← Galen

Against Those Who Have Written on Disease Patterns

§7#1

Calculation of Fever Types and Periods Without Diagrams

The author introduces a handy calculation method without a diagram to determine the number and periods of fevers (such as quartans, sextans, and octans) based on the common divisors between a 24-hour day and the given paroxysm period.

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§7#1

Τούτων ἤδη γεγραμμένων, καί τισι τῶν ἑταίρων ἐκδιδομένων, ἢ ἀξιωσάντων ἑτέρων μαθεῖν, ὅπως ἂν ᾖ τοῦ διαγράμματος,1 ἐγὼ παραχρῆμα τοῖς προβάλλουσιν ἀποκρίνομαι τὸ πλῆθος τῶν τύπων. ἔστιν οὖν ἡ μέθοδος οὐχ ἑτέρου τινὸς γένους, ἀλλ’ ὑποπεπτωκυῖα τῇ προτέρᾳ. πεισθήσῃ δὲ καὶ αὐτὸς οὕτως ἔχειν ἀναμνησθεὶς πρότερον ἀεί τε πρόχειρον ἔχων τὴν μνήμην αὐτῶν, ὡς ἡμέραν ὀνομάζομεν ἐν τῷ χρόνῳ τούτῳ τὸν συγκείμενον χρόνον ἔκ τε τῆς ἡμέρας καὶ τῆς νυκτὸς, ὅπερ ἔνιοι προσαγορεύουσι νυχθήμερον. οὕτω γοῦν καὶ τὸν ἐνιαυτὸν εἶναι λέγομεν ἡμερῶν τξε΄ καὶ τετάρτου. μιᾶς μὲν οὖν ἡμέρας τέτταρες ἐπὶ ταῖς κ΄ ὧραι γίγνονται, δυοῖν δὲ ὀκτὼ καὶ τετταράκοντα, τριῶν δὲ δύο καὶ ἑβδομήκοντα· τὰ δὲ ὀνόματα τοῖς τύποις οὐκ ἀπὸ τῶν συμπληρουμένων ἡμερῶν ἐστιν, ἀλλ’ ἀπὸ τῆς ἀνταποδόσεως τοῦ παροξυσμοῦ. τριταῖον μὲν ὀνομάζομεν ᾧ διὰ τρίτης ἡμέρας ὁ παροξυσμὸς γίγνεται, δυοῖν μεταξὺ δηλονότι καὶ συμπληρωθεισῶν·2 τεταρταῖον δὲ ᾧ κατὰ τετάρτην, τριῶν κᾀπὶ τούτῳ μεταξὺ συμπληρουμένων ἡμερῶν, ἐπί τε τῶν ἄλλων ἀνάλογον· ὥσθ’ ὅταν εὕρῃς περίοδον τύπου τεττάρων ἡμερῶν, πεμπταῖον ἐρεῖς αὐτὸν, οὐ ταὐτὸν γάρ ἐστι διὰ πέμπτης τε παροξύνεσθαι καὶ πέντε ἡμερῶν ἔχειν περίοδον. ἐν μνήμῃ τοίνυν θέμενος ταῦτα, πάλιν ἀναμνήσθητί μοι τῆς εἰρημένης ἔμπροσθεν ἐπὶ τῷ διαγράμματι μεθόδου. λέλεκται δὲ ὅτι τὸν προβληθέντα περιοδικῶν ἀριθμὸν ὡρῶν, ὃς ἐν τῷ μεταξὺ δυοῖν ἀρχῶν γίνεται παροξυσμὸς, ἐπισκέπτου πότερον μετρεῖ τὸν ἐν τῷ διαγράμματι περιεχόμενον ἀριθμὸν ὁντιναοῦν. ἦσαν δ’ ἐκεῖνοι κατὰ πολλαπλασιασμὸν ὡρῶν εἰκοσιτεσσάρων γενόμενοι. ἵνα οὖν χωρὶς διαγράμματος αὐτὸς εὑρίσκῃς ἐπὶ δακτύλου τοῦτο, ταυτὶ πρᾶττε. τοῦ μὲν ἓξ καὶ ὀκτὼ προβληθέντος, εὐκαίρως ἂν εὕροις τέσσαρας μὲν ἀμφημερινοὺς γιγνομένους, ὅταν ἓξ ὡρῶν προβεβλημένη περίοδος ᾖ· τρεῖς δ’, ὅταν ὀκτώ. τοῦ δ’ ἑπτὰ προβληθέντος, ἤ τινος ἄλλου τῶν μὴ μετρούντων τὸν τῶν εἰκοσιτεσσάρων ὡρῶν ἀριθμὸν, ἐπισκέπτου πότερον ἔχει τι μέρος ὁ προβληθεὶς, ἢ οὐδὲν, ὅτι μὴ τὴν μονάδα. εἰ μὲν ἔχει τι παρὰ τὴν μονάδα μέρος ἄλλο, καθάπερ ὁ μὲν ἐννέα τὸ τρίτον, ὁ δὲ πεντεκαίδεκα τὸ τρίτον τε καὶ τὸ πέμπτον, ἐπισκέπτου ποῖον αὐτοῦ τῶν μερῶν κοινόν ἐστι πρὸς τὸν τῶν εἰκοσιτεσσάρων. εὐθέως γοῦν τρίτον μὲν ὁ τῶν εἰκοσιτεσσάρων ὡρῶν ἀριθμὸς ἔχει, πέμπτον δ’ οὐκ ἔχει, καθάπερ ὁ τῶν πεντεκαίδεκα. ἐὰν μὲν οὖν προβεβλημένη περίοδος ὡρῶν  ἐννέα τύχῃ, τὸ τρίτον μὲν ταύτης λήψῃ, τὸ τρίτον δὲ καὶ τῶν κδ΄ τὰ ὀκτὼ,3 καὶ φήσεις ὀκτὼ τύπους εἶναι τρισὶν ἡμέραις περιγραφομένους. ἠξίουν δέ σε μεμνῆσθαι τοὺς τοιούτους τύπους τεταρταίους ὀνομάζεσθαι. εἰ δὲ ιε΄ ὡρῶν περίοδος εἴη, τῶν μὲν ιε΄ τὸ τρίτον λαβὼν, πένθ’ ἡμερῶν εἶναι τοὺς τύπους, ὅπερ ἐστιν ἑκταίους· τῶν δὲ κδ΄ ἐπειδὴ καὶ τούτων τὸ τρίτον ὀκτὼ γίγνεται, τοσούτους ἐρεῖς εἶναι καὶ τοὺς ἑκταίους τύπους· εἰ δὲ μηδὲν μόριον ὁ προβεβλημένος ἀριθμὸς ᾖ,4 οἷός πέρ ἐστιν ὁ ζ΄, κδ΄ ὀγδοαίους.

​These things having already been written, and having been distributed to some of the companions, or others having demanded to learn how it stands with the diagram, I immediately answer to those who pose the questions the multitude of the types. Therefore, the method is not of some other kind, but subordinate to the former one. And you yourself will be convinced that it is so, if you first recall and always keep handily in your memory of them, that in this context we call “day” the time composed of both day and night, which some address as a “nychthemeron” (night-and-day). In this way, at any rate, we also say that the year is of three hundred and sixty-five days and a quarter. Thus, of one day there are twenty-four hours, and of two, forty-eight, and of three, seventy-two; but the names for the types are not from the completed days, but from the recurrence of the paroxysm. For we call “tertian” that in which the paroxysm occurs every third day, with two days clearly having been completed in between; and “quartan” that in which it occurs on the fourth day, with three days completed in between in addition to this; and analogously for the others; so that when you find a period of a type to be of four days, you will call it a “quintan”, for it is not the same thing to have paroxysms every fifth day and to have a period of five days. Having put these things, therefore, in your memory, recall for me again the method mentioned before regarding the diagram. And it was said that you should examine whether the presented number of periodic hours, which is the paroxysm that occurs between two beginnings, measures any number contained in the diagram. And those [numbers] had arisen according to the multiplication of twenty-four hours. Therefore, in order that you yourself may find this on your fingers without a diagram, do these things. When six and eight are presented, you would easily find that four quotidian [fevers] arise when the presented period is of six hours, and three when it is of eight. But when seven is presented, or any other of those which do not measure the number of twenty-four hours, examine whether the presented [number] has any part (divisor), or none except for the unit. If indeed it has some other part besides the unit—just as nine has a third, and fifteen a third and a fifth—examine which of its parts is common to that of twenty-four. Immediately, at any rate, the number of twenty-four hours has a third, but it does not have a fifth, as that of fifteen [does]. If, then, the presented period happens to be of nine hours, you will take the third of this, and the third of twenty-four, which is eight, and you will say that there are eight types circumscribed by three days. And I requested you to remember that such types are called “quartans”. And if the period is of fifteen hours, taking the third of fifteen, you will say that the types are of five days, which is “sextans”; and since the third of twenty-four is also eight, you will say that there are also this many sextan types; and if the presented number has no part [in common], just as seven is, there will be twenty-four “octans”.

Syntax notes4 items
  1. 7ὅπως ἂν ᾖ τοῦ διαγράμματος

    An indirect question clause introduced by the conjunction ὅπως. The verb ᾖ combined with the genitive τοῦ διαγράμματος indicates the state or condition of the diagram ("how it stands with the diagram," similar to the usage of ἔχῃ with genitive).

  2. 7δυοῖν μεταξὺ δηλονότι καὶ συμπληρωθεισῶν

    A genitive absolute construction in the feminine plural with an implied noun ἡμερῶν ("days"). The preposition μεταξὺ governs the genitive and means "in between."

  3. 7τὸ τρίτον μὲν ταύτης λήψῃ, τὸ τρίτον δὲ καὶ τῶν κδ΄ τὰ ὀκτὼ

    Explains the calculation steps when the presented period is 9 hours. One takes a third of 9 (which is 3) and a third of 24 (which is 8). This deduces that there are 8 fever types contained within a 3-day (72-hour) period. A fever with a 3-day period (returning after a full 3 days) is called a "quartan" because the paroxysm occurs on the fourth day.

  4. 7εἰ δὲ μηδὲν μόριον ὁ προβεβλημένος ἀριθμὸς ᾖ

    The word μόριον here means a "common divisor" with 24. If the presented period (such as 7 hours) has no common divisor with 24 (i.e., they are coprime), the number of hours in a day, 24, directly becomes the number of types, and the period becomes 7 days (an "octan").

Translated by Gemini 3.5 Flash (published 2026-05-22)urn:cts:greekLit:tlg0057.tlg049.humanitext-grc1:7#1