Against Those Who Have Written on Disease Patterns

​Let one of them begin on the first day, and the other during the second night. A sixth pairing of two quintans: let one begin on the first day, and the other during the third night. A seventh pairing of two quintans: let one begin on the first day, and the other during the fourth night. These seven pairings, therefore, we have complicated, assuming that the former of the quintans begins on the first of the days. And again we shall make another seven, assuming that the former of them begins during the first night. If, then, we complicate the sextan with it in this way, it is obvious that the pairings will become more; and still more, when we complicate the septan, and still much more the octan, or indeed the decan, not to say anything about the twentieth-day, thirtieth-day, and fortieth-day [fevers], and as many besides these as were shown to follow of necessity from their hypotheses. Let those, therefore, be left aside for the present, and let our [discussion] proceed up to the decan. And first consider for me, how just now when the quintan becomes double, we spoke of the pairings, but if it should become triple, it is clear that another not small multitude of pairings arises. It is indeed possible for it to become even quadruple, with one paroxysm attacking on each day; and it would become quintuple if, during one night, a certain fifth [quintan] were mixed with the quadruple one, in addition to the four quintans mentioned, and this very thing again in four ways; for it can take its beginning either in the first night, or in one of those following, namely the second, or the third, or the fourth, or the fifth. And the same variety belongs to them also for the other types, and still more so according to those of them of more days. If, then, you complicate the whole variety of the quintan with that according to the sextan, you understand, I think, how great the multitude will be; and if you mix with them also the septan, or octan, or any of those following, and then again you make other pairings from four types thus complicated with one another, and then from five, and then again from more, I think you calculate how great the number of pairings will be, or how many books will be needed for the teaching of them. For what kind of weaving there will be according to them, I shall try to show you briefly, laying down this beginning for the discourse. First it will be necessary to go through the variety of pairings according to each of the types, as I showed a little before in the case of the quintan; after this to complicate them with one another, first indeed one pairing of those from the quintan, say, with one of those according to the sextan, so that from two pairings some other third arises, then in succession to complicate all with all, then in this way one with two, then with three, then with more, until you mix all the pairings of the complicated type with the one; and after this to mix two pairings of one type, [namely] of the quintan, with one of each of the others, then with two, or three, or four, until you complicate all with one another; then in this way again to mix four pairings with those according to each type, then five, and then six, until you mix all the pairings of the quintan with all those of the others, obviously not of all together, but of each individually, for example those of the quintan with those according to the septan, then in this way with those according to the octan, or the nonan, or the decan, or any of those following; then just as you mixed the quintan with each of the others, so now to mix the decan with each of the others, then the septan and the octan and the others. And when you do this, it will be necessary to complicate all the pairings of three types with all [the others], then of four, then of five, and then of six, then of seven, and so on in order, until we complicate all [the pairings] of all [the types]. And that there will be so great a multitude of pairings as to become countless myriads, I think anyone already understands, even if they are inexperienced in numbers. And one can also, by communicating the calculation to arithmeticians, hear from them the total. For if I should wish to demonstrate it now, I would need a book larger than those which these babblers wrote, they not having perceived that they touched on a ten-thousandth part of the complications, although they babbled much. If, then, they think that it is useful to complicate types with one another, let them know that they have found a ten-thousandth part of the useful; but if useless, let them, feeling shame at last, call Hephaestus to their books, or even if they themselves do not call [him], time will destroy them. For who else will still write from them? And who will not, cutting even these up already, consume them for daily needs?