Lucan narrates an observation of an arrangement or configuration of the heavens, which Nigidius Figulus the student of mathematics made before the civil war of C. Julius Caesar, or at least Augustus. These are the words:
Figulus also spoke, Figulus, whose study it was to know the gods and the secrets of the sky, Figulus, whom not even Egyptian Memphis could match in observation of the heavens and calculations that keep pace with the stars. "Either, " said he, "this universe strays for ever governed by no law, and the stars move to and fro with course unfixed; or else, if they are guided by destiny, speedy destruction is preparing for Rome and for mankind. Will the earth gape and cities be swallowed up? Or will burning heat destroy our temperate clime? Will the soil break faith and deny its produce? Or will water everywhere be tainted with streams of poison? What kind of disaster are the gods preparing? What form of ruin will their anger assume? The lives of multitudes are doomed to end together. If Saturn, that cold baleful planet, were now kindling his black fires in the zenith, then Aquarius would have poured down such rains as Deucalion saw, and the whole earth would have been hidden under the waste of waters. Or if the sun's rays were now passing over the fierce Lion of Nemea, then fire would stream over all the world, and the upper air would be kindled and consumed by the sun's chariot. These heavenly bodies are not active now. But Mars--what dreadful purpose has he, when he kindles the Scorpion menacing with fiery tail and scorches its claws? For the benign star of Jupiter is hidden deep in decline, the healthful planet Venus is dim, and Mercury's swift motion is stayed; Mars alone lords it in heaven. Why have the constellations fled from their courses, to move darkling through the sky, while the side of sword-girt Orion shines all too bright? The madness of war is upon us, when the power of the sword shall violently upset all legality, and atrocious crime shall be called heroism. This frenzy will last for many years; and it is useless to pray Heaven that it may end: when peace comes, a tyrant will come with it. Let Rome prolong the unbroken series of suffering and draw out her agony for ages: only while civil war lasts, shall she henceforth be free.
That is Lucan.
First off I assume that it is reasonably certain to place Figulus' observation between 50 and 38 B.C. We must now discover what year and what time. It appears clear in the passage that Saturn was in Aquarius, the sun was in Leo and Mars was near the boundary of Libra. In the 154th day of 38 B.C. (calculated back from our calendar) I find Saturn in Aquarius, the sun in Leo, Mars near the end of Libra, and Jupiter in Cancer. But according to astrologers Cancer is the exaltation of Jupiter, so perhaps this is why Lucan says: "on high." And because shortly after the sun sets in Leo, Jupiter too sets, Lucan says: "pressed by his fall." Firmicus (Book 1, chapter 8) says that planets are weak when they rise in the evening right after the sunset. But on that day I find Venus at the boundary of Taurus, which is her true alteration (?) 1`, 59o, 28', 43". Perhaps this is Lucan's reason for saying, "Venus is sluggish," because she is beginning her retrogradation, (but Taurus is called the nighttime house of Venus, and so perhaps this constellation ought to be taken a bit more slowly, since Venus had already entered Gemini, and therefore was wandering). Finally at this time I find Mercury in Cancer, and his true alteration in the upper part of the epicycle 0`. 35o, 41', 8". Because he is neither in his house, nor in his exaltation, nor in his triangle, he is wandering, and Lucan says, "he clings." And because his motion is direct, Lucan says, "swift in motion" for emphasis.
As far as Venus and Mercury go, this heavenly configuration does not seem to fit. Therefore I request that you discover exactly what time between 50 and 38 B.C. the heavens were in this configuration that Lucan described.
Letter 2: Kepler to Herwart Sept. 12, 1597
Since you, though placed in such a highranking office, nevertheless love the study of literature, the reading of history, and intimacy with astrology, I am unable, O most noble and outstanding man, to avoid applauding how you seem to have attained every aspect of the state which Aristotle designated felicity. I have struggled all the more readily to satisfy in writing the desire that you have attested in letters sent to D. Greenberg; not indeed that I hope to fulfill your request better than anyone else, but rather because I warmly embrace the opportunity to win the favor of so great a man whose letters have created hope for me. I have not, however, written my answer in any other way than that which was born in my very thoughts on your problem, which form of writing, I admit, is crude and unworthy of so great a reader. But let this inelegance cause laughter, as long as it shows both the conscientiousness I have applied to the task, and the difficulty I met therein. If you should discover anything in these crumpled pages which pleases you and on account of which I seem worthy of your benevolence, let it persuade you that your trust in me was not wasted. If you should feel the necessity to express this favor, I gratefully propose a dual possibility: that you commend me to doctor Fickler, an outstanding man who bears kinship with my parents; or that you draw out of your distinguished mathematicians their opinions on my recently published little volume (Mysterium Cosmographicum)--it matters not how favorable these are, and order by your authority (if I may speak forthright) that they be sent to me. How much this would benefit my affairs, I venture to guess from the effect of your letter, which impressed certain men to such a degree that I am certain nothing more propitious could havehappened to my standing here. Farewell most noble and outstanding man, and if any failing in my style does not suit the forum, please indulge the corrupt habits of mathematicians. Sept. 12, 1597.
Professor of Mathematics, Styria
I. Meaning of Lucan and his description of the heavens.
Before calculations are applied to the solution of your problem and we are tossed on the unknown waters of 12 years, let us ponder first each of the poetıs words used to describe the heavens. If Saturn, as he says, were at the top of the sky, that is in Cancer, which is the highest sign, and he were to ³inflame² (that is, lead by a conjunction into his influence and power) the ³black fires² (that is, the cloudy stars of the Asses and the Manger), then it would foretell a flood. But he says: ³Aquarius would have gushed with rain,² or because he is creating a poetic fiction, no other sign of the zodiac is more fitting for describing an effusion of water than Aquarius, or because the sun had suffered an eclipse in Aquarius, or because the sun was in Aquarius, it was particularly rainy of which possibilities the last seems most sensible. But from the actual description is clean that the poet puts the sun neither in Cancer nor in Aquarius. Not in Cancer, because (according to my interpretation) this was invented by the poet. If it had been in Cancer, it would have rained. For this fabrication speaks of Saturn in Cancer and not in mid heaven. So itıs clear, since we cannot figure out any other way, what the words ³inflame the black fires² wish to express: because he later places Mars in Scorpio and alongside the tail which is removed one third from the Asses, and since in this way thee would be a triangle of Saturn and Mars in the moist signs of Cancer and Scorpio, and they would be near the most powerful fixed stars, Nigidius would have concluded correctly (at least according to the ancient laws of astrology) that floods had been foretold. But the poet does not put Saturn in Aquarius I such a way that he could say that it was in Aquarius and mid-sky, because once again the poet is setting these forth as a literary trope. If Saturn were in Aquarius, then it would have rained. These words contain the ability to refute themselves.
Second, he says, ³If the sun were in Leo,² conflagrations would be predicted. This is correct: the sun would be quadrate with the tail of Leo and Mars with that of Scorpio, and when this happens astrologers predict fires, and such signs even shine for those who are cremated. Therefore it follows that the sun is not in Leo, because the poet himself denies it with these words, ³these fires are inactive.²
Third. Lucan proceeds: ³Why are you, Mars, in Scorpio? What do you foretell?² Clearly he puts Mars in Scorpio. but he adds, ³You burn the claws,² which gives rise to some difficulty. For in antiquity Libra was called the Claws and even today the claws of Scorpio make up the constellation of Libra. How therefore can Mars be in Scorpio at the same time? Therefore I believe that Lucan has used the figure of poetic synonym, and has invented claws for Scorpio. In addition, since the claws are alight or heat has been applied, he imagines the Scorpion would be ³threatening with a flaming tail.² Otherwise Mars in Libra shows nothing so frightful. Letıs take a look at Ptolemy who followed Lucan, the creator of our prophet Nigidius, by no more than 70 years. ³In the Claws,² he says, ³which are in the yoke of claws of Scorpio, the furthest stars have similar influence to that of Jupiter and Mercury, but the middle stars have a force similar to Saturn and somewhat so to Mars, etc. It makes the front and heart of Scorpio martial.² The same author affirms elsewhere, that the Claws are a variable and changeable sign, while Scorpio is thunderous and fiery. Letıs keep in mind also what we said in the first and second place, and not hesitate to put Mars in conjunction with Scorpio, and not with the stars in Libra.
Fourth. He says, ³A mild Jupiter is pressed by a deep fall.² In our temporal uncertainty several interpretations can be imagined for these words. Perhaps he wishes to say Jupiter is involved in his debilitation, that is in Gemini, a low sign so that he says that it is pressed, that is badly positioned, in decline, that is in descent, or because of descent. Although ancient astrologers distinguish between descent and debilitation, nevertheless by being in the opposite of his own house, Jupiter is imagined by the poet to have fallen from his own house. Or perhaps he wishes to say that Jupiter is sunk down profoundly, that is deeply, in his decline, that is in the sixth house. Or perhaps that he has fallen from the angle of the tenth house which would be a profound fall. Or finally that he being in Cancer, the lowest sign and in the angle of the seventh house, or rising to the rays of the sun, is oppressed by the inauspicious rays of some Malefic. Whichever of these four possibilities our calculation confirms, this will be our choice.
Fifth. ³Venus, that beneficial star, is dim.² This too has a multiple interpretation, either generally that Venus is under the rays of the sun, or specific, that her light was diminished, that is she is being more and more influenced by the rays of the sun whether directly or reversed.
Sixth. ³The swift-moving Mercury pauses.² He is using poetic antithesis. The fastest of all planets now pauses, that is, stands unmoving, or is slow and retrograde.
Seventh. ³Mars alone holds the sky.² Either because he is alone above the earth with the rest (of the planets) below, or because he alone is free of the rays of the sun, or because he alone is powerful and swift in his course, and not afflicted while the rest are pressed either by rays or retrogradation, or finally because he is governor of the configuration. Of these interpretations the second will withdraw itself when we consider the position of the sun. The first and third seem to be confirmed by the following lines: ³Why do the signs (the planets) desert their own courses (their night courses), and are borne hidden to the world.² When they are either under the rays of the sun, or (more generally) are under the earth or are retrograde, then they have deserted their courses and enter hostile ones.
Eighth. ³The side of sword bearing Orion shines too bright.² Here it is quite clear that the poet speaks of the nocturnal face of the heavens, or surely of a total eclipse of the sun. Nor let us pass over the word ³side² without any comment: its method of poetic employment could be none other than because he (Lucan) is describing either a rising or setting Orion, and probably rising, since he discloses first his left shoulder shortly after his left foot, and thus shows his ³side² to the earth. With him (Orion) positioned this way it is not possible for Jupiter either to be in Cancer or in the sixth house. Unless perhaps the poet is speaking of the side in front of the shoulder or belt near to the turned side. So much for the description of the heavens.
II. The time of This Heavenly Configuration
Now let us consider second whether our cosmic configuration expresses any particular time. and indeed there is no need for many words here. To describe the civil war between Caesar and Pompey Lucan starts with the first origins of the war, that is from the crossing of the Rubicon and the capture of Ariminum. Once a rumor of the arrival of Caesar had reached Rome Lucan describes a flight of consuls and citizens. He explains the causes of such great fear and repeats in greater detail the plan of the gods, thus passing on the most common omens of land and sky which are known to terrify the common horde. Among other prodigies, he tells of volcanoes, comets, eclipses of the sun and moon, and unnatural births, some of which we will discuss. With all of these portents displaying themselves the haruspex is summoned to the city according to the ancient custom, and this diviner somewhat ambiguouslyFigulus quite clearlypredicted a change in affairs, an affliction for the republic, and various other evils appearing in the sky.
Here we see the predictions of Figulus tied in with the prodigies and the speech of Aruntius (the haruspex), and both are connected with the flight of the people from the city in such a way that either they are the cause of it right at that time or at least at no great distance from it.
And so there is no doubt that this constellation must be sought in 49 or 50 B.C. or 51 at the outside. Since in this three year period Mars only entered Scorpio once or at the most twice, the doorway to our search lies open.
III. What could Give an Opportunity to Correct Our View of the Sky
In the third place let us consider the magnitude of the events which Figulus predicted based on his reading of the sky. for it is necessary to bring to bear more circumstances than Mars being alone in Scorpio and the other stars being in declinea situation which occurs all too frequently. I am able to deduce at most four possibilities for the circumstances which someone could have created here: that Figulus, either inspected the heavenly figure of an eclipse of the sun or moon, or of the entrance of the sun into Capricorn or Aries, or of the rising of the Dog Star, or finally of that time and hour in which he made his inspection or when the portent was born. For those times contained no conjunction or opposition of the above. One conjunction in Pisces did occur in 66 and one in Scorpio occurred in 46, but none in between. Saturn and Jupiter were able to look upon each other in quadrature from Cancer and Libra, and this perhaps is the debilitation of Jupiter. Whatever of these four possibilities holds up, astronomical calculation will uncover in the fourth section.
IV. Astronomical Calculations
Therefore on March 22, 50 B.C. of the Julian calendar which answers roughly to January of the old Roman calendar, Mars in normal motion was joined with the heart of Scorpio at 11° of Scorpio.
Since the sun reached its equinox around March 23 at that time, it seems quite possible that Nigidius saw a configuration with the sun entering into Aries. So let the movements of the planets be sought: first the entry of the sun into Aries.
On the 23rd of March in Regiomonte the equinox was three hours before midnight, at Rome almost four. So let us seek the locations of the planets during this night.
Once I had inspected the tables for the entry of the sun into Aries, it became clear that Nigidius did not speak about this configuration of the heavens. For Venus is not afflicted by rays, nor is Mercury stationary, nor (the most important item) is Mars in direct and visible motion in Scorpio, but rather in Sagittarius. Even Lucanıs own words defeat this theory of mine, since he imagines that, if the sun were in Leo, the heavenly configuration would signify conflagration. If the sun is able to be in Leo, then the configuration Lucan speaks of did not take its force from the entry of the sun into Aries, which I had guessed.
Then at the time the sun entered Aries, there already was a rumor of Caesar the enemy of the Republic. But Figulus makes his prophecy as if he spoke of an unheard of event. First he is uncertain what to declare whether a plague or earthquake or flood or fire. Then he ends with a confident prognostication of civil war. Therefore we have to climb back towards the beginning of the year 50 B.C. For we are not able to sink down to the beginning of 48 because it is necessary to prognostication that it precede its fulfillment. And at the beginning of 50 we will find Mars in Scorpio, Mercury stationary at the edge of Sagittarius, Venus afflicted by rays in Capricorn. Therefore letıs look for the winter solstice at the end of 51.
Near the end of the 51st year before Christ, on the 23rd of December figured back in the Julian reckoning (as corrected by Augustus), in the evening after the fifth hour at Rome the sun reached the solstice in the beginning of Capricorn.
Therefore letıs search the following night for the locations of the planets. And the proposition has to be corrected, because I canıt use the fifth or sixth evening hour when according to the tables of Prutenicus the sun reached its cardinal point. For Cancer is rising and Pisces is in mid heaven and Mars would be under the earth while Jupiter would be ascending and master of heaven. Perhaps therefore the Nigidian calculation differed a few hours from the Copernican. So letıs find the hour when Orion is conspicuously setting.
(insert Xerox of scheme here)
Mars is between the claws, Jupiter falls from the angle of the tenth house which is a profound decline. And since he is retrograde he is heavily afflicted by the quadrates of Mars and Saturn, which surround him. Venus is afflicted by rays, Mercury clings to the same spot. For he whom a direct course sent along before now backtracked in retrogradation, and was stationary a few days before. Because of this he moves slowly, delays, clings. Mars alone is master of the sky, the moon is in mid heaven and the sun, Venus and Mercury are ascendant (?).
The planets of light and of approaching shadows, Venus and Mercury are afflicted by rays and thus are ³born obscure to the world.² Or the sun, moon, Venus and Mercury are under the earth. The right shoulder of Orion, who was descending at that time at 21 degrees of Aries, ³shone bright in setting.²
To confess the truth, however, this configuration of mine does not seem to satisfy Lucan fully. First because the magnitude of the prophecy seems to require some sort of total eclipse, not a naked entry of the sun into Capricorn surely since there are no bad aspects anywhere. Second because Mars is not in Scorpio, whence poisoned water is able to be predicted. Third because it is not totally fitting to say that Jupiter in this situation is oppressed by a profound debilitation. Fourth because that line, ³the stars deserted their courses,² and, ³are born obscure to the world,² are not fittingly explainedit seems rather to describe some eclipse, probably of the sun rather than the moon. Not that there will be an eclipse after the beginning of the war, because he says, ³Phoebus, if you should now press the lion.² Fifth the thinking brought to bear above argues that the power and influence of the configuration do no rest on the entry of the sun into Aries, but nevertheless could be established, even though the sun were in Leo.
And so because it seems clear that a solar eclipse occurring in Pisces makes an affirmation (since he dared to prophesy floods and poisoned water), letıs see if the preceding full moon would have been ecliptic.
But at that time there was more than a 15 degree difference between the middle of this place and the head. The moon therefore experienced no eclipse. Nor should a lunar eclipse be sought, because Mars would be in Sagittarius. So letıs consider the year 52, when the tail of the dragon is around 10 degrees into Aries and Mars is in Scorpio in march.
The center of the conjunction will fall in the hours just after sunset. The moon is not yet in the tailits latitude is northerly and will be diminished by significant parallax. Jupiter will be in Gemini, Saturn in opposition, the eclipse in Virgo, Mars the master of the eclipse in Scorpio, Venus in the heart of Aries and afflicted by rays.
Once the calculation is consulted it is clear that about seven hours after the middle of the conjunction a true one would occur under the earth. Therefore this year or month must be deserted. Let the position of Mars, however, be noted: at 16°, 22´ of Scorpio.
So letıs desert the eclipses, letıs desert the entries into cardinal points and retreat to astrological problems, surely the most popular of that time period. The Roman mathematicians were devoted to Magic (Chaldean or of the Magi), a fact which Lucan even seems to attribute to Figulus, ³whose care it was to know the gods.² Likewise he says clearly ³in numbers moving the starts.² Although it is unclear whether he is talking about gods or fates or the devilnumbers moving the stars?or spells (as Vergil has the stars turn backwards through the agency of spells) or mathematical calculation. Surely mathematical research and other forms of fortune telling walk hand in hand. So be it. Above Figulus consults the portents, let him inspect the problem of what hour he took his sighting. Since at the end of December Mars is in the 27th degree of Libra, after a few days he is accustomed to be in the beginning of Scorpio, and still between the claws.
So letıs choose such a day that is likely to have a tragic aspect. No other day, however, is able to be chosen near the limits of the dictated times other than the eleventh one from the entry of the sun into Capricorn, when the sun becomes quadrate with Saturn and opposed to Jupiter.
Therefore to conclude, since from the four possibilities proposed above none of the first three could fit Lucanıs passage (with the dog star rising at these times Mars is not in Scorpio or Libra), it follows that Publius Nigidius Figulus spoke about the configuration at the very time of questioning. The Chaldeans invented no part of astrology more superstitious or closer to Magic and fortunetelling than this. Their precepts hold that an astrologer, at the very moment when he either is asked about something by another or thinks of it himself, should inspect the configuration of the heavens, and make judgment about all its details, as if the thoughts of the seeker could not exist unless under a certain sidereal arrangement. Figulus, in my opinion, inspected one of the following constellations. (insert Xeroxed tables here.)
The configuration itself is valid. If we look at the air, it is suited to creating fiery horrors. If we prefer portents concerning which Arruns was especially responsive, I would dare to judge whatever portent would appear it could be discovered in the second configuration. Indeed I recommend the second one more as better fitting Lucanıs description. 1. Saturn is not in mid heaven, nor in his exaltation, but in Cancer. 2. the sun is not in Leo. 3. Mars is in Scorpio, between the claws and the tail, that is in the front of the sign. 4. Jupiter is on high, for two reasons, because he is beyond mid heaven and he is in Cancer and he is heavily afflicted by the rays of two planets opposed to him, the quadrates of these two, and on top of that by retrogradation. One word, however, concerns me, ³fall (occursu).² For Jupiter is afflicted in mid heaven by the opposed rays of the sun which is moving towards him or meeting him. Or did Lucan perhaps place Jupiter in a deep fall because he is in the beginning of a quadrant in the western part of the cosmos, and begins to descend from the peak of heaven into a fall? Or, that which I mentioned above, because he flowed from the angle of the tenth house, he is in a falling house? Or does he metaphorically call retrogradation a fall, because stars moving in a direct course strive for their rising, while in reverse course they tend towards their fallthis type of language is unknown to me? Or finally because Jupiter is west of the sun, and therefore he (Lucan) attributed a fall to him (Jupiter)? Perhaps we are able to suspect this too, since Jupiter descends during these days cosmically (that is, when the sun is rising), that the poet wished to signify this with those words. To get back to the point, Jupiter was in the angle of the seventh house, or falling in the sixth, and this is a problem since in this way Orion would be under the earth.
Fifth. ³Venusı star is dim.² Because she is afflicted by rays, and inside of the orbit of the sun, whose rays carry 15 degrees, and Venus is only 11 from the sun. 6. Mercury clings near the second station, which several days later he will approach in retrogradation. 7. ³The rest of the stars,² that is the rest of the planets, ³have deserted their courses² on the one had, and on the other are ³borne hidden to the world.² For Jupiter is retrograde, Saturn does not move and is stationary, Mercury also begins to become stationary after his retrogradation, Venus is afflicted by rays, and thus ³they are borne hidden to the world.² The sun and moon finally are under the earth (for another kind of solar obscurity outside of eclipse is not adequate). Mars alone holds the sky in either configuration. For he is the most powerful of all the planets, because he is in his dominion (exaltation), free from rays, in direct course, and in the second configuration alone in the angle of the first house, nearest to his rising; and finally because he is master of each configuration. This is how I read Lucanıs words, ³He alone holds the sky,² that is, he alone holds power over all, or he alone moves directly and swiftly, which phrase is quite good Latin and one familiar to poets, as is this, ³He holds sway over the open field.² Although in the first configuration I indulge Mars that he is above earth and thus is said to hold heaven, nevertheless it is feeble, since he does not hold it alone, but sees Jupiter and Saturn at his side. Surely within the ten closest years Mars will hardly be found alone above the earth in Scorpio such that Orion also is apparentnot to say, which is a puny and flimsy point, that Mars is above in such a way that he falls into the 12th house. 8. Orion is above the earth and conspicuous in each configuration, but more so in the second.
Therefore I doubt not either that Nigidius saw this second configuration, or Lucan contrived it for Nigidius. And the annalists are wealthier than this one argument, those who ascribe the beginning of the civil war to the 50th year before the customary epoch of the years of Christ, since this configuration which Lucan has cited falls in the same year (if with this Beitrag or entretien we have penetrated deeply into the arrangement of the heavens proposed in Lucan). But about this let those more experienced in ancient history judge, those who perhaps have read more about this P. Nigidius.
Allow me to say something more about this explication of the words of Lucan. First it does not fit with the time, for the configuration ought to precede the civil war of Caesar and Pompey. Second, to place Saturn in Aquarius and the sun in Leo seems utterly contrary to the meaning of Lucan. Third, I allow that Jupiter be said to be ³on high,² because he is in Cancer, which is his exaltation. But with the sun in Leo, Jupiter does not happen to be placed thus in the evening neither in a cosmic system, nor a heliocentric one, rather he rises each way in the morning. Fourth, when the sun is in Leo, Venus is not capable of being at the edge of Taurus. For the boundary set by the sun for her wandering is 49 degrees. Rather, when her alteration is 62 degrees and the sun is in Leo, she herself will be in Virgo, which is called the debilitation of Venus. Similarly when the alteration of Mercury is 0´. 28ş.4, he usually is the only planet besides the sun, and therefore in the latter part of Leo. Therefore I do not believe a better fitted configuration can be found for Lucan.
 Kepler curiously contradicts this statement in his second letter, p. xxx (116).
 The text of Ptolemy actually reads: [here follows a translation of the Greek; I have no Greek font] ³Of those in the claws of the Scorpion, the ones at their very extremities exercise the same influence as do Jupiter and Mercury; those in the middle parts the same as do Saturn and, to a less degree, Mars. Of the stars in the body of Scorpio, the bright stars on the forehead act in the same way as does Mars and in some degree as does Saturn.² (Robbinsı Loeb translation.)
 This passage is obscure enough that we can assume either Kepler or Caspar to have nodded.
 The confusion of Arrunsı auspices with Figulusı astrological prognostications causes both Herwart and Kepler trouble.
 This confusion caused by the two different calendars provides us with one of the fundamental problems for interpretation. See the introduction p. xxx.
 Kepler clearly erred here. His scheme shows Saturn where we would expect him, in Libra, not in Cancer. It is difficult to say what caused this mistake.
 The four anguli are the cusps of the first, seventh, fourth, and tenth houses and are sometimes called the cardinal points. They are respectively Ascendant, Descendant, Midheaven, and Imum Caeli, or East, West, North, and South. See Ptolemyıs Tetrabiblos I.10 for details on the influence of the angles.
 Vergil, Aeneid, 4.487-489. Keplerıs Vergil was very fresh in his mind since he had been teaching it due to the low enrollments of his Mathematics classes. See Casparıs biography, p. 60.
 This passage is corrupt in Schrankıs text and not sufficiently emended in Casparıs to make complete sense to me.