§4#1Ἐπεὶ δ’ ἠνάγκασάν μέ τινες τῶν νεωτέρων δεηθέντες, ἣν ἐγὼ παίζων αὐτοὺς ἐδίδαξα μέθοδον εἰς εὕρεσιν τῶν ἐν ταῖς τοιαύταις ὑποθέσεσι τύπων, ἐν γράμμασι καταθέσθαι, δι’ ἐκείνους ἀνέθηκα καὶ τούτῳ τῷ λόγῳ μίαν ἡμέραν οὐχ ἑκών.
Since, however, some of the younger men urged and asked me to put into writing the method which I had taught them in jest for finding the types in such hypotheses, on their account I reluctantly devoted one day to this discourse.
ἀρξώμεθα οὖν ἤδη τῆς διδασκαλίας αὐτῶν ἐνθένδε.
Let us therefore now begin their instruction from this point.
τύπον οὗτοι καλοῦσιν οὐχ ἅπασαν περίοδον, ἀλλ’ ἥτις ἂν ἐξ ὁλοκλήρων ἡμερῶν τε καὶ νυκτῶν συγκέηται, καὶ καθ’ ἕκαστόν γε πλῆθος ἡμερῶν ἴδιον εἶναι βούλονται τύπον, οὐδὲ κ΄ ἢ λ΄ μόνον ἡμερῶν, ἀλλὰ καὶ τούτων ἐξωτέρω τὰς τῶν τύπων περιόδους ἐκτείνοντες.
These men call 'type' not just any period, but whichever is composed of whole days and nights, and they want there to be a proper type for each quantity of days, extending the periods of types not only to twenty or thirty days, but even beyond these.
ἐν δὲ τοῖς τύποις τούτοις ὁ τοῦ παροξυσμοῦ χρόνος ἐπὶ παροξυσμὸν οὐκέτι μὲν τύπος, αὐτὸ δὲ τοῦτο μόνον ὀνομάζεται αὐτοῖς περίοδος.
And in these types, the time from paroxysm to paroxysm is no longer called 'type', but is named by them simply 'period' itself.
ἐπυθόμην δή τινα καὶ βιβλίον ὅλον οὐ σμικρὸν γεγραφηκέναι διδάσκοντα, πῶς ἄν τις ἐφ’ ἑκάστῃ περιόδῳ παροξυντικῇ προβληθείσῃ τό τ’ εἶδος εὑρίσκοι καὶ τὸν ἀριθμὸν τῶν τύπων.
Indeed, I heard that someone has even written a whole, not small book teaching how, for each paroxysmal period presented, one might find the form and the number of the types.
καὶ νὴ τοὺς θεοὺς ἐθαύμασα, τίνα ποτ’ ἐστὶν ἃ λέγει κατὰ τὸ βιβλίον.
And, by the gods, I wondered what on earth he says in the book.
ἡ γάρ τοι μέθοδος, ἐξ ὧν ἄν τις εὑρίσκοι τὸ πόσων ἐστὶ τύπων ἐπιπλοκὴ, δι’ ἐλαχίστων ἐπῶν διδαχθῆναι δύναται, τοιαύτη τις οὖσα.
For the method by which one might find of how many types there is a complication can be taught in very few words, being something like this.
τὸν ἀριθμὸν τῶν ὡρῶν ἑκάστου τύπου πρόχειρον ἔχειν προσῆκεν ἤτοι διὰ μνήμης, ἢ γεγραμμένον ἐν χαρτίῳ, τοῦ μὲν ἀμφημερινοῦ τὸν τῶν κδ΄, τριταίου δὲ τὸν τῶν ὀκτὼ καὶ τετταράκοντα, καὶ οὕτως ἐφεξῆς, τεταρταίου μὲν οβ΄, πεμπταίου δὲ νστ΄, ἑκταίου ρκ΄, ἑβδομαίου δὲ ρμδ΄ καὶ τῶν ἄλλων, ὡς τοῦτο τὸ διάγραμμα τὸ ὑποτεταγμένον ἔχει.
One should have the number of hours of each type ready at hand, either by memory or written on a piece of paper: for the quotidian, 24; for the tertian, 48; and so on in order, for the quartan, 72; for the quintan, 96; for the sextan, 120; for the septiman, 144; and for the others, as this diagram appended below has it.
ΤΥΠΟΙ ΩΡΑΣ. Ἀμφημερινός κδ΄ Τριταῖος μη΄ Τεταρταῖος οβ΄ Πεμπταῖος לστ΄ Ἑκταῖος ρκ΄ Ἑβδομαῖος ρμδ΄ Ὀγδοαῖος ρξη΄ Ἐνναταῖος ρלβ΄ Δεκαταῖος σιστ΄ Ἑνδεκαταῖος σμ΄ Δωδεκαταῖος σξδ΄ Τρισκαιδεκαταῖος σπη΄ Τεσσαρεσκαιδεκαταῖος τιβ΄ Πεντεκαιδεκαταῖος τλστ΄ Ἑκκαιδεκαταῖος τξ΄ Ἑπτακαιδεκαταῖος τπδ΄ Ὀκτωκαιδεκαταῖος υη΄ Ἐννεακαιδεκαταῖος υλβ΄ Εἰκοσταῖος υνστ΄ Εἰκοστὸς πρῶτος υπ΄ Εἰκοστὸς δεύτερος φδ΄ Εἰκοστὸς τρίτος φκη΄ Εἰκοστὸς τέταρτος φνβ΄ Εἰκοστὸς πέμπτος φοστ΄ Εἰκοστὸς ἕκτος χ΄ Εἰκοστὸς ἕβδομος χκδ΄ Εἰκοστὸς ὄγδοος χμη΄ Εἰκοστὸς ἔννατος χοβ΄ Τριακοστός χלστ΄ Τριακοστὸς πρῶτος ψκ΄ Τριακοστὸς δεύτερος ψμδ΄ Τριακοστὸς τρίτος ψξη΄ Τριακοστὸς τέταρτος ψלβ΄ Τριακοστὸς πέμπτος ωιστ΄ Τριακοστὸς ἕκτος ωμ΄ Τριακοστὸς ἕβδομος ωξδ΄ Τριακοστὸς ὄγδοος ωπη΄ Τριακοστὸς ἔννατος Ϡιβ΄ Τεσσαρακοστός Ϡλστ΄ Τεσσαρακοστὸς πρῶτος Ϡξ΄ Τεσσαρακοστὸς δεύτερος Ϡπδ΄ Τεσσαρακοστὸς τρίτος α͵η΄ Τεσσαρακοστὸς τέταρτος α͵λβ΄ Τεσσαρακοστὸς πέμπτος α͵νστ΄ Τεσσαρακοστὸς ἕκτος α͵π΄ Τεσσαρακοστὸς ἕβδομος α͵ρδ΄ Τεσσαρακοστὸς ὄγδοος α͵ρκη΄ Τεσσαρακοστὸς ἔννατος α͵ρνβ΄ Πεντηκοστός α͵ροστ΄
Τοιοῦτον ἐχέτωσαν ἐν χαρτίῳ διάγραμμα ἐσκευασμένον οἱ μὴ δυνάμενοι ῥᾳδίως λογίζεσθαι.
TYPES AND HOURS. Quotidian 24, Tertian 48, Quartan 72, Quintan 96, Sextan 120, Septiman 144, Octan 168, Nonan 192, Deciman 216, Undeciman 240, Duodeciman 264, Thirteenth-day 288, Fourteenth-day 312, Fifteenth-day 336, Sixteenth-day 360, Seventeenth-day 384, Eighteenth-day 408, Nineteenth-day 432, Twentieth-day 456, Twenty-first-day 480, Twenty-second-day 504, Twenty-third-day 528, Twenty-fourth-day 552, Twenty-fifth-day 576, Twenty-sixth-day 600, Twenty-seventh-day 624, Twenty-eighth-day 648, Twenty-ninth-day 672, Thirtieth-day 696, Thirty-first-day 720, Thirty-second-day 744, Thirty-third-day 768, Thirty-fourth-day 792, Thirty-fifth-day 816, Thirty-sixth-day 840, Thirty-seventh-day 864, Thirty-eighth-day 888, Thirty-ninth-day 912, Fortieth-day 936, Forty-first-day 960, Forty-second-day 984, Forty-third-day 1008, Forty-fourth-day 1032, Forty-fifth-day 1056, Forty-sixth-day 1080, Forty-seventh-day 1104, Forty-eighth-day 1128, Forty-ninth-day 1152, Fiftieth-day 1176. Let those who cannot easily calculate keep such a prepared diagram on a piece of paper.
μετὰ δὲ τὴν τούτου παρασκευὴν ἐπισκοπείσθωσαν ὁ προβληθεὶς παροξυσμὸς τῶν κατὰ τοὺς παροξυσμοὺς περιοδικῶν ὡρῶν οὗ τινος τῶν πρῶτον γεγραμμένων ἀριθμῶν ἐστι μόριον.
And after preparing this, let them examine of which of the numbers written first the presented paroxysm of periodic hours during the paroxysms is a fraction.
εὑρόντες γὰρ αὐτὸν ἕξουσι τὸ γένος τοῦ τύπου, γένος δὲ, ἢ εἶδος, ἢ ἰδέαν, ἢ φύσιν ἐν τῷ παρόντι λέγειν οὐ διοίσει, τὸν δὲ ἀριθμὸν, τῶν τύπων εὑρεθέντων, κατὰ τὸ μόριον.
For having found it, they will have the genus of the type—and at present it will make no difference whether we say genus, form, idea, or nature—and the number of the types found will correspond to the fraction.
εἰ μὲν γὰρ τρίτον εἴη τὸ μόριον ὁ κατὰ τὴν περίοδον ἀριθμὸς τῶν ὡρῶν τοῦ τύπου, τρεῖς ἐρεῖς ἀλλήλοις ἐκείνους περιπεπλέχθαι τοὺς τύπους· εἰ δὲ τέταρτον, τέτταρας· εἰ δὲ πέμπτον, πέντε, παρώνυμον ἀεὶ τὸν ἀριθμὸν τοῦ μέρους ποιούμενος.
For if the number of hours in the period is a third part of the type, you will say that three of those types are complicated with one another; if a fourth, four; if a fifth, five, always making the number homonymous with the part.
ἵνα δὲ καὶ διὰ παραδείγματος εὑρεθῇ σαφεστέρα ἡ μέθοδος, ἔστω τινὰ παροξύνεσθαι μὲν ὥραις στ΄, ἐξανίεσθαι δὲ δυοῖν, ὥστε τὴν ὅλην περίοδον ὑπάρχειν ὡρῶν ὀκτώ·
So that the method may become clearer also through an example, let someone suffer a paroxysm for six hours, and have a remission for two, so that the entire period is eight hours.
κατὰ ταύτην τὴν ὑπόθεσιν ἐπισκέψῃ, τί μέρος ἐστὶ τὰ η΄ τῶν κδ΄, εἶθ’ εὑρὼν ὅτι τρίτον, ἀμφημερινοὺς ἐρεῖς ἐπιπεπλέχθαι τρεῖς· ἀμφημερινοὺς μὲν, ὅτι τοῦ τῶν κδ΄ ἀριθμοῦ μόριόν ἐστιν ὁ τῶν ὀκτώ· τρεῖς δὲ, ὅτι τρίτον.
Under this hypothesis, you will examine what part 8 is of 24, and then, having found that it is a third, you will say that three quotidian fevers are complicated; quotidians, because 8 is a fraction of the number 24, and three, because it is a third.