The Star of the Magi
Courtney Roberts, M.A.
Chapter 9 Pisces and Precession
In his unique work, The Birth of Christ – Exploding the Myth, the astrophysicist, Dr. Percy Seymour, remarks on the Magi and the Age of Pisces:
Start With Hipparchus
But was he the first to notice? This point has been debated at length, and the bottom line is: no, of course he wasn’t. The ancient Egyptians aligned their buildings to fixed stars, so the next generation or two couldn’t help but see that something had shifted, and that’s only one example of many. As the authors of Hamlet’s Mill demonstrated, people noticed this motion long ago, and entire bodies of myth and legend developed around it.
Hipparchus was the first astronomer working in the Greek scientific tradition to attempt to derive precession from a series of systematic observations, and to try to place a mathematical value upon it. That was original...or at least, we think it was. The fact is, we don’t really know for sure, because almost none of the work of Hipparchus and his contemporaries has survived. Of the 14 books attributed to his hand, the only one still extant is his Commentary on the Phenomena of Aratus and Eudoxus, which doesn’t really deal with the question of precession.
Consider this: Most histories of science proclaim Hipparchus the most important astronomer of the ancient world. He is credited with developing the first trigonometric tables, the first reliable method of predicting solar and lunar eclipses, the first star catalogue of the western world, the discovery of precession, and maybe even the invention of the astrolabe. And yet, every bit of this work was deemed unsuitable for transmission in the medieval monasteries.
We know his writings were widely published and survived at least into the 4th century CE. For instance, his influence is evident in the writings of Strabo (1st century BCE) and the Roman author Pliny in the 1st Century CE. Ptolemy obviously had ready access to Hipparchus’s most technical material in Alexandria in the 2nd century CE, and relied on it in compiling his Almagest. Pappus of Alexandria (3rd century CE) and Theon of Alexandria (4th century CE) also knew his work, but after that, 13 of his 14 books disappear.
As it is, we have only a few very late, second-hand sources for this, the greatest astronomer of the ancient world; but of course, everyone knows that Hipparchus discovered precession. Further complicating the issue is the lack of any surviving references to precession from the period between Hipparchus and Ptolemy. Whatever anyone else thought about it at the time is also lost to us now. That’s 300 years of silence on the matter. All we have is Ptolemy.
Why?
Historians generally agree that the popularity of Ptolemy himself may have meant Hipparchus’s undoing. Both Neugebauer and G.J. Toomer theorize that Ptolemy’s Almagest was so dominant that it made the earlier astronomers and their work redundant, resulting in what Neugebauer called “an almost total obliteration of the prehistory of the Ptolemaic astronomy.”3
As Toomer puts it, ‘being obsolete, they ceased to be copied.”4
Claudius Ptolemaeus as portrayed by a Medieval Artist
Hipparchus and Astrology
That may well be, but perhaps there were other factors at work too, at least in certain quarters.
Liba Taub, in his article on The Starry Messenger, the excellent Cambridge University website on the history of astronomy, broadens the whole question by pointing out that “the work of Hipparchus … dealing with the calculation and prediction of celestial positions would have been very useful to those engaged in the sort of astronomy known as astrology”5
In fact, the advances made by Hipparchus in observation and mathematics were driven largely by the need for greater accuracy in astrology. After all, no one was trying to send up a communications satellite or put a man on the moon in the 2nd century BCE, but as a writer and teacher of astrology, Hipparchus would have had a lot of interested readers.
Otto Neugebauer had this to say about it:
“Hipparchus is often quoted in the astrological literature.... It was F. Boll who first emphasized that the ancient reports connecting Hipparchus with astrology have to be taken seriously....”6
Franz Cumont rather blithely pointed out that, “It is remarkable that the great astronomer, Hipparchus ... was also a convinced supporter of one of the leading doctrines of stellar religion.”7 Pliny extols Hipparchus in Book 2, Ch. XXVI of hisNatural History as a man who “can never be sufficiently praised, no one having done more to prove that man is related to the stars and that our souls are a part of heaven.” Or as Cumont has it, “that our souls are particles of heavenly fire." D.R. Dicks adds: “It would seem that Hipparchus' contemporary fame rested largely on his astrological works…”8
G.J. Toomer, who authored both a biography of Hipparchus and a translation of Ptolemy's Almagest, is even more emphatic on this point, and believed that:
“…astrology had no importance in the Greek world until after Hipparchus, and that his role, both directly as an advocate of astrology, and indirectly as a developer of astronomical methods which became an essential part of it, was pivotal.”9
That’s a pretty strong statement, and whether or not that is the case, it does cement Hipparchus’s reputation as an astrologer; one who not only measured the motions of the heavens, but who also interpreted its meanings. And if he interpreted this meaning, is it not possible that he, and his students or associates, may have attached some astrological, chronological, or even quasi-religious meaning to the precession of the equinoxes, no matter how dimly they understood the mechanics?
If we consider the question of how Hipparchus’ discovery of precession might have been received as an astrological doctrine, or how it might have impacted contemporary religious cosmologies and chronologies, we are suddenly faced with a startling realization.
Shortly after the time of Hipparchus, in the 1st centuries BCE and CE, the ancient world experienced an explosion of radical, new religious chronologies, based upon the idea of the end of the old world, and the beginning of a new age and a new world order.
The most lasting and influential of these was Christianity, which from the very beginning proclaimed the apocalyptic coming of the Kingdom of God. With its aion and imminent parousia, Alpha and Omega, and the Piscean symbolism of the Christ/fish, Christianity was the original “New Age’ religion. This elaborate Christian eschatology did not arise in a vacuum, but fit well within the broader social spectrum, where the early Christians were surrounded by other cults and sects who believed along much the same lines, for instance: The Gnostics, the cults of the Aeon and Mithras, and of course, the solar/emperor worship at the very heart of the Roman Empire.
In 1989, David Ulansey published The Origins of the Mithraic Mysteries. In this work and related articles, Ulansey developed the idea that the symbolism of the Roman cults of the god Mithras, particularly their taurectonomy, the ever-present bull-slaying scene, represented a contemporary religious response to the discovery of precession. Ulansey’s work raised some very good questions about how the discoveries of Hipparchus would have been received; questions which remain unresolved.10
Perhaps we have been looking in all the wrong places for the impact of the discovery of precession.
Perhaps it is hidden in the symbolism of the Mithraeums. There, many of the older cosmological myths and deities were attached to the Mithraic iconography in a new way, and Mithras was increasingly portrayed as a composite of the gods in charge of a changing cosmos.
Perhaps it survives in the fish stories in the Christian gospels, or in the Fisher Saga of the Mandean cults of John the Baptist, in the symbolic guise of the Good Fisher who comes to save his fish.
Perhaps it survives in the poetry of Virgil, who in the opening to his 4th Ecologue, written in 37 BCE, heralded the dawn of a new age, with the return of Saturn and the Virgin Justice:
“Now the last age by Cumae’s Sibyl sung has come and gone,
and the majestic roll of circling centuries begins anew”
All these breathtaking new visions of time, wherein circling aions and swirling centuries were all cycling up to their inevitable conclusion and glorious rebirth, emerged in the wake of the discoveries of Hipparchus. And who is to say they were wrong? After all, we still organize time, whether BC/AD or BCE/CE, along these same lines.
Perhaps at least one of the reasons the books of Hipparchus and his unknown commentators did not survive the copying process was because some of the ideas in them were too controversial, and too uncomfortably close to orthodox Christian eschatology.
But nowhere in all of this fascinating religious chronology do we find anything even remotely akin to the declaration in the rock musical, Hair, of the dawning of Age of Pisces – and there was very good reason for that. As excited as people were about all the religious and chronological implications of the heavens in motion, they really did not understand the mechanics or the math sufficiently to think about it in that way.
A Little Misunderstanding Goes a Long Way
Regarding the lack of references to precession in the interval between Hipparchus and Ptolemy, Noel Swerdlow said:
“...it is most likely that the precession was not mentioned for three hundred years because Hipparchus' description was so tentative, and so uncertain of what his observations showed, that no one paid any attention to it until Ptolemy demonstrated that it really existed.”12
While we don’t want to be too quick to declare whether it was or was not mentioned, Hipparchus was uncertain about what he had observed. He even offered several hypotheses to both explain and test his observations. Ptolemy reports that Hipparchus’s first hypothesis was that only zodiacal stars, particularly bright zodiacal stars like Spica, moved with the equinoxes.13 Hipparchus also questioned whether the fixed stars were really fixed at all. He proposed the possibility that they had other, independent motions, and included detailed descriptions of stellar alignments in his work so that later observers could check to see if any changes had taken place. Ptolemy did check them, and was able to show that all of the alignments were still in place, exactly as Hipparchus described them.14
Hipparchus was also unsure about the actual rate of precession. In fact, somewhere between Hipparchus and Ptolemy, the rate got hopelessly distorted, with long-term consequences.
In the Almagest, Ptolemy (Almagest, VII.2) quotes Hipparchus himself from On the Precession of Solstitial and Equinoctial Points (no longer extant), for a series of observations of the star, Spica.15 These observations would have yielded a precessional rate of 1 degree in a little over 75 years, had Ptolemy checked the math.
Instead, Ptolemy quoted another rate, 1 degree in 100 years, which Hipparchus had tentatively proposed in his On the Magnitude of the Solar Year (no longer extant).16 Even though Hipparchus only suspected this was the rate, subject to a number of conditions, this latter value was accepted by Theon of Alexandria and remained in use for centuries, confusing astronomers everywhere, while the former, and more accurate value had to be rediscovered many times over before it was finally accepted.17
The Fabulous Eighth Sphere
In the pre-Copernican, geocentric cosmology, with its system of interactive planetary spheres,
precession was believed to be a result of the motion of the fabulous ‘eighth sphere.’
This ‘eighth sphere’ was the home of the fixed stars of the constellations, and it revolved somewhere beyond the seven planetary spheres.18
The misconception of the 8th Sphere, along with Ptolemy’s miscalculation of its rate of motion, created big problems in astronomy for over one thousand years.
There were perceptive astronomers who came closer to the real rate of precession in their calculations. Albategni (d. 929 CE) believed that it was approximately 1 degree in 66 years, and Al-Biruni (d. 1048 CE) calculated it to 1 degree in 68 years. Petro de Abano (13th century) refers to the precessional cycle of one ‘Azolphi’ (25,200 years), which is remarkably close to the accurate rate.19
It was Isaac Newton, in the 17th century, who produced the first full theoretical explanation of precession, and accurately calculated its annual rate.20 Before Newton, much of the work of the intervening centuries quotes Ptolemy’s nice, round number of 100 years.
For instance, the Sphaera Mundi of Rabbi Abraham bar Hiyya, published in 1546, contains a history of the theories of the eighth sphere, and opens with the assertion that it moves 1 degree in 100 years, and makes a complete rotation in 36,000 years.21 Edward Grant notes that:
“During the Middle Ages, numerous periods were proposed for the Great Year, the most popular being 36,000 and 49,000 years. The former was derived from Ptolemy’s Almagest, based upon a value of precession of the equinoxes of 1 degree in 100 years.”22
The Rate of Precession
1 degree of Zodiacal longitude every 71.6 years
One complete cycle
of the Zodiac in
The Theory of Trepidation
Further adding to the confusion, ancient astronomers did not assume that precession was a simple, straightforward motion. Most of them believed that the eighth sphere not only precessed at a regular pace, but that it also periodically reversed itself and went back in the other direction, at various and confusing intervals. This was the theory of trepidation, and it too would plague the study of precession for more than a thousand years.
The origin of this theory remains a mystery, and still clouds our understanding of how precession was received in the ancient world. Swerdlow claims that Hipparchus may also have proposed 'that the sphere of the fixed stars might oscillate back and forth over a short arc of eight degrees, ' but there is little evidence that he did.23
The earliest reference to Trepidation is found in Theon of Alexandria's small commentary to Ptolemy's Handy Tables (4th century CE). Theon claims that Ptolemy specifically did not ascribe to a theory of 'the ancient makers of talismans' in which the vernal equinox oscillates back and forth between zero and eight degrees of Aries at a rate of one degree every 80 years. Now just who these mysterious talisman makers were is anybody's guess. Later Arabic astronomers like Al-Biruni thought they were Babylonians, while Neugebauer believed the term was an oblique reference to earlier Greek astronomers.24
The most widely-used theory of trepidation during the Middle Ages was that of the ninth-century astronomer Thabit ibn Qurra. Thabit hailed from Harran, a town famous for the stellar religion of the Sabians, but he lived and worked for most of his adult life in Baghdad under the Abbasids. I can't help but wonder if those old talisman makers may have, like Thabit, come from the mysterious star cults of Harran. Nevertheless, in his On the Motion of the Eighth Sphere, Thabit postulated the theory of the progressive and regressive motion of the stars, also known as access and recess. He defined trepidation as an alternative, or substitute theory for the precession of the equinoxes, and it soon became common practice for astronomers to treat both trepidation and precession as two separate and distinct motions.25
J. D. North claims that if Ptolemy had gotten the precessional rate right in the Almagest, the theory of trepidation might have never come into play, for it was necessary adjustment astronomers had to make as they tried to square their own observations with Ptolemy?s fictitious precessional rate.
?The fact is that most of the best astronomers of the time believed that Arabic writers had established the reality of the phenomenon beyond doubt... (and were) not sufficiently careful readers of Ptolemy's Almagest to appreciate the source of the fallacy... '26
Whether the notion of trepidation arose before Hipparchus, with Hipparchus, or post-Ptolemy, is still a matter of debate. However, in the ceaseless, and ultimately, thankless efforts to refine the notion of trepidation, not only were various values proposed for the rate, and various intervals designated as recessional, or backwards periods, but also, whole new spheres were eventually required; the ninth, the tenth, the eleventh, ad infinitum, to account for these varying degrees of motion.
St. Albertus Magnus, in his Metaphysics, Book 2, attributed three separate motions to the eighth sphere of the fixed stars: 1) the obvious east-to-west motion observed every night 2) the precession of the equinoxes and 3) the trepidation, or motion of accession and recession described by Thabit.27
However, other astronomers disagreed, and believed that extra spheres, or orbs, were necessary to explain such complicated motion. Peter of Abano (Petro de Abano) in his Lucidator, argued for nine spheres; assigning the daily, east-to-west motion of the fixed stars to the eighth sphere and the precession of the equinoxes to the ninth sphere. An impressive contingent fell in behind the idea of ten spheres, controlling the three separate motions of the fixed stars. These included: Albert of Saxony, Roger Bacon, Themon Judaeus, and Pierre d'Ailly. Albert of Saxony assigned precession to the eighth sphere, trepidation to the ninth, and the daily motion to the tenth sphere.28
Europe's Medieval Magi
Even though astronomers completely misunderstood the mechanics and the math of precession, that never stopped them from speculating on what it all meant. While there is no record of the use of astrological world ages such as Seymour described, medieval European astronomers entertained a whole range of astro-chronological schemes using precession and trepidation, many of which employed distinctly Persian and Zoroastrian imagery.
The idea that significant intervals in these movements coincided with turning points in world history certainly flourished. In describing the work of the 14th century astronomer/historian Walter of Odington, J.D. North maintains that:
"...it would have been appropriate to include a discussion of precession and trepidation in a work on the age of the world; first, it was widely thought that vicissitudes of the world's history were linked with the periodicities of trepidation - notice how Alfonsine trepidation had a turning point near the time of Incarnation."29
Turrel used a regular precessional movement in which the entire sky revolved once in 49,000 years, against a periodic, or trepidational movement of 7,000 years.31 Turrel believed that there were four stations in the trepidational period, occurring quarterly, or every 1750 years, and to these pivotal stations he assigned the Flood, Exodus, the destruction of Jerusalem, and the end of the world.
Thorndike maintains that Turrel probably derived his methods from the earlier, 15th century work of Jean de Bruges, De Veritate astronomiae. De Bruge, in turn, may have been influenced by the Summa astrologie of John Ashenden (14th century), which also discusses trepidation and the theories of the highly influential Thabit ibn Qurra. J.D. North quotes from the Lucidator and Conciliator of Petro d'Abano (13th century) the following tale in which the diminishing life span of man is linked to an ill-defined movement through the constellations of the zodiac.
"The worlde (sic) is divided into 3 partes. The first from the Creation unto Noah his flod and after then untille 2000 years...' The age to which a man might live was supposed to reduce in steps from 1200 years (and that begane in the head of <Sagittarius>) to a mere 75. The top of the page has been torn away, and this might have given some clue as to what 'it' was which was supposed to move steadily around the zodiac, starting at the head of Sagittarius at the Creation, occupying each sign for 500 years, and finishing at the end of Scorpio at the end of the world, Anno Mundi 6000."32
Another famous 14th century astrologer, Cecco d'Ascoli (d. 1327 CE, at the stake), in his commentary of the Sphaera of Sacrobosco, quoted from a work falsely attributed to Hipparchus, called De hierarchiis spirituum, for this strange story about the incubi and sucubi who reside at the colures (the great circles on the celestial sphere which pass through the north and south poles and define the solstices and equinoxes).
Cecco recounts that at pivotal moments in world history, these spirits combine to produce great men 'as of the Godhead.' North describes how:
'Cecco then goes on to relate a similar account from a pseudo-Zoroastrian work ...entitled Liber de dominio quartarum octave spere. A quadrant of the eighth sphere is said to dominate every historical period of 12,000 years and at the turning points of which men of divine attributes are born of incubi and sucubi...'33
In tracing these references back through time, two things become apparent:
By all accounts, the precession of the equinoxes and its medieval concomitant, trepidation, were widely used in European astronomy/astrology to apportion history. Further, the influence of Persian and Zoroastrian ideas upon these efforts is obvious. Still, we don't find any astrologers or astronomers dividing time into Zodiacal world ages based upon a steady precession of the equinoxes. The obvious reason for that is that they didn't understand the phenomenon and the math sufficiently to do so. That understanding came in the age of Newton.
Certainly, Newton and his post-Copernican contemporaries had a great advantage in their more accurate understanding of the true nature and rate of precession. Newton put this advantage to use in The Chronology of Ancient Kingdoms Amended, his own contribution to the ongoing effort to measure the course of human history against the rhythm of precession.
The lack of understanding never stopped their predecessors from trying, but in spite of all their efforts, the modern theory of astrological world ages based upon a steady precession of the equinoxes arose post-Newton. The earliest references for this kind of thinking appear in the late 19th century, in the lectures of Gerald Massey, and these ideas were further popularized in theosophical circles by Madam Blavatasky and her associates.34
The Mighty Intihat
Just because Persian astrologers didn't divide time into Zodiacal world ages based upon a steady precession of the equinoxes, that doesn't mean they weren't thinking along those lines. The Persians had their own traditional ways of dividing up the millennia along both the ecliptic and the celestial equator, for instance: the Intiha'at and the Tasyirat.
As Kennedy describes these techniques, it is useful to think of them as the moving hand on a clock, with the ecliptic circling the dial instead of the hours. 'At the beginning of the world year, all hands depart from 0° Aries and sweep around with different speeds. At any given instant a unique point on the zodiac will be designated by any one of the hands.' While these periods were used in natal astrology to determine the timing of an individual's fate, they were also used on a much grander scale in mundane astrology to indicate significant turning points in the world year.35
Like the Jupiter-Saturn conjunctions, the tasyir and intiha'at were classed according to their influence: mighty, big, middle, and small. The 'mighty' world-tasyir, which travels along the celestial equator, moves 1° in 1,000 years. The 'big' world-tasyir moves 1° in 100 years, with a rotational period of 36,000 years, corresponding to Ptolemy's rate of precession. The Intiha'at moves along the ecliptic and is measured in zodiacal signs. The 'mighty' intiha moves through a zodiac sign in 1,000 years, and its period is 12,000 years, corresponding to the traditional Persian millenniums.36
Masha'allah's work is full of references to these systems. For instance, in commenting upon the chart for the Jupiter-Saturn conjunction proceeding the birth of Muhammad, he says, 'Verily it (the divisor) reached Libra from the conjunction of the Deluge, and from the sign of the intiha of the cycle to Gemini.'37
So there was significant interest in Persian astrology in measuring millennia and world-years by zodiac signs, and by movement along the ecliptic, but these techniques were limited by the same misunderstanding of precession that plagued later European astrologers.
The Persian Precessional Year
Persians also made efforts to accommodate Ptolemy's precessional rate of one degree every hundred years, and its resulting World Year of 36,000 years, into their millennial system. In the Persian zij of Shams-i Munajjim we find:
'...according to the claim of the people of Fars (Pars, Persia) it (the beginning of the world-year) was from that time when the conjunction of the planets occurred at the first of Aries until the year of the Flood a hundred and eighty thousand solar years passed. According to their claim the days of the world are three hundred and sixty thousand years, and the astrologers (ashab-i ahkam) put the beginning of the tasyirat and intiha'at and fardarat then.'38
This Persian World year of 360,000 solar years was equal to 10 complete circuits of the Ptolemy's precessional cycle, and in this system, the Great Deluge occurred exactly at the halfway point.
The Fish and the Virgin
The Persians and their Magi were as fascinated by the possibilities of precession as anyone, and they contrived creative ways of working it into their chronologies. They had plenty of company in these efforts, as many of their contemporaries strove to incorporate precession in some meaningful way into their world view and soteriology. They tiptoed all around the idea of the Age of Pisces, but it's doubtful that their state of knowledge would have led them to such a conclusion.
On reflection, perhaps the only place where precession goes completely missing is in the astronomy, especially that crucial period between Hipparchus and Ptolemy, and why that is remains open to question.
Certainly Matthew's Magi would have been equally interested in precession, and probably would have discussed it with their Christian associates. It is entirely possible, even probable, that someone, somewhere, could have been sufficiently inspired by the approaching shift of the vernal equinox into the constellation Pisces to conceive of it as the harbinger of a 'new age.' These speculations could have eventually focused on Pisces as a symbol for the saviour, or the guiding spirit of the age.
The presence of both the virgin and the fish together in certain literature from the early Christian era does make it seem that at least someone saw Christ and his holy mother symbolized in the two signs, Virgo and Pisces, which were just then taking up their posts at the equinoxes. But there are no texts that clearly spell this out for us, so we dealing here with speculation, not evidence; all the while raising very good questions about some important symbolism of the early Christian church. I hope to explore this more fully in another book, where these questions could receive the kind of detailed analysis they deserve.
Ultimately, the assumptions regarding the Magi's belief in the astrological Age of Pisces are a lot more complex than most imagine, and I, for one, would not be so quick to say that the Magi would have preferred the Pisces triple conjunction of 7 BCE on that basis.
Reviews & Signed Copies
United Nations Girls Education
United Nations Girls Education
Apocalypse Not?
Endnotes
All Sources and References Can be found in the Bibliography:
1. Among Seymour's innovative works are Cosmic Magnetism (1986), Astrology: The Evidence of Science (1991),The Scientific Basis of Astrology (1997), and The Scientific Proof of Astrology (2004)
2. O. Neugebauer, 1950, pp. 1-8. Schnabel (1923 and 1927) argued that the Babylonian astronomer Kidinnu discovered precession, but Neugebauer presumably put his arguments to rest.
3. Otto Neugebauer, 1975, p. 5
4. Toomer, G.J. , 1998, pg. 1
5. Taub, L., 1999
6. Neubebauer, 1969, pg. 87
7. Cumont, Franz, 1960, pg. 40
8. Dicks, D.R. 1960, pg. 14
9. Toomer, G.J., 1978, pp. 207-224.
10. Ulansey, Hipparchus's Understanding of the Precession, athttp://www.well.com/user/davidu/appendix4.html
11. For the full text of Virgil's 4th Eclogue, see: http://classics.mit.edu/Virgil/eclogue.4.iv.html For an alternative translation, see: http://www.sacred-texts.com/cla/virgil/ecl/ecl04.htm
12. Noel Swerdlow, 1991, pg. 59
13) Toomer, G. J., 1998, pg. 322
14) Ibid, pp. 321-327
15) Ibid, pp. 327-8 'From this we find that the 1° rearward motion takes place in approximately 100 years, as Hipparchus too seems to have suspected, according to the following quotation from his work, 'On the length of the year': 'For if the solstices and equinoxes were moving, from that cause, not less than 1/100 of a degree in advance (i.e. in the reverse order) of the signs, in the 300 years they should have moved not less than 3°.'
16) North, 1976, pg. 253
17) Ibid
18) Did Hipparchus believe in the Ptolemaic, geocentric universe? Did Hipparchus believe in the moving spheres? Toomer recounts: Note that the motion which in modern terminology is 'precession of the equinoxes' (i.e. a motion in the direction of decreasing longitudes of the tropical points with respect to the fixed stars) is described by Ptolemy as a motion of the fixed stars with respect to the tropical points in the direction of increasing longitudes. This accords with his taking the tropical points as the primary reference points (III I p. 132). Hipparchus, however, seems at times to have adopted the modern convention to judge from the title of his work 'On the displacement of the solstitial and equinoctial points' (III I p. 132 and VII 2 pp. 327 and 329) (Almagest, p. 321, n. 2)
19) North, 1989, pg. 108
20) Manuel, 1963, pg. 67. In Book III of his Principia (Prop. xxix, problem xx) published both his theoretical explanations and his computations.
21) North, 1976, pg. 265
22) Grant, 1996, pg. 498
23) Swerdlow, N., 1991, pg. 59
24) Neugebauer, 1950, pg. 7-8
25) Grant, 1996, pg. 315
26) North, 1976, pg. 238
27) Grant, 1996, pg. 315
28) Grant, 1996, pp. 315-16
29) North, 1976, III, pg. 262
30) Thorndike, 1941, V, pp. 310-11
31) North, 1989, pg. 106
32) North, 1989, pg. 108: Bodleian MS Ashmole 802, f. 86
33) North, 1989, pg. 85 & Thorndike, 1949, pg. 387-8
34) Massey, Gerald, 1886, pg. 6-7: 'In the course of Precession, about 255 B.C., the vernal birthplace passed into the sign of the Fishes, and the Messiah who had been represented for 2155 years by the Ram or Lamb, and previously for other 2155 years by the Apis Bull, was now imaged as the Fish, or the "Fish-man," called Ichthys in Greek.' Also,Blavatsky, H.P. 1887, pg. 96 'There are several remarkable cycles that come to a close at the end of this century. First, the 5,000 years of the Kaliyug cycle; again the Messianic cycle of the Samaritan (also Kabalistic) Jews of the man connected with Pisces (Ichthys or "Fish-man" Dag). It is a cycle, historic and not very long, but very occult, lasting about 2,155 solar years, but having a true significance only when computed by lunar months. It occurred 2410 and 255 B.C., or when the equinox entered into the sign of the Ram, and again into that of Pisces. When it enters, in a few years, the sign of Aquarius, psychologists will have some extra work to do, and the psychic idiosyncrasies of humanity will enter on a great change.'
Both citations can be found, along with a detailed analysis of the question, at the website of Dr. Shepherd Simpson athttp://www.geocities.com/astrologyages/searchingforanewage.htm
35) Kennedy, 1962, pg. 26
36) Ibid
37) Kennedy & Pingree, 1971, pg. 48
38) Kennedy, 1962, pg. 24: Shams-i Munajjim's Zij. Survey no. 35, written c. 1320..., f.30v