems to be more complementary and not decisive, meaning that there are others factors one should investigate altogether which perhaps may strongly overcome the North-South brass-tacks.

Assists-Destroy: Which One? Thus when there are two or more on each side, assisting and, vice versa, destroying, we must consider which of them prevails, both by the number of those that co-operate and by power;

By Number: by number when one group is perceptibly more numerous than the other, [Suppose Mars square Hyleg, but Jupiter trine the last and it also in terms with Venus while sextile the planet and the Moon, while Mars aspects Nothing, in the 12th place (cadent/falling) and detriment (by power) etc.]

By Power: and with regard to power when some of the assisting or of the destroying planets are in their own proper places [Domiciles], and some are not, and particularly when some are rising and others setting [prefer the one (malefic or benefic w/ Hyleg) configured with the rising planet].”  

Planets/Points Conjunct the Sun [Under Beams] Do not Take or Aid: “…For in general we must not admit any planet, either to destroy or to aid, that is under the Rays of the Sun…

Except the Moon when is Hyleg: …except that when the Moon is Prorogator [because it conjunct the Sun it has power alike of a planet containing “Life”] the place of the Sun itself is destructive [Anaeretic Degrees], when it is changed about by the presence of a maleficent planet and is not released [not helped during a direction?] by any of the beneficent ones.” – Even though in the radix the Moon may be under the Sun’s beams (conjunction), I think Ptolemy wasn’t talking about early direction (conjunction) and the death of a baby, but the expiration of a young to an adult’s body which the Sun perfects a square to the significtor Hyleg Moon only later in life if not helped by a benefic.

Between Hyleg and Destroyer and # of Years: “However, the number of years [when the Hyleg meets/met the “Killer” or “Destroyer” by Primary Directions will equal (an Arc of) a certain amount of Solar Years], determined by the distances between the prorogative [vital] place and the destructive [Anaeretic of a]  planet, ought not to be taken simply or offhand, in accordance with the usual traditions, from the times of Ascension [Oblique Ascension] of each [Zodiacal] degree [on the Equator and rising in any particular latitude]…

Except the Hyleg Asc or Hyleg Planet Rising: …except only when the eastern horizon [Asc] itself is the Prorogator [Hyleg], or some one of the planets that are rising in that region.”  – if this is the case, you won’t count, add or consume off Arc because of planets, you simple count the Arc as it is.

Each 1° of Motion = 4′ minutes in Time = 1 Solar Year: “…For one method alone is available for him who is considering this subject in a natural manner – to calculate after how many equinoctial periods [degrees of the Equator where Time is Measured] the place of the following body or aspect comes to the place of the one preceding at the actual time of birth, because the equinoctial periods pass evenly through both the horizon and the mid-heaven, to both of which are referred the proportions of spatial distances, and, as is reasonable, each one of the periods has the value of one solar year.” 

In Directions, every point/planet in the Zodiac has its own diurnal circle in the wheel while parallel to the Equator, therefore, in the span of 24h such ecliptical point or celestial body will rise, culminate, descend and finally “perish” in its own rythm. Therefore, in Primary Directions there is always a/the Single element/body/point possessing its own semi-Arc that is moving to a corresponding other element used as a fixed reference which is also settled in its own Semi-Arc – Never both elements move at the same time, it has to be either Promissor or Significator.

After we were born the planets continued to move foward in space & time, while then humans, animals and things on Earth experience throught the rotation of the planet the “curvature of the universe”. Therefore, when the “wheel of life” turns and we do the math (easily achieved by computer nowadays), we discover that planets and points “will hit” certain major degree(s) in the chart/radix soon after birth left by others elements; yet in practical life this will have  effect only years later the native was born, unless planets are very close to each or to their bodies, angles or by aspect, then shall events of major magnitude to “hit” the native quite earlier in life. 

Note: It takes 4′ minutes (actually 3’m59″s333″‘ms of the daily Sun’s mean motion!) for each 1° degree of motion on the Equator to fully ascend, which equals 1 (one) Solar Year in practical reality. Thus, it takes 24h for the whole 360° degrees to complete full rotation (4′ x 360° = a Day has about 1440′ minutes then 1440’/24h = 60′ minutes each 1 (one) hour). 

Note II on “Keys”: Astrologers foward in time, gave others “Keys” in order to adjust such Arcs to fit reality, sometimes because they were too very far from the origin point; let the Key of Naibod (the “favorite” key used by medieval astrologer Willian Lilly for example) be applied where each 4′ minutes equals narrowed 0°59’08” degrees of motion (which equals 1 Solar Year) and not exactly 1° degree as Ptolemy ‘stablished’ – this seems not to make a tremendous difference but Arcs later in life may actually take a few more months to years to perfect using such “Keys”. Of all the keys mostly used by astrologers in the 1st Millenium C.E., contemporary author Martin Gansten summarized “Placidus” key as the “less predictable” [cited on page 79 of his book on Primary Directions 2009].

When the Hyleg is the Asc: “…Whenever the prorogative and preceding place is actually on the eastern horizon [Asc], we should take the times of ascension of the degrees up to the meeting place; for after this number of equinoctial period the destructive [Anaereta] planet comes to the place of the Prorogator, that is, to the eastern horizon.” – This is wierd because Ptolemy won’t allow directions of lenght of life to happen below the horizon circle, and it is only possible for a Direct Direction to occur if Promissor Anaereta is below the horizon so we could Direct direct the Anaeretic body to the Hyleg Asc. Now, if Promissor Anaereta is above the horizon, then it would have to happen a Converse direction in order to join Hyleg Asc and “kill” it. This changes if we select Hyleg Asc as Promissor and the Anaereta above the horizon as Significator, then a Direct direction of the Asc to Significator Anaereta is achieved. This will also change the interpretation as I discussed in this chapter already, if we direct Asc Direct to the murderous degree would then the native actually attract his/her own end/undoing? – Definitly something to investigate further in my own researches.

When the Hyleg is the Mc: “…But when it is actually at the mid-heaven [Mc], we should take the ascensions on the right sphere in which the segment in each case passes mid-heaven;

When the Hyleg is the Dsc: and when it is on the western horizon [Dsc], the number in which each of the degrees of the interval descends, that is, the number in which those directly opposite them ascend.”

Intervals between Asc/Mc/Dsc: “… But if the precedent place is not on these three limits [Asc/Mc/Dsc] but in the intervals between them, in that case the times of the aforesaid ascensions, descensions, or culminations will not carry the following places to the places of the preceding, but the periods will be different. 

For a place is similar and the same if it has the same position in the same direction with reference both to the horizon and to the meridian [perhaps let it be Conjunct 11th house cusp by counting?]. This is most nearly true of those which lie upon one of those semicircles which are described through the sections of the meridian and the horizon, each of which at the same position makes nearly the same temporal hour. Even as, if the revolution is upon the aforesaid arcs, it reaches the same position with reference to both the meridian and horizon, but makes the periods of the passage of the zodiac unequal with respect to either, in the same way also at the positions of the other distances it makes their passages in times unequal to the former. We shall therefore adopt one method only, as follows, whereby, whether the preceding place occupies the orient, the mid-heaven, the occident, or any other position, the proportionate number of equinoctial times that bring the following place to it will be apprehended.

Above/Under Earth: For after we have first determined the culminating degree of the Zodiac and furthermore the degree of the precedent and that of the subsequent, in the first place we shall investigate the position of the precedent, how many ordinary hours it is removed from the meridian, counting the ascensions that properly intervene up to the very degree of mid-heaven, whether over [Mc] or under the earth [Ic], on the right sphere, and dividing them by the amount of the horary periods of the precedent degree, diurnal if it is above the earth and nocturnal if it is below. But since the sections of the zodiac which are an equal number of ordinary hours removed from the meridian lie upon one and the same of the aforesaid semicircles, it will also be necessary to find after how many equinoctial periods the subsequent section will be removed from the same meridian by the same number of ordinary hours as the precedent. When we have determined these, we shall inquire how many equinoctial hours at its original position the degree of the subsequent was removed from the degree at mid-heaven, again by means of ascensions in the right sphere, and how many when it made the same number of ordinary hours as the precedent, multiplying these into the number of the horary periods of the degree of the subsequent; if again the comparison of the ordinary hours relates to the mid-heaven above the earth, multiplying into the number of diurnal hours, but if it relates to that below the earth, the number of nocturnal hours. And taking the results from the difference of the two distances, we shall have the number of years for which the inquiry was made.”

Ptolemy then finishes the chapter with Final Exemplification, click here