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Among them there is disagreement according to the tables. They speak of stars as being 'bodyguarded' when they are in the middle of other stars in a continuous succession of signs — for instance, if of the same sign one star occupies the first degrees and another the last, the one in the middle is said to be 'escorted' by those occupying the degrees on either side of it.
They are said to 'look upon' one another and to be looked upon by one another as visible things are. And forming configurations, those which have an interval of three signs between them behold one another in trine aspect, and those with two signs in square aspect. As the head suffers together with the parts subject to it, and the subject parts with the head, so too the things upon the earth suffer with the things above the moon. But there is some difference and lack of sympathy between these, inasmuch as they do not have one and the same union.
Making use of these things, Euphrates the Peratic and Acembes the Carystian and the rest of their chorus, naming them after the Word (Logos) of truth, speak of a standing and falling-away of aeons, of good powers turning to evil, and of concords of good with evil, calling them 'toparchs' and 'suburban' powers and a great many other names. I shall set forth and refute the whole of the sect they have undertaken to form, when we come to the discourse concerning these matters.
But now, lest anyone suppose that the things believed by the Chaldeans concerning astrological learning are trustworthy and sure, we shall not hesitate to set forth briefly a refutation directed against them, demonstrating that the art is vain and is able rather to lead astray and destroy a soul that hopes in vain things than to benefit it. In this we do not rely on experience of the art, but on the knowledge of practical reasoning.
Those who have practiced this learning, having become disciples of the Chaldeans, imparting mysteries as strange and marvelous to men, and altering the names, have from this constituted a sect. But since, supposing the art of the astrologers to be efficacious, and making use of the testimonies derived from them, they wish the things attempted through them to be believed, we shall now, as seemed good, demonstrate that astrology is untenable, being about hereafter to invalidate the Peratic sect also, as a branch that has grown from a root that is itself untenable.
The beginning, then, and as it were the foundation, is to establish the horoscope (the ascendant). For from this the rest of the centers are derived — the declining places and the succeeding places, the trines and squares, and the configurations of the stars themselves; and from all these come the predictions.
Hence, once the horoscope is removed, of necessity neither the mid-heaven, nor the setting point, nor the point opposite the mid-heaven is knowable; and when these cannot be apprehended, the whole Chaldean method vanishes along with them. That the ascending sign is undiscoverable by them can be shown in various ways.
For in order that this be apprehended, it is necessary, first, that the birth of the one falling under examination be firmly grasped; second, that the instrument that marks it, the horoscopic instrument, be free from error; and third, that the rising of the sign be observed with precision.
For at the moment of birth, let the rising of the sign ascending in heaven be observed; since the Chaldeans, having determined the ascendant, on the basis of its rising determine the configuration of the stars, which they so call, upon which they base their dogmatic predictions. But, as I shall show, it is possible neither to grasp the birth of those falling under examination, nor is the horoscopic instrument free from error, nor is the ascending sign apprehended with precision.
Let us now say, then, how the method of the Chaldeans is untenable. Having first determined to inquire into the birth of those who are to fall under examination, they reckon it either from the emission of the seed and conception, or from parturition.
And if one should attempt to reckon from conception, the precise account of this is ungraspable, being a rapid moment of time; and reasonably so, for we cannot say whether conception occurred at the same instant as the transmission of the seed, or not.
For it is possible for this to happen in an instant of thought, just as fat brought near to red-hot ovens sticks to them at once. But it is also possible for it to happen after an interval of time. For since there is a distance from the mouth of the womb to its innermost recess, where physicians say that conceptions take place, the nature of the deposited seed must of necessity traverse this distance in some period of time.
Being ignorant, then, of the precise quantity of this time, the Chaldeans will never grasp the moment of conception, since the seed sometimes travels straight and falls at once upon the parts of the womb naturally suited for conception, and sometimes is scattered widely, and is able to be gathered together into one place by the womb itself; and it remains unknown when the first case occurs and when the second, and how much time is spent for that kind of conception and how much for this — and from this, the precise apprehension of conception is also taken away.
That is, if, as some of the natural philosophers have said, the seed, first being concocted and undergoing a preliminary transformation in the womb, then approaches its opened-up vessels, just as seeds of the earth approach the earth. Hence those who do not know the quantity of the time of this transformation will not know the moment of conception either.
Furthermore, just as women differ from one another in the other parts of the body according to their activity and other causes, so too according to the activity of the womb, some conceive more quickly and others more slowly. And this is not surprising, since even the same woman, compared with herself, is at one time observed to conceive easily and at another time not at all. This being so, it is impossible to state with precision when the deposited seed is retained, so that from this moment the Chaldeans might establish the horoscope of the nativity.
By this reasoning it is impossible to establish the horoscope from conception. But neither is it possible from parturition. For, first, it is a matter of difficulty to determine when birth is to be reckoned as occurring — is it when the child that is being born begins to emerge into the outer air, or when it has entirely come forth, or when it is brought down to the ground? Nor is it possible, in any of these cases, to grasp the exact moment of birth, or to define the time.
For, on account of presence of mind, and fitness of body, and choice of position, and the skill of the midwife, and countless other circumstances, the time at which the child, once the membranes have broken, begins to emerge, or comes forth entirely, or is brought down to the ground, is not the same in every case, but differs from one instance to another.
This, again, the Chaldeans, being unable to measure precisely and definitely, will fail properly to define the hour of birth. That the Chaldeans profess to know the horoscope from the times of birth, but do not in fact know it, is evident from these considerations. That the horoscopic instrument itself is not free from error is also possible to reckon.
For when they say that the one attending the woman in labor, at the moment of birth, gives a signal by a gong to the Chaldean who is watching the stars from a mountain-top, and he, looking up at the sky, marks the ascending sign, let us first show them that, since the moment of birth is indeterminate, as we established a little earlier, it is not even easy to signal it by the gong.
Then, let it be granted that the moment of birth can be apprehended. Even so, it is not possible to mark it to an exact time; for it happens that the sound of the gong, being capable of division and of taking a considerable and appreciable amount of time to move up to the mountain-top.
A proof of this is observed in the case of those cutting down trees at a distance; for a considerable interval after the axe has come down, the sound of the blow is heard, as reaching the hearer only after a longer time. And for this reason, then, it is not possible for the Chaldeans to take with precision the time of the ascending sign that is truly rising as the horoscope.
And indeed, it will appear that not only does a considerable time elapse after the birth before the attendant of the woman in labor strikes the gong, and then further time before the man on the mountain-top hears the striking, but also, while he is looking about and observing in which of the signs the moon is, and in which each of the other stars is, it necessarily appears that the arrangement of the stars becomes altered, since the motion of the heavenly pole is carried along with indescribable speed, before he can carefully observe and note the hour of the one born as seen in the sky.
Thus the Chaldean art will be shown to be untenable. But if someone should say that the birth of the inquirer is examined by means of questioning, or concerning †...† questions, we reply that not even in this way can precision be attained. For if such great diligence is reported among them concerning the art, and yet they themselves cannot attain to precision, as we have shown, how can the layman have precisely apprehended the time of birth, so that the Chaldean, learning it from him, might truly establish the horoscope?
Moreover, according to the appearance of the horizon, the same star will not appear rising everywhere in the same way, but in one place what will be reckoned as the declining place will be taken as the horoscope, and in another place what will be reckoned as the horoscope will be the succeeding place, according to the surface of the various regions, whether lower or higher; so that in this respect too the prediction will not appear precise, since many people are born at the same hour throughout the whole world, and different observers see the stars differently.
Vain, too, is the apprehension supposed to be gained by means of water-clocks. For a jar pierced at the bottom will not flow in the same way when full as when nearly empty, even though, according to their own reasoning, the pole itself moves with a single, equally swift motion.
But if, changing their position, they should say that they do not take the exact time but only, as it happens, in a broad approximation, they will be refuted, one might almost say, by the very outcomes themselves. For those born at the same time have not lived the same life; but some, for instance, have become kings, while others have grown old in fetters.
At any rate, no one has become equal to Alexander the Macedonian, although many throughout the inhabited world were born at the same time as he; nor has anyone become equal to Plato the philosopher. So that the Chaldean will not be able to say precisely, on the basis of the broad interval of the nativity, whether the one born at the same time will be fortunate.
At any rate, many born at the same time have met with misfortune, so that the supposed similarity according to the configurations is also vain. Having thus refuted, in various and manifold ways, the futile-toiling speculation of the Chaldeans, we shall not omit this point either: that their predictions will end up in insoluble difficulty.
For if the one born under the arrow-point of the Archer must, as the astrologers say, be slain, how did so many myriads of barbarians, fighting against the Greeks at Marathon or Salamis, get slaughtered all at once? For surely the same horoscope did not hold for them all.
And again, if the one born under the water-jar of the Waterman is destined to be shipwrecked, how did the Greeks, sailing back from Troy, all together sink at the Hollows of Euboea? For it is not credible that all of them, differing from one another by a long span of time, were born under the water-jar of the Waterman.
For it is not possible to say that often, on account of one man for whom it is fated to perish at sea, all those in the ship perish together with him. For why should this man's fate prevail over the fates of all the others, rather than that, on account of the one man for whom it is fated to die on land, all should be saved together?
But since they also make an argument concerning the influence of the signs, to which they say the children born become similar, we shall not omit this either: for instance, they say that the one born under Leo will be courageous; but the one born under Virgo will have straight hair, be fair-skinned, childless, and modest.
These things, and things like them, deserve rather to be laughed at than taken seriously. For according to them, no Ethiopian is born under Virgo; but if he were, it would make such a one white, straight-haired, and so forth.
I think, rather, that the ancients affixed the names of the animals depicted to the stars merely for the sake of a name applied to them, and not because of any resemblance of nature. For what do the seven stars, standing apart from one another, have in common with a bear? Or the five stars of the dragon's head, as Aratus says: "But two are at the temples, two at the eyes, and one beneath holds the outermost edge of the terrible monster's jaw."
Thus these things too are shown, to those who have chosen to think rightly and who do not attend to the puffed-up pretensions of the Chaldeans, not to be worth so much effort — men who both bring kings to ruin by instilling cowardice in them, and embolden private persons to attempt great things.
But if he himself, running into misfortune, should fail, the one harmed does not become a teacher to everyone. And wishing to deceive the minds of these men, pushing their intellect into the infinite in the face of their failures, they say that the same configuration of the same stars cannot come about otherwise than through the restoration of the Great Year, which takes place over seven thousand seven hundred and seventy-seven years. How, then, could human observation ever manage to keep pace, over so many ages, in respect of a single nativity?
And this not once but many times [...]. I think it needed that the Chaldean art be refuted through a greater number of considerations, although we have mentioned it for the sake of other matters, not specifically for its own sake.
But since we have chosen to leave out none of the doctrines held among the nations, on account of the many-tongued cunning of the sects, let us see what those who have ventured to speak concerning magnitudes also say — men who, observing the futile labor of the majority, each of whom had been mistaken in a different way and yet had won esteem, dared to say something still greater, so that they might be esteemed all the more by those who had greatly esteemed even small falsehoods.
These men posit circles and measures, triangles and squares, double and triple ratios; but the discussion of this is extensive, and not necessary for our present purpose.
I consider it sufficient, then, to set forth what is fabulously reported by them. Wherefore, making use of summaries of what they themselves say, I shall turn to other matters. They say the following: the Craftsman (Demiurge) gave dominance to the revolution of the Same and the Like; for he left this one undivided, but the inner one he divided sixfold into seven unequal circles, according to the interval of the double and the triple in each case, there being three of each; and he ordered the circles to move in directions opposite to one another. Three of them move with like speed, but the other four move unlike one another and unlike the three, though carried in due proportion. Dominance, then, was given to the...
...the motion of the Same, he says — not only because it encompasses the motion of the Other, that is, the wandering stars (planets), but also because it possesses so much dominance, that is, so much power, that it carries around with itself even those moving in the opposite direction, the wandering stars that move from west to east, by its own...
...proper strength, likewise carrying them around together with itself from east to west as well. He says that this motion is left one and undivided, first of all, because the revolutions of all the fixed stars are of equal duration, and not divided into greater and lesser times; and secondly, because they all have one and the same surface, that of the outermost revolution, whereas the wandering stars (planets) are divided both into more numerous and differing times of motion, and into unequal distances from the earth.
He says that the motion of the Other has been divided sixfold into seven circles, and reasonably so; for however many cuts there are in each thing, the resulting divisions are always one more than the number of cuts. For instance, if something is divided by a single cut, there will be two divisions; if by two cuts, three divisions. Thus, if something is cut sixfold, there will be seven divisions.
He says that their distances have been set out alternately according to double and triple ratios, there being three of each, which he also showed in the composition of the Soul, based on the seven numbers.
For three of them are double from unity [the specific numerals are corrupt in the transmitted text], and three are [numerals corrupt in the text] stades, while the circumference of the earth is [a number, corrupt in the text] stades. And as for the distance from the surface of the earth to the circle of the moon: Aristarchus of Samos records it as [a number, corrupt in the text] stades; Apollonius records it as [a number, corrupt in the text] myriads of stades; and Archimedes records it as five hundred and fifty-four myriads of stades, and one hundred and thirty-odd units [the last digit uncertain in the text].
From the circle of the moon to the circle of the sun, [a number, corrupt in the text] myriads and 265 units of stades. From this to the circle of Venus, [a number, corrupt in the text] myriads and 265 units of stades. From this to the circle of Mercury, [a number, corrupt in the text] myriads and 7,165 units of stades. From this to the circle of the Fiery One (Mars), [a number, corrupt in the text] myriads, 554 [uncertain], and 454 units of stades. From this to the circle of Zeus (Jupiter), [a number, corrupt in the text] myriads, 27 [uncertain], and 565 units of stades. From this to the circle of Cronus (Saturn), [a number, corrupt in the text] myriads, 437 [uncertain] units of stades. From this to the zodiac and the outermost circumference, [a number, corrupt in the text] myriads, 8 [uncertain] units of stades.
The distances of the circles from one another, and the depths of the spheres, are given by Archimedes. He takes the circumference of the zodiac as [a number, corrupt in the text] of stades of the second order (that is, in myriads of myriads), so that the straight line from the center to the surface of the outermost earth turns out to be a sixth of the number stated, while the distance from the surface of the earth, on which we stand, to the zodiac — being the sixth part of the number just mentioned, less four myriads of stades — is that which remains from the center of the earth to its surface. He says the distance from the circle of Saturn to the earth is, in stades of the second order, two units, and [a number, corrupt in the text] myriads, and [a number, corrupt in the text] units. From the circle of Jupiter to the earth, [a number, corrupt in the text] units of the second order, and [a number, corrupt in the text] myriads, and [a number, corrupt in the text] units. From the circle of the Fiery One (Mars) to the earth, in numbers of the second order, one unit, and [a number, corrupt in the text] myriads, and [a number, corrupt in the text] units. From the sun to the earth, in numbers of the second order, one unit, and [a number, corrupt in the text] myriads, and [a number, corrupt in the text] units. From Mercury (Stilbon) to the earth, [a number, corrupt in the text] myriads and [a number, corrupt in the text] units. From Venus to the earth, [a number, corrupt in the text] myriads and [a number, corrupt in the text] units.
Concerning the moon it was spoken of before. The distances and depths of the spheres, then, are given by Archimedes in this way, but they have been stated otherwise concerning them by Hipparchus, and otherwise by Apollonius the mathematician. For us, following the Platonic opinion, it is sufficient to suppose that the distances of the wandering stars from one another are double and triple; for in this way the principle is preserved, that the universe is composed according to harmony, in concordant ratios, according to these distances.
But if the numbers set forth by Archimedes, and the ratios stated by the others concerning the distances, should not be in concordant ratios, that is, in the double and triple ratios stated by Plato, but should be found to lie outside such concordances, they would not preserve the principle that the universe has been constructed according to harmony.
For it is neither plausible nor possible that their distances should be irrational and outside of concordant and harmonious ratios — except, perhaps, in the case of the moon alone, concerning whose distance alone, derived from eclipses and the shadow of the earth, one might indeed trust Archimedes, that is, the distance of the moon from the earth. Once this figure has been taken, it will be easy, following the Platonic method, increasing it according to the double and triple ratio, as Plato requires, to comprehend the remaining distances also in number.
If, then, according to Archimedes, the moon is distant from the surface of the earth 5,540,000 and 130-odd stades [numeral partly corrupt in the text], it is easy, by increasing these numbers according to the double and triple ratio, to find the distances of the rest as well, taking as a single unit the number of stades by which the moon is distant from the earth. But that the remaining numbers, stated by Archimedes concerning the distance of the wandering stars, are not in concordant ratios, is easy to know by considering how they stand to one another and in what ratios they are. And that these, being parts of a universe constructed according to harmony, should not be in harmony, is impossible. Of the first number, then — that by which the moon is distant from the earth, being [a number, corrupt in the text] myriads and [a number, corrupt in the text] units — the second number, that by which the sun is distant from the moon, being [a number, corrupt in the text] myriads and 265 units, is in a ratio greater than ninefold. And compared to this, the number above it, being [a number, corrupt in the text] myriads and [a number, corrupt in the text] units, is in a ratio less than one-half. And compared to this, the number above it, being [a number, corrupt in the text] myriads and 7,165 units [corrupt], is in a ratio greater than double. And compared to this, the number above it, being [a number, corrupt in the text] myriads and [a number, corrupt in the text] units, will be in a ratio less than one and one-quarter. And compared to this, the number above it, being [a number, corrupt in the text] myriads and [a number, corrupt in the text] units, is in a ratio greater than one-half. And compared to this, the highest number, being [a number, corrupt in the text] myriads and 45-odd units [corrupt], is in a ratio less than double.
These ratios, then — greater than ninefold, and less than one-half, and greater than double, and less than one and one-quarter, and greater than one-half, and less than double — are all outside every concordance, from which no harmonious and concordant system could arise; whereas the whole universe and its parts are, in every respect alike, composed harmoniously and concordantly.
But the harmonious and concordant ratios are preserved, as we have said before, by the double and triple distances. If, then, we shall consider Archimedes trustworthy only in the first distance, that from the moon to the earth...
...then it is easy to find the rest also by increasing according to the double and triple ratio. Let, then, according to Archimedes, the distance from the earth to the moon be [a number, corrupt in the text] myriads and 130-odd units [corrupt] of stades; then the doubled number of stades by which the sun is distant from the moon will be [a number, corrupt in the text] myriads and 860-odd units [corrupt], and the sun will be distant from the earth [a number, corrupt in the text] myriads of stades; and Venus will be distant from the sun [a number, corrupt in the text] myriads and [a number, corrupt in the text] stades.
And from the earth, [Venus is distant] [a number, corrupt in the text] myriads of stades. Mercury is distant from Venus [a number, corrupt in the text] myriads and [a number, corrupt in the text] stades; and from the earth [a number, corrupt in the text] myriads, five hundred and forty-four [corrupt], and [a number, corrupt in the text] stades. Mars is distant from Mercury [a number, corrupt in the text] myriads, eighty-nine [corrupt], and 170-odd stades; and from the earth ten thousand myriads and 533-odd stades [corrupt].
...stades. Jupiter is distant from Mars 435-odd [corrupt] myriads and [a number, corrupt in the text] stades; and from the earth ten thousand myriads and [a number, corrupt in the text] stades. Saturn is distant from Jupiter ten thousand myriads and [a number, corrupt in the text] stades; and from the earth ten thousand myriads, nine hundred and thirty-eight [corrupt], and [a number, corrupt in the text] stades.
Who would not marvel at such great diligence, produced with such great labor? Indeed, this Ptolemy, the one concerned with these matters, does not seem to me useless. But this alone grieves me — that, having come into being only recently, he proved of no use to the sons of the Giants, who, being ignorant of these measurements, and supposing the heights of heaven to be near, attempted in vain to build a tower; whereas, if he had been present in that time and had related these measurements to them, they would not have made their vain attempt.
But if anyone claims to disbelieve this, let him make the measurement and be persuaded; for against unbelievers he has no clearer proof than this. O vain labor, O puffed-up soul, O unfaithful faith — all so that Ptolemy might by all means be reckoned wise among those who have practiced a like wisdom!
Some, having paused in part over these matters, judging them to be great and deeming them worthy of argument, have put together countless and boundless heresies. One of these is Colarbasus, who undertakes to expound [his system] by means of measures and numbers; and likewise others, whom we shall expose when we begin to speak concerning them, who attend to the Pythagorean calculus as though it were valid, and [pursue] the "secure" philosophy through numbers
and elements, rashly divining vain things; and certain persons, having gathered similar arguments from these, lead simple folk astray, claiming to be able to foreknow, sometimes hitting upon one true thing amid much divining, and while not ashamed at their many failures, boasting over the one success. Not even the unwise wisdom of these men will I pass over in silence, but having set forth those who from these attempt to establish piety toward the divine, I will refute them as disciples full of novelty, sprung from an unstable root
Those, then, who suppose they can divine by means of calculi and numbers, elements and names, make this the starting point of their undertaking of the doctrine according to them, asserting that there is a "foundation" (root-number) belonging to each of the numbers: in the case of the thousands, as many units as there are thousands — for example, the foundation of six thousand is six units, of seven thousand seven units, of eight thousand eight units, and likewise in the same manner for the rest;
and in the case of the hundreds, however many hundreds there are, that many units is their foundation — for example, seven hundred has seven hundreds, its foundation is seven units; six hundred has six hundreds, its foundation is [the text is corrupt: "three"] units. The same holds also for the tens: of eighty the units are eight, of sixty the units are six, of forty the units are four, of ten the unit is one
and in the case of the units, the units themselves are the foundation — for example, of nine [the foundation] is nine, of eight is eight, of seven is seven. So then one must do likewise also with the letters; for each letter is assigned according to some number — for example, [a letter] is of [the text is corrupt] units; the foundation of fifty units is five, and the foundation of the [corresponding] letter is likewise five
It is possible to obtain certain foundations from a name. For example, from the name "Agamemnon" there results: of [the first letter] one unit, of [the second] three units, of another [letter] one unit, of [another] four units, of [another, the text is corrupt] units, of [another] four units, of [another] five units, of [another, corrupt] units, of [another, corrupt] units; these added together amount to [corrupt], [corrupt, four], [corrupt, four], [corrupt, corrupt, corrupt] — these, put together, make thirty-six units
Again, they take the foundations of these [numbers], and there result: of the thirty, three; of the six, six itself. So the three and the six added together make nine, and the foundation of nine is nine. The name "Agamemnon," then, comes down to the foundation nine
Let one likewise do the same also for another name, "Hector." The name Hector has the letters [the text is corrupt], of these the foundations are [two, and others]; these added together make nineteen units. Again, the foundation of ten is one, of nine is nine, which added together make ten, and the foundation of ten becomes a unit. So the name Hector, when reckoned, produced the foundation of one unit
It is easier to do it this way: take the foundations found from the letters — as we just now found in the case of the name Hector, [nineteen] units — and divide it by nine, and call the remainder the foundation. For example, if I divide [that number] by nine, one unit remains, for nine times two is [eighteen], and one remains. For if I take away eighteen from nineteen, one remains;
so that the foundation of the name Hector will be a unit. Again, the foundations of the name Patroclus are these numbers: [the text is corrupt: seven, two, seven, two]; added together they make thirty-four units. Of these, the remainder is seven units — of the thirty, three, and of the four, the four itself. The foundation of the name Patroclus, then, is seven units
Those, then, who calculate according to the rule of nine take the ninth part of the number gathered from the foundations, and determine the remaining quantity as the foundation; but those who calculate according to the rule of seven take the seventh part. For example, in the case of the name Patroclus it was found that the sum of the foundations was thirty-four units; this, divided into sevens, makes four [sevens], that is [twenty-eight], with six units remaining; they say that the foundation of the name Patroclus is six according to the rule of seven
But if it should be [forty-two], the rule of seven gives forty-two: for seven times six is [forty-two], and nothing remains; the foundation, then, becomes a unit — this from [forty-three] according to the rule of seven. One must, however, take care in case the number taken divides evenly when apportioned — for example, if from some name, adding up the foundations, I find, say, thirty-six units; and thirty-six, divided by nine, comes out evenly to four nines — for nine times four is thirty-six, and nothing remains — in such a case it is clear that the foundation itself is nine