§4#2ὑποκείσθω δὲ πάλιν ἑκκαίδεκα ὡρῶν εἶναι τὴν κατὰ τοὺς παροξυσμοὺς περίοδον.
Let it be assumed again that the period during the paroxysms is sixteen hours.
ἐπεὶ τοίνυν τὰ δεκαὲξ τῶν κδ΄ οὐδέν ἐστι μόριον, τῶν τε μή τρίτον ἐστί· τὰ δὲ μη΄ τριταίης ἐστὶν ἀριθμὸς περιόδου· τριταίους ἐρεῖς πυρετοὺς τρεῖς ἀλλήλοις ἐπιπεπλέχθαι.
Since, then, sixteen is no fraction of twenty-four, and forty-eight is the number of the tertian period [and sixteen is a third part of forty-eight], you will say that three tertian fevers are complicated with one another.
ὑποκείσθω πάλιν ἡ τῶν παροξυσμῶν περίοδος ὡρῶν ὑπάρχειν ὀκτωκαίδεκα.
Let it be assumed again that the period of the paroxysms is eighteen hours.
μέρος δέ ἐστιν οὗτος οὔτε τῶν κατὰ τὸν ἀμφημερινὸν ὡρῶν ἀριθμοῦ, οὔτε τῶν κατὰ τὸν τριταῖον, ἀλλὰ τοῦ κατὰ τὸν τεταρταῖον, ὅς ἐστιν οβ΄.
This is a part neither of the number of hours in the quotidian, nor of those in the tertian, but of those in the quartan, which is seventy-two.
φήσεις οὖν ἐπιπεπλέχθαι τεταρταίους ἀλλήλοις τέτταρας· τεταρταίους μὲν, ὅτι ἐκ τοῦ τῶν οβ΄ ὡρῶν ἀριθμοῦ· τέτταρας δὲ, ὅτι τέταρτόν ἐστι μέρος ὁ τῶν ὀκτωκαίδεκα ὡρῶν ἀριθμὸς τοῦ τῶν οβ΄.
You will say, therefore, that four quartans are complicated with one another; quartans, because it is from the number of seventy-two hours, and four, because the number of eighteen hours is a fourth part of seventy-two.
ὑποκείσθω πάλιν ἡ τῶν παροξυσμῶν περίοδος ὡρῶν εἶναι ε΄.
Let it be assumed again that the period of the paroxysms is five hours.
μέρος δέ εἰσιν αἱ ε΄ τῶν ρη΄ εἰκοστοτέταρτον· ἐρεῖς οὖν εἶναι τύπους ἑκταίους ἐπιπεπλεγμένους ἀλλήλοις κδ΄.
And five is a twenty-fourth part of one hundred and eight; you will say, therefore, that there are twenty-four sextan types complicated with one another.
ὑποκείσθω πάλιν ἡ τῶν κατὰ τοὺς παροξυσμοὺς ὡρῶν περίοδος ζ΄.
Let it be assumed again that the period of hours during the paroxysms is seven.
μέρος δέ εἰσιν αὗται τῶν ρξη΄, τουτέστιν ὀγδοαίου τύπου, τὸ εἰκοστὸν τέταρτον.
And these are a twenty-fourth part of one hundred and sixty-eight, which is of the octan type.
ἐρεῖς οὖν εἶναι τύπους ὀγδοαίους εἰκοσιτέτταρας.
You will say, therefore, that there are twenty-four octan types.
ὑποκείσθω πάλιν ἡ τῶν κατὰ τοὺς παροξυσμοὺς περίοδος ὡρῶν θ΄.
Let it be assumed again that the period during the paroxysms is nine hours.
μέρος δέ εἰσιν αὗται τῶν σιστ΄ εἰκοστοτέταρτον.
And these are a twenty-fourth part of two hundred and sixteen.
αὗται δὲ αἱ σιστ΄ περίοδός ἐστι δεκάτου τύπου.
And this two hundred and sixteen is the period of the deciman type.
γενήσονται γοῦν ἐπὶ τῆς ὑποθέσεως ταύτης δεκαταῖοι τύποι τέτταρες καὶ εἴκοσιν.
Under this hypothesis, therefore, there will be twenty-four deciman types.
ὑποκείσθω πάλιν κατὰ τοὺς παροξυσμοὺς περίοδος ὡρῶν δέκα.
Let it be assumed again that the period during the paroxysms is ten hours.
δωδέκατον δέ ἐστι μέρος ἀριθμὸς οὗτος τῶν ρκ΄, ὅστις ἐστιν ἑκταίας περιόδου, διὰ ταῦτα οὖν ἑκταῖοι γενήσονται δώδεκα.
This number is a twelfth part of one hundred and twenty, which is of the sextan period; for these reasons, therefore, there will be twelve sextans.
ὑποκείσθω πάλιν ἡ κατὰ τοὺς παροξυσμοὺς περίοδος ὡρῶν ὑπάρχειν ἕνδεκα, μετρεῖται δὲ ὁ τῶν σξδ΄ ἀριθμὸς ὑπὸ τῶν ἕνδεκα κατὰ τὸν κδ΄.
Let it be assumed again that the period during the paroxysms is eleven hours; and the number two hundred and sixty-four is measured by eleven by twenty-four.
ἔσονται οὖν κδ΄ ἀλλήλοις ἐπιπλεκόμενοι τύποι δωδεκαταῖοι, διότι κατὰ τὸν τῶν κδ΄ ἀριθμὸν ὁ τῶν ια΄ μετρεῖ τὸν τοῦ δωδεκαταίου τύπου τῶν ὡρῶν ἀριθμὸν, ὅστις ἐστιν ὁ τῶν σξδ΄.
There will be, therefore, twenty-four duodeciman types complicated with one another, because eleven measures the number of hours of the duodeciman type, which is two hundred and sixty-four, by the number of twenty-four.
ἀεὶ τοίνυν εὑρεθήσεταί σοι τὸ μὲν εἶδος τῶν τύπων ἐκ τῶν ἐν τῷ διαγράμματι γεγραμμένων ἀριθμῶν· τὸ δὲ πλῆθος αὐτῶν ἐκ τοῦ γνῶναι πόστον ἐστὶ τὸ τοῦ ἀριθμοῦ μέρος ὁ τῶν κατὰ τοὺς παροξυσμοὺς ὡρῶν ἀριθμὸς, ὅπερ ταὐτόν ἐστι τῷ γνῶναι κατὰ τίνα τῶν ἀριθμῶν ὁ κατὰ τοὺς παροξυσμοὺς μετρεῖ τὸν τοῦ τύπου· παρονομάζονται γὰρ ἀλλήλοις ὅ τ’ ἀριθμὸς οὗτος καὶ τὸ μόριον.
Always, then, the form of the types will be found by you from the numbers written in the diagram; and their quantity from knowing what fraction of the number the number of hours during the paroxysms is, which is the same as knowing by which of the numbers the [number of hours] during the paroxysms measures that of the type; for this number and the fraction are homonymous with each other.
οὐδὲν γοῦν διαφέρει τρίτον εἶναι μέρος φάναι τῶν ιβ΄ τὸν τῶν δ΄ ἀριθμὸν, ἢ μετρεῖσθαι πρὸς τοὺς τέσσαρας τὸν δώδεκα κατὰ τὸν τρία.
For indeed, it makes no difference to say that the number four is a third part of twelve, or that twelve is measured in relation to four by three.
ταὐτὸν δέ ἐστι τούτῳ κᾂν οὕτως εἴπωμεν, ὁ τέσσαρα τὸν δώδεκα μετρεῖ κατὰ τὸν τρία.
It is the same as this even if we say: 'four measures twelve by three'.
γράψας οὖν πάλιν ἐν κεφαλαίοις βραχέσι τὴν μέθοδον, ἐφ’ ἕτερον ἐφεξῆς μεταβήσομαι λόγον.
Having written, then, the method again in brief summaries, I shall proceed to another discourse in order.
ἔσονται δ’ ὥσπέρ τινες αὐτῆς ἀφορισμοὶ τοιοίδε.
And there will be certain rules of it like these.
ἐπισκέπτεσθαι χρὴ τῶν κατὰ τοὺς παροξυσμοὺς περιόδων τὰς ὥρας, πόστον μέρος εἰσὶ τῶν κατὰ τοὺς τύπους ὡρῶν.
One must examine the hours of the periods during the paroxysms, what fraction they are of the hours of the types.
ὁ μὲν γὰρ τῷ μέρει παρονομαζόμενος ἀριθμὸς τὸ πλῆθος ἔσται τῶν τύπων· ὁ δ’ ὑπὸ τούτων μετρούμενος αὐτὸς ὁ τύπος.
For the number homonymous with the part will be the quantity of the types, and the number measured by these will be the type itself.
ἑτέρᾳ δὲ λέξει ταὐτὸν ἑρμηνευθήσεται οὕτως· τῆς κατὰ τοὺς παροξυσμοὺς περιόδου τὸν ἀριθμὸν τῶν ὡρῶν ἐπισκέπτου, κατὰ τίνα μετρεῖ τῶν ἐκ τοῦ διαγράμματος ὁντιναοῦν.
In another wording, the same will be explained thus: examine the number of hours of the period during the paroxysms, by what number it measures any of those in the diagram.
αὐτὸς μὲν γὰρ ὁ ἐκ τοῦ διαγράμματος ἀριθμὸς τὸ εἶδος τῶν τύπων δηλώσει· καθ’ ὃν δὲ τοῦτον ἐμέτρησεν ὁ τῆς περιόδου, τὸ πλῆθος αὐτῶν.
For the number in the diagram itself will show the form of the types, and the number by which that of the period measured this will show their quantity.
ἄλλῃ δὲ λέξει ταὐτὸν οὕτως ἑρμηνευθήσεται.
In another wording, the same will be explained thus.
ὁ κατὰ τοὺς παροξυσμοὺς ἀριθμὸς τῶν περιοδικῶν ὡρῶν ὁσάκις ἂν μετρῇ τινα τῶν κατὰ τοὺς τύπους, τοσαυτάκις ὁ τύπος ἐκεῖνος ἑαυτῷ συμπλέκεται.
As many times as the number of periodic hours during the paroxysms measures any of those of the types, so many times is that type complicated with itself.
συμπλέκεται δὲ ἢ ἐπιπλέκεται λέγειν οὐ διοίσει.
And it will make no difference whether we say sympleketai or epipleketai.