Now that we’ve worked out the mean speed of Venus about the epicycle, we can now determine where it was on the epoch date.
Ptolemy again uses the observation from Timocharis. He gives the time between the epoch date and that observation as a period of $475$ Egyptian years, $346 \frac{3}{4}$ days.
Looking up the appropriate intervals in the mean motion table for Venus in the anomaly column, I find an increase of $180;59º$ which Ptolemy rounds to $181º$.
At the time of the observation from Timocharis, we determined Venus to be at a position of $252;07º$ past apogee. Thus, if we subtract $181º$ from this, we find that Venus was at $71;07º$ at the time of epoch.
Meanwhile, Ptolemy reminds us that the mean position is, based on our model, the same as that of the sun, or $0;45º$ in Pisces at the epoch time.
Additionally, the apogee would have moved at the same rate as the precession of the equinoxes ($1º$ per $100$ years) which means, in that interval of time, it would have increased $4 \frac{3}{4}º$ and thus had a position, at epoch, of about $16;10º$ into Taurus.
