§5Πολλαῖς δὲ καὶ ἄλλαις λέξεσιν ἔστιν ἑρμηνεῦσαι τὴν αὐτὴν μέθοδον, ἀλλ’ ἀρκεῖ καὶ μέχρι τοσούτου προεληλυθέναι τῆς ματαιοτεχνίας αὐτῶν, ἵνα καὶ διὰ βραχέων κεφαλαίων ἐπιδεῖξαι δυνηθῶμεν ἕκαστον τῶν ἑπομένων ἁμαρτημάτων, ἀρξάμενοι πάλιν ἀπὸ τῶν προχειροτέρων.
It is possible to explain the same method in many other wordings as well, but it is enough to have proceeded up to this point in their useless art, so that we may be able to demonstrate each of the following errors by means of brief summaries, beginning again from those more close at hand.
ἐπειδὴ γὰρ ὅταν ἡ κατὰ τοὺς παροξυσμοὺς περίοδος ὡρῶν ᾖ δώδεκα, δύνανται μὲν εἶναι καὶ δύο ἀμφημερινοὶ, δύνανται δὲ καὶ τριταῖοι τέτταρες, καὶ τεταρταῖοι δ’ οὐδὲν ἧττον ἓξ, καὶ ὀκτὼ πεμπταῖοι, καὶ δέκα ἑκταῖοι, καὶ δώδεκα ἑβδομαῖοι, καὶ δεκατέσσαρες ὀγδοαῖοι, καὶ δεκαὲξ ἐνναταῖοι, καὶ δεκαοκτὼ δεκαταῖοι.
For since, when the period during the paroxysms is twelve hours, there can be two quotidians, and there can also be four tertians, and no less than six quartans, and eight quintans, and ten sextans, and twelve septimans, and fourteen octans, and sixteen nonans, and eighteen decimans.
πάλιν οὖν κατὰ τόνδε τὸν τρόπον ὁδὸς εὑρίσκεται φλυαρίας οὐ σμικρὰ, στῆναι μὴ δυναμένη, μηδέ τινα σκοπὸν ὡρισμένον ἔχειν, ἔνθα περιγράφειν αὐτὴν ἀναγκαῖον ἔσται.
Again, therefore, in this manner a path of no small nonsense is found, which is unable to stand still, nor has any defined target where it will be necessary to limit it.
τί γὰρ μᾶλλον ἄχρι τῶν ὀκτωκαίδεκα δεκαταίων, ἢ τῶν εἴκοσι δωδεκαταίων, ἢ τῶν εἰκοσιδύο δωδεκαταίων προαίρεσθαι προσῆκεν, ἤ τινος τῶν ἐφεξῆς περιόδων;
For why was it more appropriate to choose to advance up to eighteen decimans, or twenty duodecimans, or twenty-two duodecimans, rather than to any of the subsequent periods?
ἔξεστι γὰρ λέγειν εἰκοσιτέσσαρας μὲν εἶναι τρισκαιδεκαταίους, ἓξ δὲ καὶ εἴκοσι τεσσαρεσκαιδεκαταίους, ὀκτὼ δὲ ἐπὶ ταῖς εἴκοσι πεντεκαιδεκαταίους.
For it is possible to say that there are twenty-four tridecimans, twenty-six tetradecimans, and twenty-eight quindecimans.
ὁμοίως τε τούτοις ἔξεστι δὴ προστιθέναι.
And it is indeed possible to add to these in like manner.
διάκορον μὲν γὰρ ἤδη τοῦτο καὶ κατὰ τοὺς ἀμφημερινούς ἐστιν, ἔτι δὲ ληρωδέστερον ἐπὶ τῶν τριταίων καὶ τεταρταίων, καὶ πολὺ μᾶλλον ἁπάντων τῶν ἐφεξῆς.
For this is already tedious even in the case of quotidians, and still more nonsensical in the case of tertians and quartans, and much more so in all the subsequent ones.
ἡ γοῦν τῶν ἑκκαίδεκα ὡρῶν περίοδος οὐδὲν μᾶλλόν ἐστι τριῶν τριταίων, ἢ ἓξ πεμπταίων, ἢ ἑβδομαίων θ΄.
At any rate, the period of sixteen hours is no more [a complication] of three tertians than of six quintans, or nine septimans.
δύναται δὲ αὕτη δώδεκα μὲν ἐνναταίων εἶναι, πεντεκαίδεκα δὲ δεκαταίων, ὀκτωκαίδεκα τρισκαιδεκαταίων, ἑνὸς δὲ ἐπὶ τῶν κ΄ πεντεκαιδεκαταίων, ἀνάλογόν τε τῶν ἐφεξῆς ἁπάντων.
And this can be of twelve nonans, fifteen decimans, eighteen tridecimans, twenty-one quindecimans, and analogously of all the subsequent ones.
ἀλλ’ ἐμοὶ τὴν ὁδὸν ἀρκεῖ μόνον ἐνδεδεῖχθαι τῆς περὶ τὰ τοιαῦτα ἀπωλείας τοῦ χρόνου.
But for me it is enough only to have indicated the path of the waste of time on such matters.
καὶ γάρ τοι καὶ ἡ τῶν η΄ καὶ ι΄ ὡρῶν περίοδος, ἐνδειξάμενος γὰρ ἔτι καὶ τὴν ταύτης ὁδὸν ἐπ’ ἄλλο τι μεταβήσομαι, τεττάρων μέν ἐστι τεταρταίων, ὀκτὼ δὲ ἑβδομαίων, δεκαταίων δὲ δώδεκα.
For indeed, the period of eighteen hours—for having indicated the path of this one as well, I shall proceed to something else—is of four quartans, eight septimans, and twelve decimans.
καὶ τούτων ἁπάντων ἐστὶν ἑκάστου μέθοδος, ὥστε ἐπὶ δακτύλων λογίσασθαι μὴ δεηθέντα διαγράμματος.
And of all these there is a method for each, so as to calculate on one's fingers without needing a diagram.
ἀλλ’ ἐγὼ μὲν ἀντὶ παιδείας ἕκαστον τούτων ἀποκρίνομαι τοῖς προλαβοῦσι παραχρῆμα, διὰ τὸ γεγυμνάσθαι τὴν παιδικὴν ἡλικίαν ἐν ἀριθμοῖς· ἀγύμναστος δὲ ἄνθρωπος οὐ μηνῶν, ἀλλ’ ἐτῶν ὅλων εἰς αὐτοὺς δεῖται χάριν τοῦ γενέσθαι σοφὸς ἐν ἀχρήστοις πράγμασιν, ἃ μετὰ σπουδῆς τινες ἀλλήλοις προβάλλοντες οὐκ αἰδοῦνται.
But I, instead of a display of education, answer each of these to those who ask beforehand on the spot, because of having been trained in numbers during childhood; whereas an untrained person needs not months, but whole years for them, for the sake of becoming wise in useless matters, which some people, proposing to one another with earnestness, are not ashamed of.
ὅτι μὲν οὖν ἁμαρτάνουσι διττὰ πάντες οἱ τὰ περὶ τύπων ὑπομνήματα γράψαντες, οὔτε τὰς ἰδέας τῶν νοσημάτων διδάσκοντες οὔτε τοῖς εὐχρήστοις τρίβοντες τὸν χρόνον, αὐτάρκως ἡγοῦμαι δεδεῖχθαι.
That indeed all those who have written commentaries on types err in a twofold way, neither teaching the forms of diseases nor spending their time on useful things, has, I think, been sufficiently demonstrated.