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,178    The subject of the numerical system employed by the Gnostics, and their occult mysteries, is treated of by the learned Kircher, Œdipi Ægypt., tom. ii. part i., de Cabalâ Hebræorum; also in his Arithmolog. in the book De Arithmomantia Gnosticor., cap. viii., de Cabalâ Pythagoreâ. See also Mersennes, Comment. on Genes. 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 easier179    This subject is examined by Cornelius Agrippa in his celebrated work, De vanitate et incertitudine Scientiarum, chap. xi., De Sorte Pythagoricâ. Terentius 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. 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,180    That is, the division by 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,181    That is, calculated according to the rule of a division by seven. 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 enneads; 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 nine182    We should expect rather five instead of 9, if the division be by nine. 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,183    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. 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.184    Miller says there is an error in the calculation here. Is there, then, not any annexed, and (is there) not a proper name for Ulysses?185    This is as near the sense of the passage as a translation in some respects conjectural can make it. 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 Asteropæus (are instances). Achilles makes four monads, Asteropæus 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 do 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.

[14] Οἱ μὲν οὖν διὰ ψήφων τε καὶ ἀριθμῶν, στοιχείων τε καὶ ὀνομάτων μαντεύεσθαι νομίζοντες ταύτην ἀρχὴν ἐπιχειρήσεως τοῦ κατ' αὐτοὺς λόγου ποιοῦνται, φάσκοντες πυθμένα εἶναι ἑκάστου τῶν ἀριθμῶν ἐπὶ μὲν τῶν χιλιάδων τοσαύτας μονάδας, ὅσαι ἂν ὦσι χιλιάδες: οἷον τῶν ἑξακισχιλίων ὁ πυθμὴν μονάδες ἕξ, τῶν ἑπτακισχιλίων μονάδες ἑπτά, τῶν ὀκτακισχιλίων μονάδες ὀκτώ, καὶ ἐπὶ τῶν λοιπῶν ὁμοίως κατὰ τὰ αὐτά. καὶ ἐπὶ τῶν ἑκατοντάδων ὅσαι ἂν ὦσιν αἱ ἑκατοντάδες, τοσαῦται μονάδες ὁ πυθμήν ἐστιν αὐτῶν: οἷον τῶν ἑπτακοσίων ἑπτά εἰσιν ἑκατοντάδες, ὁ πυθμὴν αὐτῶν ἑπτὰ μονάδες: τῶν ἑξακοσίων ἓξ ἑκ[ατ]οντάδες, ὁ πυθμὴν αὐτῶν [ἓξ μονάδες: τῶν τριακοσίων τρεῖς ἑκατοντάδες, ὁ πυθμὴν αὐτῶν] τρεῖς μονάδες. τὸ ὅμοιον [δὲ] καὶ ἐπὶ τῶν δεκάδων: τῶν μὲν ὀγδοήκοντα [ὁ πυθμὴν] μονάδες ὀκτώ, τῶν δὲ ἑξήκοντα μονάδες ἕξ, τῶν [δὲ] τεσσαράκοντα μονάδες τέσσαρες, τῶν [δὲ] δέκα μονὰς μία. ἐπὶ δὲ τῶν μονάδων πυθμὴν αὐταί εἰσιν αἱ μονάδες: οἷον τοῦ ἐννέα ὁ ἐννέα, τοῦ ὀκτὼ ὁ ὀκτώ, τοῦ ἑπτὰ ὁ ἑπτά. οὕτως οὖν καὶ ἐπὶ τῶν στοιχείων ποιεῖν δεῖ: ἕκαστον γὰρ στοιχεῖον κατά τινα τέτακται ἀριθμόν: οἷον τὸ [ν] [πεντή]κοντα μονάδ(ων) [ἐστί]ν, τῶν [δὲ] πεντήκοντα μονάδων πυθμήν ἐστιν ὁ πέντε, καὶ τοῦ [ν] στοιχείου πυθμὴν ἔσται ὁ πέντε. Ἔστω ἔκ του ὀνόματος τοὺς τούτου πυθμένας λαβεῖν: οἷον τοῦ Ἀγαμέμνων ὀνόματος γίνεται τοῦ μὲν [α] [πυθμὴν] μονὰς μία, τοῦ δὲ [γ] μονάδες τρεῖς, τοῦ ἄλλου [α] μονὰς μία, τοῦ [μ] μονάδες δʹ, τοῦ [ε] μονάδες εʹ, τοῦ [μ] μονάδες δʹ, τοῦ [ν] μονάδες πέντε, τοῦ [ω] μονάδες ηʹ, τοῦ [ν] μονάδες εʹ: ὁμοῦ ἐπὶ τὸ αὐτὸ ἔσονται αʹ γʹ αʹ δʹ εʹ δʹ [εʹ] ηʹ εʹ: ταῦτα συντεθέντα ποιεῖ μονάδας λϚʹ. πάλιν τούτων πυθμένας λαμβάνουσι, καὶ γίνονται τῶν μὲν λʹ τρεῖς, τῶν δὲ ἓξ αὐτὰ τὰ ἕξ: συντεθέντα οὖν τὰ τρία καὶ τὰ ἓξ ποιεῖ ἐννέα, τῶν δὲ ἐννέα πυθμὴν ὁ ἐννέα. κατέληξεν οὖν τὸ Ἀγαμέμνων ὄνομα εἰς τὸν ἐννέα πυθμένα. ἔστω τὸ αὐτὸ καὶ ἐπὶ ἄλλου ὀνόματος ποιῆσαι, τοῦ Ἕκτωρ. τὸ Ἕκτωρ ὄνομα ἔχει στοιχεῖα [ε] καὶ κάππα καὶ ταῦ καὶ [ω] καὶ [ρ]: τούτων πυθμένες εʹ βʹ γʹ ηʹ αʹ: ταῦτα συντεθέντα ποιεῖ μονάδας ιθʹ. πάλιν τῶν δέκα πυθμὴν εἷς, τῶν ἐννέα ἐννέα, ἃ συντεθέντα ποιεῖ δέκα: τοῦ [δὲ] δέκα γίνεται πυθμὴν μονάς. ψηφισθὲν οὖν τὸ Ἕκτωρ ὄνομα ἐποίησε πυθμένα μονάδα. εὐκολώτερον δέ ἐστι τὸ [αὐτὸ] οὕτως ποιεῖν: τοὺς εὑρεθέντας ἐκ τῶν στοιχείων πυθμένας, ὡς νῦν ἐπὶ τοῦ Ἕκτωρ ὀνόματος εὕρομεν μονάδας ιθʹ, εἰς ἐννέα μέριζε καὶ τὸ περιλειπόμενον πυθμένα λέγε: οἷον τὰ ιθʹ ἐὰν εἰς ἐννέα μερίζω, περιλείπεται μονάς_ἐννάκις γὰρ δύο ιηʹ καὶ λοιπὴ μονάς: ἐὰν γὰρ ὑφέλω τῶν ιθʹ τὰ δεκαοκτώ, λοιπὴ μονάς_: ὥστε τοῦ Ἕκτωρ ὀνόματος πυθμὴν ἔσται μονάς. πάλιν τοῦ Πάτροκλος ὀνόματος πυθμένες εἰσὶν ἀριθμοὶ οὗτοι: ηʹ αʹ γʹ αʹ ζʹ βʹ γʹ ζʹ βʹ, [καὶ] συντεθέντες ποιοῦσι μονάδας λδʹ. τούτων τὸ ἐκλεῖπον μονάδες ἑπτά: τῶν λʹ τρεῖς, καὶ τῶν δʹ αὐταὶ αἱ δʹ: πυθμὴν οὖν εἰσι τοῦ Πάτροκλος ὀνόματος μονάδες ζʹ. Οἱ μὲν οὖν κατὰ τὸν ἐννεαδικὸν κανόνα ψηφίζοντες [τὸ] ἔννατον λαμβάνουσι τοῦ ἀθροισθέντος ἐκ τῶν πυθμένων ἀριθμοῦ καὶ τὸ περιλειφθὲν πλῆθος τὸν πυθμένα ὁρίζονται, οἱ δὲ κατὰ τὸν ἑβδοματικὸν τὸ ἕβδομον. οἷον εὑρέθη ἐπὶ τοῦ Πάτροκλος ὀνόματος τὸ ἐκ τῶν πυθμένων ἄθροισμα μονάδες λδʹ: τοῦτο μερισθὲν εἰς ἑβδομάδας ποιεῖ δʹ, ὅ ἐστιν κηʹ, [καὶ] λοιπαὶ μονάδες ἕξ: λέγουσιν [οὖν] ὅτι ὁ πυθμὴν τοῦ Πάτροκλος ὀνόματός εἰσιν ἓξ κατὰ τὸν ἑβδοματικόν. εἰ δὲ ἔσται μγʹ, τὸ ἕβδομον ποιεῖ μβʹ_ἑπτάκις γὰρ ἓξ μβʹ_καὶ λοιπὸν ἕν: μονὰς οὖν γίνεται ὁ πυθμὴν ὁ ἀπὸ τῶν μγʹ κατὰ τὸν ἑβδοματικόν. δεῖ δὲ προσέχειν ἐὰν ὁ ληφθεὶς ἀριθμὸς μεριζόμενος ἀπαρτίσῃ: οἷον ἐὰν ἔκ τινος ὀνόματος συντιθεὶς τοὺς πυθμένας εὕρω λόγου χάριν μονάδας λϚʹ: ὁ δὲ λϚʹ μεριζόμενος εἰς τὸν ἐννέα δʹ ἀπαρτίζει ἐννεάδας_ἐννάκις γὰρ δʹ λϚʹ καὶ οὐδὲν περιλείπεται_: τὸν πυθμένα οὖν αὐτὸν τὸν θʹ δῆλον εἶναι. καὶ πάλιν [ἐὰν] τὸν τεσσαράκοντα πέντε ἀριθμὸν μερίζοντες εὕρωμεν ἀπαρτίζοντα ἐννέα_καὶ γὰρ ἐννάκις πέντε μεʹ καὶ [περι]λείπεται οὐδέν_ἐπὶ τῶν τοιούτων αὐτὸν τὸν ἐννέα λέγουσι πυθμένα. καὶ ἐπὶ τοῦ ἑβδοματικοῦ ὁμοίως: ἐὰν λόγου χάριν τὸν κηʹ εἰς τὸν ἑπτὰ μερίζοντες ἀπαρτίσωμεν_ ἑπτάκις γὰρ δʹ κηʹ καὶ περιλείπεται οὐδέν_, [αὐτὸν] τὸν ἑπτὰ λέγουσι πυθμένα. Ὅταν μέντοι [τις] ψηφίζῃ τὰ ὀνόματα καὶ εὑρίσκῃ δὶς τὸ αὐτὸ [φωνῆεν] γράμμα, ἅπαξ αὐτὸ ψηφίζει. οἷον τὸ Πατρόκ[α]λος ὄνομα καὶ τὸ [[π]] [α] δὶς ἔχει καὶ τὸ [ο] δίς: ἅπαξ οὖν τὸ [α] ψηφίζουσι καὶ ἅπαξ τὸ [ο]. κατὰ τοῦτο οὖν πυθμένες ἔσονται ηʹ αʹ γʹ αʹ ζʹ βʹ γʹ βʹ, καὶ συντεθέντες ποιοῦσι μονάδας κζʹ, καὶ ἔσται πυθμὴν τοῦ ὀνόματος κατὰ μὲν τὸν ἐννεαδικὸν αὐτὸς ὁ ἐννέα, κατὰ δὲ τὸν ἑβδοματικὸν ἕξ. ὁμ(οίως) Σαρπηδὼν ψηφισθεὶς ποιεῖ μονάδας κατὰ τὸν ἐννεαδικὸν δύο [πυθμένα], Πάτροκλος δὲ ποιεῖ μονάδας θʹ: νικᾷ Πάτροκλος. ὅταν γὰρ ᾖ ὁ μὲν εἷς περισσός, ὁ δὲ ἕτερος ἄρτιος, ὁ περισσὸς νικᾷ ἐὰν μείζων ᾖ. πάλιν δὲ ἐὰν ᾖ ὀκτὼ ἄρτιος καὶ πέντε περισσός, ὁ ὀκτὼ νικᾷ: μείζων γάρ ἐστιν. εἰ δέ εἰσιν ἀριθμοὶ [δύο οἷον] ἀμφότεροι ἄρτιοι ἢ ἀμφότεροι περισσοί, ὁ ἐλάσσων νικᾷ. πῶς δὲ ὁ Σαρπηδὼν κατὰ τὸν ἐννεαδικὸν ποιεῖ μονάδας δύο; παραλείπεται γὰρ τὸ [ω] στοιχεῖον. ὅταν γὰρ ᾖ ἐν ὀνόματί [τινι] στοιχεῖα [ω] καὶ [η], παραλιμπάνουσι τὸ [ω] ἑνὶ στοιχείῳ χρώμενοι: ἰσοδυναμεῖν γὰρ λέγουσι τὰ ἀμφότερα, δὶς δὲ τὸ αὐτὸ οὐ ψηφίζεται, ὡς ἄνωθεν εἴρηται. πάλιν Αἴας [κατὰ τὸν ἐννεαδικὸν] ποιεῖ μονάδας δʹ, Ἕκτωρ δὲ κατὰ τὸν ἐννεαδικὸν ποιεῖ μονάδα μίαν: καὶ ἔστιν ἡ μὲν τετρὰς ἄρτιος, ἡ δὲ μονὰς περισσή, ἐπὶ δὲ τῶν τοιούτων τὸν μείζονα ἐλέγομεν νικᾶν: νικᾷ ὁ Αἴας. πάλιν Ἀλέξανδρος καὶ Μενέλαος: Ἀλέξανδρος κύριον ἔχει ὄνομα [Πάρις:] Πάρις δὲ ποιεῖ μονάδας κατὰ τὸ[ν] ἐννεαδικὸν δʹ, Μενέλαος δὲ κατὰ τὸν ἐννεαδικὸν μονάδας θʹ. νικῶσι δὴ αἱ ἐννέα τὰς τέσσαρας_εἴρηται γάρ, ὁπόταν ὁ μὲν περισσὸς ᾖ, ὁ δὲ ἄρτιος, ὁ μείζων νικᾷ, ὅταν δὲ ἀμφότεροι ἄρτιοι ἢ ἀμφότεροι περισσοί, ὁ ἐλάσσων. _πάλιν Ἄμυκος καὶ Πολυδεύκης: Ἄμυκος μὲν ποιεῖ μονάδας δύο κατὰ τὸν ἐννεαδικόν, [καὶ] Πολυδεύκης δὲ ἑπτά: νικᾷ Πολυδεύκης. Αἴας καὶ Ὀδυσσεὺς ἐπάλαισαν ἐν τῷ ἐπιταφίῳ: Αἴας ποιεῖ κατὰ τὸν ἐννεαδικὸν μονάδας δʹ, Ὀδυσσεὺς ὀκτὼ κατὰ τὸν ἐννεαδικόν: ἆρ' οὖν μήτι τὸ Ὀδυσσέως ἐπίθετον καὶ οὐ κύριόν ἐστιν; ἐνίκησε γάρ: κατὰ μὲν τοὺς ἀριθμοὺς νικᾷ Αἴας, ἡ δ' ἱστορία Ὀδυσσέα παραδίδωσιν. [πάλιν] Ἀχιλεὺς καὶ Ἕκτωρ: Ἀχιλεὺς κατὰ τὸν ἐννεαδικὸν ποιεῖ [μονάδας] τέσσαρας, Ἕκτωρ μίαν: νικᾷ Ἀχιλεύς. πάλιν Ἀχιλεὺς καὶ Ἀστεροπαῖος: Ἀχιλεὺς ποιεῖ [μονάδας] τέσσαρας, Ἀστεροπαῖος τρεῖς: νικᾷ Ἀχιλεύς. πάλιν Μενέλαος καὶ Εὔφορβος: Μενέλαος ἔχει μονάδας ἐννέα, Εὔφορβος ὀκτώ: νικᾷ Μενέλαος. Τινὲς δὲ κατὰ τὸν ἑβδοματικὸν μόνοις τοῖς φωνήεσι χρῶνται, ἄλλοι δὲ διαστέλλουσιν ἰδίᾳ μὲν τὰ φωνήεντα, ἰδίᾳ δὲ τὰ ἡμίφωνα, ἰδίᾳ δὲ τὰ ἄφωνα, καὶ τρεῖς τάξεις ποιήσαντες λαμβάνουσι τοὺς πυθμένας ἰδίᾳ μὲν τῶν φωνηέντων, ἰδίᾳ δὲ τῶν ἡμιφώνων, ἰδίᾳ [δὲ] τῶν ἀφώνων, καὶ συγκρίνουσι χωρὶς ἕκαστον. ἄλλοι δὲ οὐδὲ τούτοις τοῖς νενομισμένοις ἀριθμοῖς χρῶνται, ἀλλ' ἄλλοις: οἷον ὑποδείγματος ἕνεκα τὸ [π] [στοιχεῖον] οὐ θέλουσι πυθμένα ἔχειν [μονάδας] ηʹ, ἀλλὰ εʹ, καὶ τὸ [ξ] στοιχεῖον πυθμένα μονάδας [Ϛʹ, ἀλλὰ] δʹ, καὶ παντοίως στρεφόμενοι οὐδὲν ὑγιὲς εὑρίσκουσιν. ὅταν μέντοι δεύτερόν τινες ἀγωνίζωνται, ἀφ' ἑκατέρου τῶν ὀνομάτων τὸ πρῶτον στοιχεῖον ἀφαιροῦσιν, ὅταν δὲ τρίτον, τὰ δύο ἑκατέρωθεν, καὶ τὰ λοιπὰ ψηφίσαντες συγκρίνουσιν.