3. Irenaeus, Refutation of All Heresies, 1.2.1, 1.15.1, 3.4.1, 3.21.2, 4.134.16, 4.374.39, 4.37.1 (2nd cent. CE  3rd cent. CE)
 4.13. 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, 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 assume as secure the philosophy by numbers and elements. Now certain (speculators), appropriating similar reasonings from these, deceive unsophisticated individuals, alleging themselves endued with foresight; 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 school weak and full of knavery. 4.14. Those, then, who suppose that they prophesy by means of calculations and numbers, 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 easier 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, 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, 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 εννεαδς; 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 fortyfive, we find nine and nothing over  for nine times five are fortyfive, 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, 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. Is there, then, not any annexed, and (is there) not a proper name for Ulysses? 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 semivowels, and by themselves the mutes; and, having formed three orders, they take the roots by themselves of the vowels, and by themselves of the semivowels, 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. 4.15. 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 art 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 allwise 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 forehead 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 ideas and dispositions of men, assigning the reason of this to births (that have taken place) under particular stars; they thus express themselves: Those who are born under Aries will be of the following kind: long head, red hair, contracted eyebrows, pointed forehead, eyes grey and lively, drawn cheeks, longnosed, expanded nostrils, thin lips, tapering chin, wide mouth. These, he says, will partake of the following nature: cautious, subtle, perspicuous, prudent, indulgent, gentle, overanxious, 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, estranged from their own homes, giving dissatisfaction in everything, accusers, like madmen in their cups, scorners, year by year losing something serviceable in friendship through goodness; they, in the majority of cases, end their days in a foreign land. 4.16. Those, however, who are born in Taurus will be of the following description: round head, thick hair, broad forehead, square eyes, and large black eyebrows; in a white man, thin veins, sanguine, long eyelids, coarse huge ears, round mouths, thick nose, round nostrils, thick lips, strong in the upper parts, formed straight from the legs. The same are by nature pleasing, reflective, of a goodly disposition, devout, just, uncouth, complaisant, labourers from twelve years, quarrelsome, dull. The stomach of these is small, they are quickly filled, forming many designs, prudent, niggardly towards themselves, liberal towards others, beneficent, of a slow body: they are partly sorrowful, heedless as regards friendship, useful on account of mind, unfortunate. 4.37. And they make moon and stars appear on the ceiling after this manner. In the central part of the ceiling, having fastened a mirror, placing a dish full of water equally (with the mirror) in the central portion of the floor, and setting in a central place likewise a candle, emitting a faint light from a higher position than the dish  in this way, by reflection, (the magician) causes the moon to appear by the mirror. But frequently, also, they suspend on high from the ceiling, at a distance, a drum, but which, being covered with some garment, is concealed by the accomplice, in order that (the heavenly body) may not appear before the (proper) time. And afterwards placing a candle (within the drum), when the magician gives the signal to the accomplice, he removes so much of the covering as may be sufficient for effecting an imitation representing the figure of the moon as it is at that particular time. He smears, however, the luminous parts of the drum with cinnabar and gum; and having pared around the neck and bottom of a flagon of glass ready behind, he puts a candle in it, and places around it some of the requisite contrivances for making the figures shine, which some one of the accomplices has concealed on high; and on receiving the signal, he throws down from above the contrivances, so to make the moon appear descending from the sky. And the same result is achieved by means of a jar in sylvan localities. For it is by means of a jar that the tricks in a house are performed. For having set up an altar, subsequently is (placed upon it) the jar, having a lighted lamp; when, however, there are a greater number of lamps, no such sight is displayed. After then the enchanter invokes the moon, he orders all the lights to be extinguished, yet that one be left faintly burning; and then the light, that which streams from the jar, is reflected on the ceiling, and furnishes to those present a representation of the moon; the mouth of the jar being kept covered for the time which it would seem to require, in order that the representation of full moon should be exhibited on the ceiling. 4.38. But the scales of fishes  for instance, the seahorse  cause the stars to appear to be; the scales being steeped in a mixture of water and gum, and fastened on the ceiling at intervals. 4.39. The sensation of an earthquake they cause in such a way, as that all things seem set in motion; ordure of a weasel burned with a magnet upon coals (has this effect). 
