And what exactly would that knowledge entail? According to the wikipedia article (https://en.wikipedia.org/wiki/Fertility_awareness) most signs were discovered in the 20th century, but it also talks about St. Augustine mentioning periodic abstinence to avoid pregnancy. Can anyone provide more information?
Well, of course many of them would not have known before my collection of all the knowledge in the Empire of our beloved emperor Vespasianus, long may he reign, in my well known encyclopaideia, the history of the natural world. In fact, I have gathered many strange and interesting phenomena about the female menstruation! Did you know that menstrual blood can reportedly have the most peculiar effects? It turns new wine sour, it can make crops barren, fruits fall of the trees when touched by it, and even whole hives of bees have been known to die! (see book VII, 15)
I should probably warn you also, if you didn't know this already, that intercourse with a menstruating woman during a solar or lunar eclipse, or when moon and sun are in conjunction, can and probably will kill you (see book XXVIII, 23).
Now, where was I? Ah, yes, conception! Well, it has long been understood that blood is necessary for the generation of new life. Aristotle informs us how the female blood quickened by the male sperm (which is the highest form of blood, cooked to its very essence - which women can't do, owing to their lower body temperature) will bring forth new life. You can read about this in particular in his Generation of Animals. Thus, when menstruation stops in their 40th or 50th year, they are no longer fertile.
In any case, almost all my contemporaries agree with me^1 in that the chances for conception are the highest shortly after the beginning and towards the end of the menstrual cycle (book VII, 67).