Chapter I.-System of the Astrologers; Sidereal Influence; Configuration of the Stars.
But in each zodiacal sign they call limits of the stars those in which each of the stars, from any one quarter to another, can exert the greatest amount of influence; in regard of which there is among them, according to their writings, no mere casual divergency of opinion. But they say that the stars are attended as if by satellites when they are in the midst of other stars, in continuity with the signs of the Zodiac; as if, when any particular star may have occupied the first portions of the same sign of the Zodiac, and another the last, and another those portions in the middle, that which is in the middle is said to be guarded by those holding the portions at the extremities. And they are said to look upon one another, and to be in conjunction with one another, as if appearing in a triangular or quadrangular figure. They assume, therefore, the figure of a triangle, and look upon one another, which have an intervening distancehyperlink extending for three zodiacal signs; and they assume the figure of a square those which have an interval extending for two signs. But as the underlying parts sympathize with the head, and the head with the underlying parts,hyperlink so also things terrestrial with superlunar objects.hyperlink But there is of these a certain difference and want of sympathy, so that they do not involve one and the same point of juncture.
Chapter II.-Doctrines Concerning Aeons; The Chaldean Astrology; Heresy Derivable from It.
Employing these (as analogies), Euphrates the Peratic, and Acembeshyperlink the Carystian, and the rest of the crowd of these (speculators), imposing names different from the doctrine of the truth, speak of a sedition of Aeons, and of a revolt of good powers over to evil (ones), and of the concord of good with wicked (Aeons), calling them Toparchai and Proastioi, and very many other names. But the entire of this heresy, as attempted by them, I shall explain and refute when we come to treat of the subject of these (Aeons). But now, lest any one suppose the opinions propounded by the Chaldeans respecting astrological doctrine to be trustworthy and secure, we shall not hesitate to furnish a brief refutation respecting these, establishing that the futile art is calculated both to deceive and blind the soul indulging in vain expectations, rather than to profit it. And we urge our case with these, not according to any experience of the art, but from knowledge based on practical principles. Those who have cultivated the art, becoming disciples of the Chaldeans, and communicating mysteries as if strange and astonishing to men, having changed the names (merely), have from this source concocted their heresy. But since, estimating the astrological art as a powerful one, and availing themselves of the testimonies adduced by its patrons, they wish to gain reliance for their own attempted conclusions, we shall at present, as it has seemed expedient, prove the astrological art to be untenable, as our intention next is to invalidate also the Peratic system, as a branch growing out of an unstable root.
Chapter III.-The Horoscope the Foundation of Astrology; Indiscoverability of the Horoscope; Therefore the Futility of the Chaldean Art.
The originating principle,hyperlink and, as it were, foundation, of the entire art, is fixinghyperlink the horoscope.hyperlink For from this are derived the rest of the cardinal points, as well as the declinations and ascensions, the triangles and squares, and the configurations of the stars in accordance with these; and from all these the predictions are taken. Whence, if the horoscope be removed, it necessarily follows that neither any celestial object is recognisable in the meridian, or at the horizon, or in the point of the heavens opposite the meridian; but if these be not comprehended, the entire system of the Chaldeans vanishes along with (them). But that the sign of the horoscope is indiscoverable by them, we may show by a variety of arguments. For in order that this (horoscope) may be found, it is first requisite that the (time of) birth of the person falling under inspection should be firmly fixed; and secondly, that the horoscope which is to signify this should be infallible; and thirdly, that the ascensionhyperlink of the zodiacal sign should be observed with accuracy. For fromhyperlink (the moment) of birthhyperlink the ascension of the zodiacal sign rising in the heaven should be closely watched,hyperlink since the Chaldeans, determining (from this) the horoscope, frame the configuration of the stars in accordance with the ascension (of the sign); and they, term this-disposition, in accordance with which they devise their predictions. But neither is it possible to take the birth of persons, falling under consideration, as I shall explain, nor is the horoscope infallible, nor is the rising zodiacal sign apprehended with accuracy.
How it is, then, that the system of the Chaldeanshyperlink is unstable, let us now declare. Having, then, previously marked it out for investigation, they draw the birth of persons falling under consideration from, unquestionably, the depositing of the seed, and (from) conception or from parturition. And if one will attempt to take (the horoscope) from conception, the accurate account of this is incomprehensible, the time (occupied) passing quickly, and naturally (so). For we are not able to say whether conception takes place upon the transferencehyperlink of the seed or not. For this can happen even as quick as thought, just also as leaven, when put into heated jars, immediately is reduced to a glutinous state. But conception can also (take place) after a lapse of duration. For there being an interval from the mouth of the womb to the fundament, where physicianshyperlink say conceptions take place, it is altogether the nature of the seed deposited to occupy some time in traversinghyperlink this interval. The Chaldeans, therefore, being ignorant of the quantity of duration to a nicety, never will comprehend the (moment of) conception; the seed at one time being injected straight forward, and falling at one spot upon actual parts of the womb well disposed for conception, and at another time dropping into it dispersedly, and being collected into one place by uterine energies. Now, while these matters are unknown, (namely), as to when the first takes place, and when the second, and how much time is spent in that particular conception, and how much in this; while, I say, ignorance on these points prevails on the part of these (astrologers), an accurate comprehension of conception is put out of the question.hyperlink And if, as some natural philosophers have asserted, the seed, remaining stationary first, and undergoing alteration in the womb, then enters the (womb's) opened blood-vessels, as the seeds of the earthhyperlink sink into the ground; from this it will follow, that those who are not acquainted with the quantity of time occupied by the change, will not be aware of the precise moment of conception either. And, moreover, as womenhyperlink differ from one another in the other parts of the body, both as regards energy and in other respects, so also (it is reasonable to suppose that they differ from one another) in respect of energy of womb, some conceiving quicker, and others slower. And this is not strange, since also women, when themselves compared with themselves, at times are observed having a strong disposition towards conception, but at times with no such tendency. And when this is so, it is impossible to say with accuracy when the deposited seed coalesces, in order that from this time the Chaldeans may fix the horoscope of the birth.
Chapter IV.-Impossibility of Fixing the Horoscope; Failure of an Attempt to Do This at the Period of Birth.
For this reason it is impossible to fix the horoscope from the (period of) conception. But neither can this be done from (that of) birth. For, in the first place, there exists the difficulty as to when it can be declared that there is a birth; whether it is when the foetus begins to incline towards the orifice,hyperlink or when it may project a little, or when it may be borne to the ground. Neither is it in each of these cases possible to comprehend the precise moment of parturition,hyperlink or to define the time. For also on account of disposition of soul, and on account of suitableness of body, and on account of choice of the parts, and on account of experience in the midwife, and other endless causes, the time is not the same at which the foetus inclines towards the orifice, when the membranes are ruptured, or when it projects a little, or is deposited on the ground; but the period is different in the case of different individuals. And when the Chaldeans are not able definitely and accurately to calculate this, they will fail, as they ought, to determine the period of emergence.
That, then, the Chaldeans profess to be acquainted with the horoscope at the periods of birth,hyperlink but in reality do not know it, is evident from these considerations. But that neither is their horoscope infallible, it is easy to conclude. For when they allege that the person sitting beside the woman in travail at the time of parturition gives, by striking a metallic rim, a sign to the Chaldean, who from an elevated place is contemplating the stars, and he, looking towards heaven, marks down the rising zodiacal sign; in the first place, we shall prove to them, that when parturition happens indefinitely, as we have shown a little before, neither is it easyhyperlink to signify this (birth) by striking the metallic rim. However, grant that the birth is comprehensible, yet neither is it possible to signify this at the exact time; for as the noise of the metallic plate is capable of being divided by a longer time and one protracted, in reference to perception, it happens that the sound is carried to the height (with proportionate delay). And the following proof may be observed in the case of those felling timber at a distance. For a sufficiently long time after the descent of the axe, the sound of the stroke is heard, so that it takes a longer time to reach the listener. And for this reason, therefore, it is not possible for the Chaldeans accurately to take the time of the rising zodiacal sign, and consequently the time when one can make the horoscope with truth. And not only does more time seem to elapse after parturition, when he who is sitting beside the woman in labour strikes the metallic plate, and next after the sound reaches the listener, that is, the person who has gone up to the elevated position; but also, while he is glancing around and looking to ascertain in which of the zodiacal signs is the moon, and in which appears each of the rest of the stars, it necessarily follows that there is a different position in regard of the stars, the motionhyperlink of the pole whiffing them on with incalculable velocity, before what is seen in the heavenshyperlink is carefully adjusted to the moment when the person is born.
Chapter V.-Another Method of Fixing the Horoscope at Birth; Equally Futile; Use of the Clepsydra in Astrology; The Predictions of the Chaldeans Not Verified.
In this way, the art practised by the Chaldeans will be shown to be unstable. Should any one, however, allege that, by questions put to him who inquires from the Chaldeans,hyperlink the birth can be ascertained, not even by this plan is it possible to arrive at the precise period. For if, supposing any such attention on their part in reference to their art to be on record, even these do not attain-as we have proved-unto accuracy either, how, we ask, can an unsophisticated individual comprehend precisely the time of parturition, in order that the Chaldean acquiring the requisite information from this person may sethyperlink the horoscope correctly? But neither from the appearance of the horizon will the rising star seem the same everywhere; but in one place its declination will be supposed to be the horoscope, and in another the ascension (will be thought) the horoscope, according as the places come into view, being either lower or higher. Wherefore, also, from this quarter an accurate prediction will not appear, since many may be born throughout the entire world at the same hour, each from a different direction observing the stars.
But the supposed comprehension (of the period of parturition) by means of clepsydrashyperlink is likewise futile. For the contents of the jar will not flow out in the same time when it is full as when it is half empty; yet, according to their own account, the pole itself by a single impulse is whiffed along at an equable velocity. If, however, evading the argument,hyperlink they should affirm that they do not take the time precisely, but as it happens in any particular latitude,hyperlink they will be refuted almost by the sidereal influences themselves. For those who have been born at the same time do not spend the same life, but some, for example, have been made kings, and others have grown old in fetters. There has been born none equal, at all events to Alexander the Macedonian, though many were brought forth along with him throughout the earth; (and) none equal to the philosopher Plato. Wherefore the Chaldean, examining the time of the birth in any particular latitude, will not be able to say accurately, whether a person born at this time will be prosperous. Many, I take it, born at this time, have been unfortunate, so that the similarity according to dispositions is futile.
Having, then, by different reasons and various methods, refuted the ineffectual mode of examination adopted by the Chaldeans, neither shall we omit this, namely, to show that their predictions will eventuate in inexplicable difficulties. For if, as the mathematicians assert, it is necessary that one born under the barb of Sagittarius' arrow should meet with a violent death, how was it that so many myriads of the Barbarians that fought with the Greeks at Marathon or Salamishyperlink were simultaneously slaughtered? For unquestionably there was not the same horoscope in the case, at all events, of them all. And again, it is said that one born under the urn of Aquarius will suffer shipwreck: (yet) how is it that so manyhyperlink of the Greeks that returned from Troy were overwhelmed in the deep around the indented shores of Euboea? For it is incredible that all, distant from one another by a long interval of duration, should have been born under the urn of Aquarius. For it is not reasonable to say, that frequently, for one whose fate it was to be destroyed in the sea, all who were with him in the same vessel should perish. For why should the doom of this man subdue the (destinies) of all? Nay, but why, on account of one for whom it was allotted to die on land, should not all be preserved?
Chapter VI.-Zodiacal Influence; Origin of Sidereal Names.
But since also they frame an account concerning the action of the zodiacal signs, to which they say the creatures that are procreated are assimilated,hyperlink neither shall we omit this: as, for instance, that one born in Leo will be brave; and that one born in Virgo will have long straight hair,hyperlink be of a fair complexion, childless, modest. These statements, however, and others similar to them, are rather deserving of laughter than serious consideration. For, according to them, it is possible for no Aethiopian to be born in Virgo; otherwise he would allow that such a one is white, with long straight hair and the rest. But I am rather of opinion,hyperlink that the ancients imposed the names of received animals upon certain specified stars, for the purpose of knowing them better, not from any similarity of nature; for what have the seven stars, distant one from another, in common with a bear, or the five stars with the head of a dragon?-in regard of which Aratushyperlink says:-
"But two his temples, and two his eyes, and one beneath
Reaches the end of the huge monster's law."
Chapter VII.-Practical Absurdity of the Chaldaic Art; Development of the Art.
In this manner also, that these points are not deserving so much labour, is evident to those who prefer to think correctly, and do not attend to the bombast of the Chaldeans, who consign monarchs to utter obscurity, by perfecting cowardicehyperlink in them, and rouse private individuals to dare great exploits. But if any one, surrendering himself to evil, is guilty of delinquency, he who has been thus deceived does not become a teacher to all whom the Chaldeans are disposed to mislead by their mistakes. (Far from it); (these astrologers) impel the minds (of their dupes, as they would have them), into endless perturbation, (when) they affirm that a configuration of the same stars could not return to a similar position, otherwise than by the renewal of the Great Year, through a space of seven thousand seven hundred and seventy and seven years.hyperlink How then, I ask, will human observation for one birth be able to harmonize with so many ages; and this not once, (but oftentimes, when a destruction of the world, as some have stated, would intercept the progress of this Great Year; or a terrestrial convulsion, though partial, would utterly break the continuity of the historical tradition)?hyperlink The Chaldaic art must necessarily be refuted by a greater number of arguments, although we have been reminding (our readers) of it on account of other circumstances, not peculiarly on account of the art itself.
Since, however, we have determined to omit none of the opinions advanced by Gentile philosophers, on account of the notorious knavery of the heretics, let us see what they also say who have attempted to propound doctrines concerning magnitudes,-who, observing the fruitless labour of the majority (of speculators), where each after a different fashion coined his own falsehoods and attained celebrity, have ventured to make some greater assertion, in order that they might be highly magnified by those who mightily extol their contemptible lies. These suppose the existence of circles, and measures, and triangles, and squares, both in twofold and threefold array. Their argumentation, however, in regard of this matter, is extensive, yet it is not necessary in reference to the subject which we have taken in hand.
Chapter VIII.-Prodigies of the Astrologers; System of the Astronomers; Chaldean Doctrine of Circles; Distances of the Heavenly Bodies.
I reckon it then sufficient to declare the prodigieshyperlink detailed by these men. Wherefore, employing condensed accounts of what they affirm, I shall turn my attention to the other points (that remain to be considered). Now they make the following statements.hyperlink The Creator communicated pre-eminent power to the orbital motion of the identical and similar (circle), for He permitted the revolution of it to be one and indivisible; but after dividing this internally into six parts, (and thus having formed) seven unequal circles, according to each interval of a twofold and threefold dimension, He commanded, since there were three of each, that the circles should travel in orbits contrary to one another, three indeed (out of the aggregate of seven) being whirled along with equal velocity, and four of them with a speed dissimilar to each other and to the remaining three, yet (all) according to a definite principle. For he affirms that the mastery was communicated to the orbital motion of the same (circle), not only since it embraces the motion of the other, that, is, the erratic stars, but because also it possesses so great mastery, that is, so great power, that even it leads round, along with itself, by a peculiar strength of its own, those heavenly bodies-that is, the erratic stars-that are whirled along in contrary directions from west to east, and, in like manner, from east to west.
And he asserts that this motion was allowed to be one and indivisible, in the first place, inasmuch as the revolutions of all the fixed stars were accomplished in equal periods of time, and were not distinguished according to greater or less portions of duration. In the next place, they all present the same phase as that which belongs to the outermost motion; whereas the erratic stars have been distributed into greater and varying periods for the accomplishment of their movements, and into unequal distances from earth. And he asserts that the motion in six parts of the other has been distributed probably into seven circles. For as many as are sections of each (circle)-I allude to monads of the sectionshyperlink -become segments; for example, if the division be by one section, there will be two segments; if by two, three segments; and so, if anything be cut into six parts, there will be seven segments. And he says that the distances of these are alternately arranged both in double and triple order, there being three of each,-a principle which, he has attempted to prove, holds good of the composition of the soul likewise, as depending upon the seven numbers. For among them there are from the monad three double (numbers), viz., 2, 4, 8, and three triple ones, viz., 3, 9, 27. But the diameter of Earth is 80, 108 stadii; and the perimeter of Earth, 250, 543 stadii; and the distance also from the surface of the Earth to the lunar circle, Aristarchus the Samian computes at 8, 000, 178 stadii, but Apollonius 5, 000, 000, whereas Archimedes computeshyperlink it at 5, 544, 1300. And from the lunar to solar circle, (according to the last authority,) are 50, 262, 065 stadii; and from this to the circle of Venus, 20, 272, 065 stadii; and from this to the circle of Mercury, 50, 817, 165 stadii; and from this to the circle of Mars, 40, 541, 108 stadii; and from this to the circle of Jupiter, 20, 275, 065 stadii; and from this to the circle of Saturn, 40, 372, 065 stadii; and from this to the Zodiac and the furthest periphery, 20, 082, 005 stadii.hyperlink
Chapter IX.-Further Astronomic Calculations.
The mutual distances of the circles and spheres, and the depths, are rendered by Archimedes. He takes the perimeter of the Zodiac at 447, 310, 000 stadii; so that it follows that a straight line from the centre of the Earth to the most outward superficies would be the sixth of the aforesaid number, but that the line from the surface of the Earth on which we tread to the Zodiac would be a sixth of the aforesaid number, less by four myriads of stadii, which is the distance from the centre of the Earth to its surface. And from the circle of Saturn to the Earth he says the distance is 2, 226, 912, 711 stadii; and from the circle of Jupiter to Earth, 502, 770, 646 stadii; and from the circle of Mars to Earth, 132, 418, 581. From the Sun to Earth, 121, 604, 454; and from Mercury to the Earth, 526, 882, 259; and from Venus to Earth, 50, 815, 160.
Chapter X.-Theory of Stellar Motion and Distance in Accordance with Harmony.
Concerning the Moon, however, a statement has been previously made. The distances and profundities of the spheres Archimedes thus renders; but a different declaration regarding them has been made by Hipparchus; and a different one still by Apollonius the mathematician. It is sufficient, however, for us, following the Platonic opinion, to suppose twofold and threefold distances from one another of the erratic stars; for the doctrine is thus preserved of the composition of the universe out of harmony, on concordant principleshyperlink in keeping with these distances. The numbers, however, advanced by Archimedes,hyperlink and the accounts rendered by the rest concerning the distances, if they be not on principles of symphony,-that is, the double and triple (distances) spoken of by Plato,-but are discovered independent of harmonies, would not preserve the doctrine of the formation of the universe according to harmony. For it is neither credible nor possible that the distances of these should be both contrary to some reasonable plan, and independent of harmonious and proportional principles, except perhaps only the Moon, on account of wanings and the shadow of the Earth, in regard also of the distance of which alone-that is, the lunar (planet) from earth-one may trust Archimedes. It will, however, be easy for those who, according to the Platonic dogma itself, adopt this distance to comprehend by numerical calculation (intervals) according to what is double and triple, as Plato requires, and the rest of the distances. If, then, according to Archimedes, the Moon is distant from the surface of the Earth 5, 544, 130 stadii, by increasing these numbers double and triple, (it will be) easy to find also the distances of the rest, as if subtracting one part of the number of stadii which the Moon is distant from the Earth.
But because the rest of the numbers-those alleged by Archimedes concerning the distance of the erratic stars-are not based on principles of concord, it is easy to understand-that is, for those who attend to the matter-how the numbers are mutually related, and on what principles they depend. That, however, they should not be in harmony and symphony-I mean those that are parts of the world which consists according to harmony-this is impossible. Since, therefore, the first number which the Moon is distant from the earth is 5, 544, 130, the second number which the Sun is distant from the Moon being 50, 272, 065, subsists by a greater computation than ninefold. But the higher number in reference to this, being 20, 272, 065, is (comprised) in a greater computation than half. The number, however, superior to this, which is 50, 817, 165, is contained in a greater computation than half. But the number superior to this, which is 40, 541, 108, is contained in a less computation than two-fifths. But the number superior to this, which is 20, 275, 065, is contained in a greater computation than half. The final number, however, which is 40, 372, 065, is comprised in a less computation than double.
Chapter XI.-Theory of the Size of the Heavenly Bodies in Accordance with Numerical Harmonies.
These (numerical) relations, therefore, the greater than ninefold, and less than half, and greater than double, and less than two-fifths, and greater than half, and less than double, are beyond all symphonies, from which not any proportionate or harmonic system could be produced. But the whole world, and the parts of it, are in all respects similarly framed in conformity with proportion and harmony. The proportionate and harmonic relations, however, are preserved-as we have previously stated-by double and triple intervals. If, therefore, we consider Archimedes reliable in the case of only the first distance, that from the Moon to the Earth, it is easy also to find the rest (of the intervals), by multiplying (them) by double and treble. Let then the distance, according to Archimedes, from Earth to Moon be 5, 544, 130 stadii; there will therefore be the double number of this of stadiiwhich the Sun is distant from the Moon, viz. 11, 088, 260. But the Sun is distant from the Earth 16, 632, 390 stadii; and Venus is likewise distant from the Sun 16, 632, 390 stadii, but from the Earth 33, 264, 780 stadii; and Mercury is distant from Venus 22, 176, 520 stadii, but from Earth 55, 441, 300 stadii; and Mars is distant from Mercury 49, 897, 170 stadii, and from Earth 105, 338, 470 stadii; and Jupiter is distant from Mars 44, 353, 040 stadii, but from Earth 149, 691, 510 stadii; Saturn is distant from Jupiter 149, 691, 510 stadii, but from Earth 299, 383, 020 stadii.
Chapter XII.-Waste of Mental Energy in the Systems of the Astrologers.
Who will not feel astonishment at the exertion of so much deep thought with so much toil? This Ptolemy, however-a careful investigator of these matters-does not seem to me to be useless; but only this grieves (one), that being recently born, he could not be of service to the sons of the giants, who, being ignorant of these measures, and supposing that the heights of heaven were near, endeavoured in vain to construct a tower. And so, if at that time he were present to explain to them these measures, they would not have made the daring attempt ineffectually. But if any one profess not to have confidence in this (astronomer's calculations), let him by measuring be persuaded (of their accuracy); for in reference to those incredulous on the point, one cannot have a more manifest proof than this. O, pride of vain-toiling soul, and incredible belief, that Ptolemy should be considered pre-eminently wise among those who have cultivated similar wisdom!
Chapter XIII.-Mention of the Heretic Colarbasus; Alliance Between Heresy and the Pythagorean Philosophy.
Certain, adhering partly to these, as if having propounded great conclusions, and supposed things worthy of reason, have framed enormous and endless heresies; and one of these is Colarbasus,hyperlink who attempts to explain religion by measures and numbers. And others there are (who act) in like manner, whose tenets we shall explain when we commence to speak of what concerns those who give heed to Pythagorean calculation as possible; and uttering vain prophecies, hastily assumehyperlink as secure the philosophy by numbers and elements. Now certain (speculators), appropriatinghyperlink similar reasonings from these, deceive unsophisticated individuals, alleging themselves endued with foresight;hyperlink sometimes, after uttering many predictions, happening on a single fulfilment, and not abashed by many failures, but making their boast in this one. Neither shall I pass over the witless philosophy of these men; but, after explaining it, I shall prove that those who attempt to form a system of religion out of these (aforesaid elements), are disciples of a schoolhyperlink weak and full of knavery.
Chapter XIV.-System of the Arithmeticians; Predictions Through Calculations; Numerical Roots; Transference of These Doctrines to Letters; Examples in Particular Names; Different Methods of Calculation; Prescience Possible by These.
Those, then, who suppose that they prophesy by means of calculations and numbers,hyperlink and elements and names, constitute the origin of their attempted system to be as follows. They affirm that there is a root of each of the numbers; in the case of thousands, so many monads as there are thousands: for example, the root of six thousand, six monads; of seven thousand, seven monads; of eight thousand, eight monads; and in the case of the rest, in like manner, according to the same (proportion). And in the case of hundreds, as many hundreds as there are, so many monads are the root of them: for instance, of seven hundred there are seven hundreds; the root of these is seven monads: of six hundred, six hundreds; the root of these, six monads. And it is similar respecting decades: for of eighty (the root is) eight monads; and of sixty, six monads; of forty, four monads; of ten, one monad. And in the case of monads, the monads themselves are a root: for instance, of nine, nine; of eight, eight; of seven, seven. In this way, also, ought we therefore to act in the case of the elements (of words), for each letter has been arranged according to a certain number: for instance, the letter n according to fifty monads; but of fifty monads five is the root, and the root of the letter n is (therefore) five. Grant that from some name we take certain roots of it. For instance, (from) the name Agamemnon, there is of the a, one monad; and of the g, three monads; and of the other a, one monad; of the m, four monads; of the e, five monads; of the m, four monads; of the n, five monads; of the (long) o, eight monads; of the n, five monads; which, brought together into one series, will be 1, 3, 1, 4, 5, 4, 5, 8, 5; and these added together make up 36 monads. Again, they take the roots of these, and they become three in the case of the number thirty, but actually six in the case of the number six. The three and the six, then, added together, constitute nine; but the root of nine is nine: therefore the name Agamemnon terminates in the root nine.
Let us do the same with another name-Hector. The name (H)ector has five letters-e, and k, and t, and o, and r. The roots of these are 5, 2, 3, 8, 1; and these added together make up 19 monads. Again, of the ten the root is one; and of the nine, nine; which added together make up ten: the root of ten is a monad. The name Hector, therefore, when made the subject of computation, has formed a root, namely a monad. It would, however, be easierhyperlink to conduct the calculation thus: Divide the ascertained roots from the letters-as now in the case of the name Hector we have found nineteen monads-into nine, and treat what remains over as roots. For example, if I divide 19 into 9, the remainder is 1, for 9 times 2 are 18, and there is a remaining monad: for if I subtract 18 from 19, there is a remaining monad; so that the root of the name Hector will be a monad. Again, of the name Patroclus these numbers are roots: 8, 1, 3, 1, 7, 2, 3, 7, 2; added together, they make up 34 monads. And of these the remainder is 7 monads: of the 30, 3; and of the 4, 4. Seven monads, therefore, are the root of the name Patroclus.
Those, then, that conduct their calculations according to the rule of the number nine,hyperlink take the ninth part of the aggregate number of roots, and define what is left over as the sum of the roots. They, on the other hand, (who conduct their calculations) according to the rule of the number seven, take the seventh (part of the aggregate number of roots); for example, in the case of the name Patroclus, the aggregate in the matter of roots is 34 monads. This divided into seven parts makes four, which (multiplied into each other) are 28. There are six remaining monads; (so that a person using this method) says, according to the rule of the number seven, that six monads are the root of the name Patroclus. If, however, it be 43, (six) taken seven times,hyperlink he says, are 42, for seven times six are 42, and one is the remainder. A monad, therefore, is the root of the number 43, according to the rule of the number seven. But one ought to observe if the assumed number, when divided, has no remainder; for example, if from any name, after having added together the roots, I find, to give an instance, 36 monads. But the number 36 divided into nine makes exactly 4 enneadj; for nine times 4 are 36, and nothing is over. It is evident, then, that the actual root is 9. And again, dividing the number forty-five, we find ninehyperlink and nothing over-for nine times five are forty-five, and nothing remains; (wherefore) in the case of such they assert the root itself to be nine. And as regards the number seven, the case is similar: if, for example we divide 28 into 7, we have nothing over; for seven times four are 28, and nothing remains; (wherefore) they say that seven is the root. But when one computes names, and finds the same letter occurring twice, he calculates it once; for instance, the name Patroclus has the pa twice,hyperlink and the o twice: they therefore calculate the a once and the o once. According to this, then, the roots will be 8, 1, 3, 1, 7, 2, 3, 2, and added together they make 27 monads; and the root of the name will be, according to the rule of the number nine, nine itself, but according to the rule of the number seven, six.
In like manner, (the name) Sarpedon, when made the subject of calculation, produces as a root, according to the rule of the number nine, two monads. Patroclus, however, produces nine monads; Patroclus gains the victory. For when one number is uneven, but the other even, the uneven number, if it is larger, prevails. But again, when there is an even number, eight, and five an uneven number, the eight prevails, for it is larger. If, however, there were two numbers, for example, both of them even, or both of them odd, the smaller prevails. But how does (the name) Sarpedon, according to the rule of the number nine, make two monads, since the letter (long) o is omitted? For when there may be in a name the letter (long) o and (long) e, they leave out the (long) o, using one letter, because they say both are equipollent; and the same must not be computed twice over, as has been above declared. Again, (the name) Ajax makes four monads; (but the name) Hector, according to the rule of the ninth number, makes one monad. And the tetrad is even, whereas the monad odd. And in the case of such, we say, the greater prevails-Ajax gains the victory. Again, Alexander and Menelaus (may be adduced as examples). Alexander has a proper name (Paris). But Paris, according to the rule of the number nine, makes four monads; and Menelaus, according to the rule of the number nine, makes nine monads. The nine, however, conquer the four (monads): for it has been declared, when the one number is odd and the other even, the greater prevails; but when both are even or both odd, the less (prevails). Again, Amycus and Polydeuces (may be adduced as examples). Amycus, according to the rule of the number nine, makes two monads, and Polydeuces, however, seven: Polydeuces gains the victory. Ajax and Ulysses contended at the funeral games. Ajax, according to the rule of the number nine, makes four monads; Ulysses, according to the rule of the number nine, (makes) eight.hyperlink Is there, then, not any annexed, and (is there) not a proper name for Ulysses?hyperlink for he has gained the victory. According to the numbers, no doubt, Ajax is victorious, but history hands down the name of Ulysses as the conqueror, Achilles and Hector (may be adduced as examples). Achilles, according to the rule of the number nine, makes four monads; Hector one: Achilles gains the victory. Again, Achilles and Asteropaeus (are instances). Achilles makes four monads, Asteropaeus three: Achilles conquers. Again, Menelaus and Euphorbus (may be adduced as examples). Menelaus has nine monads, Euphorbus eight: Menelaus gains the victory.
Some, however, according to the rule of the number seven, employ the vowels only, but others distinguish by themselves the vowels, and by themselves the semi-vowels, and by themselves the mutes; and, having formed three orders, they take the roots by themselves of the vowels, and by themselves of the semi-vowels, and by themselves of the mutes, and they compare each apart. Others, however, do not employ even these customary numbers, but different ones: for instance, as an example, they no not wish to allow that the letter p has as a root 8 monads, but 5, and that the (letter) x (si) has as a root four monads; and turning in every direction, they discover nothing sound. When, however, they contend about the second (letter), from each name they take away the first letter; but when they contend about the third (letter), they take away two letters of each name, and calculating the rest, compare them.
Chapter XV.-Quibbles of the Numerical Theorists; The Art of the Frontispicists (Physiognomy); Connection of This Art with Astrology; Type of Those Born Under Aries.
I think that there has been clearly expounded the mind of arithmeticians, who, by means of numbers and of names, suppose that they interpret life. Now I perceive that these, enjoying leisure, and being trained in calculation, have been desirous that, through the arthyperlink delivered to them from childhood, they, acquiring celebrity, should be styled prophets. And they, measuring the letters up (and) down, have wandered into trifling. For if they fail, they say, in putting forward the difficulty, Perhaps this name was not a family one, but imposed, as also lighting in the instance they argue in the case of (the names) Ulysses and Ajax. Who, taking occasion from this astonishing philosophy, and desirous of being styled "Heresiarch," will not be extolled?
But since, also, there is another more profound art among the all-wise speculators of the Greeks-to whom heretical individuals boast that they attach themselves as disciples, on account of their employing the opinions of these (ancient philosophers) in reference to the doctrines tempted (to be established) by themselves, as shall a little afterwards be proved; but this is an art of divination, by examination of the foreheadhyperlink or rather, I should say, it is madness: yet we shall not be silent as regards this (system) There are some who ascribe to the stars figures that mould the ideashyperlink and dispositions of men, assigning the reason of this to births (that have taken place) under particular stars; they thus express themselves: Those whohyperlink are born under Aries will be of the following kind: long head, red hair, contracted eyebrows, pointed forehead, eyes grey and lively,hyperlink drawn cheeks, long-nosed, expanded nostrils, thin lips, tapering chin, wide mouth. These, he says, will partake of the following nature: cautious, subtle, perspicuous,hyperlink prudent, indulgent, gentle, over-anxious, persons of secret resolves fitted for every undertaking, prevailing more by prudence than strength, deriders for the time being, scholars, trustworthy, contentious, quarrellers in a fray, concupiscent, inflamed with unnatural lust, reflective, estrangedhyperlink from their own homes, giving dissatisfaction in everything, accusers, like madmen in their cups, scorners, year by year losing somethinghyperlink serviceable in friendship through goodness; they, in the majority of cases, end their days in a foreign land.
Footnotes
1 Or, "interval."
2 Hippolytus gives the substance of Sextus Empiricus' remarks, omitting, however, a portion of the passage followed. (See Sextus Empiricus' Mathem., v. 44.)
3 Or, "celestial."
4 Or, "Celbes," or "Ademes." The first is the form of the name employed in book v. c, viii.; the second in book x. c. vi.
5 This passage occurs in Sextus Empiricus.
6 Or, "the knowledge of."
7 Horoscope (from wpa skopoj) is the act of observing the aspect of the heavens at the moment of any particular birth. Hereby the astrologer alleged his ability of foretelling the future career of the person so born. The most important part of the sky for the astrologer's consideration was that sign of the Zodiac which rose above the horizon at the moment of parturition. This was the "horoscope ascendant," or "first house." The circuit of the heavens was divided into twelve "houses," or zodiacal signs.
8 Or, "difference."
9 Or," during."
10 apotecewj; some would read apotacewj.
11 The passage is given more explicitly in Sextus Empiricus. (See Adversus Astrol., v. 53.)
12 Sextus uses almost these words.
13 Or "lodgment" (Sextus), or "deposition."
14 Or, "attendants of physicians."
15 Or, "make."
16 Or, "vanishes."
17 Not in Sextus Empiricus.
18 The passage is more clearly given in Sextus.
19 Or, "the cold atmosphere."
20 Or, "manifestation."
21 Or, "manifestation."
22 Or, "reasonable."
23 Or, "but the motion... is whirled on with velocity."
24 This rendering of the passage may be deduced from Sextus Empiricus.
25 The text is corrupt, but the above seems probably the meaning, and agrees with the rendering of Schneidewin and Cruice.
26 Or, "view."
27 The clepsydra, an instrument for measuring duration, was, with the sun-dial, invented by the Egyptians under the Ptolemies. It was employed not only for the measurernent of time, but for making astronomic calculations. Water, as the name imports, was the fluid employed, though mercury has been likewise used. The inherent defect of an instrument of this description is mentioned by Hippolytus.
28 Literally, "twisting, tergiversating."
29 This seems the meaning, as deducible from a comparison of Hippolytus with the corresponding passage in Sextus Empiricus.
30 Omitted by Sextus.
31 The Abbe Cruice observes, in regard of some verbal difference here in the text from that of Sextus, that the MS. of The Refutationwas probably executed by one who heard the extracts from other writers read to him, and frequently mistook the sound. The transcriber of the MS. was one Michael, as we learn from a marginal note at the end.
32 This was the great doctrine of astrology, the forerunner of the science of astronomy. Astrology seems to have arisen first among the Chaldeans, out of the fundamental principle of their religion -the assimilation of the divine nature to light. This tenet introduced another, the worship of the stars, which was developed into astrology. Others suppose astrology to have been of Arabian or Egyptian origin. From some of these sources it reached the Greeks, and through them the Romans, who held the astrologic art in high repute. The art, after having become almost extinct, was revived by the Arabians at the verve of the middle ages. For the history of astrology one must consult the writings of Manilius, Julius Firmicus, and Ptolemy. Its greatest medieval apologist is Cardan, the famous physician of Paris (see his work, De Astron. Judic., lib. vi.-ix. tom. v. of his collected works).
33 Sextus adds, "bright-eyed."
34 Hippolytus here follows Sextus.
35 Aratus, from whom Hippolytus quotes so frequently in this chapter, was a poet and astronomer of antiquity, born at Soli in Cilicia. He afterwards became physician to Gonatus, son of Demetrius Poliorcetes, king of Macedon, at whose court he rose high into favour. The work alluded to by Hippolytus is Aratus' Phaenomena,-a versified account of the motions of the stars, and of sidereal influence over men. This work seems to have been a great favourite with scholars, if we are to judge from the many excellent annotated editions of it that have appeared. Two of these deserve notice, viz., Grotius' Leyden edition, 1600, in Greek and Latin; and Buhle's edition, Leipsic, 1803. See also Dionysius Petavius' Uranoiogion. Arbutus must always be famous, from the fact that St. Paul (Acts xiii. 28) quotes the fifth line of the Phaenomena. Cicero considered Aratus a noble poet, and translated the Phaenimena into Latin, a fragment of which has been preserved, and is in Grotius' edition. Aratus has been translated into English verse, with notes by Dr. Lamb, Dean of Bristol (London: J. W. Parker, 1858).
36 The Abbe Cruice suggests "freedom from danger," instead of "cowardice," and translates thus: "whereby kings are slain, by having impunity promised in the predictions of these seers."
37 Sextus makes the number "nine thousand nine hundred and seventy and seven years."
38 The parenthetical words are taken from Sextus Empiricus, as introduced into his text by the Abbe Cruice. Schneidewin alludes to the passage in Sextus as proof of some confusion in Hippolytus' text, which he thinks is signified by the transcriber in the words, "I think there is some deficiency or omissions," which occur in the MS. of The Refutation.
39 As regards astological predictions, see Origen's Comment. on Gen.; Diodorus of Tarsus, De Fato; Photii Biblioth., cod, ccxxiii.; and Bardesanis, De Legibus Nationum, in Cureton's Spicilegium Syriacum.
40 See Plato's Timaeus.
41 Schneidewin, on Roeper's suggestion, amends the passage thus, though I am not sure that I exactly render his almost unintelligible Latin version: "For as many sections as there are of eacb, there are educible from the monad more segments than sections; for example, if," etc. The Abbe Cruice would seemingly adopt the following version: "For whatsoever are sections of each, now there are more segments than sections of a monad, will become; for example, if," etc.
42 Schneidewin, on mathematical authority, discredits the numerical calculations ascribed to Archimedes.
43 This is manifestly erroneous; the total could only be "four myriads!"
44 The Abbe Cruice thinks that the word should be "tones," supporting his emendation on the authority of Pliny, who states that Pythagoras called the distance of the Moon from the Earth a tone, deriving the term from musical science (see Pliny's Hist. Nat., ii. 20).
45 These numerical speculations are treated of by Archimedes in his work On the Number of the Sand, in which he maintains the possibility of counting the sands, even on the supposition of the world's being much larger than it is (see Archimedes, ta mexri nun swzomena apanta, Treatise yammithj, p. 120, ed. Eustoc. Ascalon., Basil, 1544).
46 Colarbasus is afterwards mentioned in company with Marcus the heretic, at the beginning and end of book vi of The Refutation.
47 This word ( sleoiazousi), more than once used by Hippolytus, is applied to anything done offhand, e.g., an extempore speech. It therefore might be made to designate immaturity of opinion. Sxediameans something hastily put together, viz., a raft; sxeoioj, sudden.
48 Schneidewin suggests omwj instead of oimoiwj. The word ( ehanisamenoi) translated "appropriating" is derived from eranoj, which signifies a meal to which those who partake of it have each contributed some dish (pic-nic). The term, therefore, is an expressive one for Hippolytus' purpose.
49 proynwstikouj. Some would read proj ynwstkouj.
50 Some propose dochj. "opinion." Hippolytus, however, used the word oizhj (translated "school") in a similar way at the end of chap. i. of book iv. "Novelty" is read instead of "knavery;" and for anapleou, "full," is proposed (1) anapleontaj, (a) anapterountaj.
51 The subject of the numerical system employed by the Gnostics, and their occult mysteries, is treated of by the learned Kircher, Aedipi Aegypt.., tom. ii. part i, de Cabala Hebraeorum; also in his Arithmolog. in the book De Arithmomantiaa Gnosticor., cap. viii., de Cabala Pythagorea. See also Mersennes, Comment. on Genes.
52 This subject is examined by Cornelius Agrippa in his celebrated work, De vanitate et incertitudine Scientiarum, chap. xi., De Sorte Pythagoriea. Terentiuc Maurus has also a versified work on Letters and Syllables and Metres, in which he alludes to similar interpretations educible from the names Hector and Patroclus.
53 - That is, the division by nine.
54 That is, calculated according to the rule of a division by seven.
55 We should expect rather five instead of 9, if the division be by nine.
56 There is some confusion in the text. Miller conjectures that the reading should be: "As, for instance, the name Patroclus has the letter o occurring twice in it, they therefore take it into calculation once." Schneidewin suggests that the form of the name may be Papatroclus.
57 Miller says there is an error in the calculation here.
58 This is as near the sense of the passage as a translation in some respects conjectural can make it.
59 The word qelein occurs in this sentence, but is obviously superfluous.
60 In the margin of the Ms. is the note, "Opinion of the Metopiscopists."
61 These words are out of place. See next note.
62 There is evidently some displacement of words here. Miller and Schneidewin suggest: "There are some who ascribe to the influence of the stars the natures of men: since, in computing the births of individuals, they thus express themselves as if they were moulding the species of men." The Abbe Cruice would leave the text as it is, altering only tupountej ideaj into tupwn te ideaj.
63 Literally, "jumping; " others read "blackish," or "expressive" (literally, "talking"). The vulgar reading, upo alloij, is evidently untenable.
64 Or "cowardly," or "cowards at heart;" or some read, laropoioi, i.e., "causative of gl"
65 Or, "diseased with unnatural lust," i.e., nosountej for noountej.
