Almagest Book X: The Location of Venus’ Apogee

Despite the second chapter of Book X ostensibly being about the epicycle of Venus, Ptolemy instead continues discussing the line of apsides. Specifically, we determined that the line of apsides runs through the points $25º$ into Taurus and Sagittarius, but have not determined which is the apogee and which is the perigee2.

In this post, we’ll follow along as Ptolemy determines which of these two points is which. Continue reading “Almagest Book X: The Location of Venus’ Apogee”

Almagest Book IX: Position of Mercury About Epicycle 139 CE, May 17/18

One of the biggest keys to understanding the model of Mercury3, is that the eccentre which drives the main motion4, is tied to the motion of the sun. Again, we can see this by comparing the values in the mean motion table for this rotation to those of the sun and seeing they’re identical.

However, we’ll also need to contend with the motion of the second eccentre which controls Mercury’s distance. We’ve talked a fair bit about this, but now it’s time to start seeing how it impacts the basic motion and anomaly. In short, it will offer a “correction” to these. So let’s get started. Continue reading “Almagest Book IX: Position of Mercury About Epicycle 139 CE, May 17/18”

Almagest Book IX: The Eccentricities of Mercury

Now that Ptolemy has explained why the eccentric eccentre on which the center of the epicycle resides is necessary, Ptolemy informs us

we have still to demonstrate the position of the point on $\overline{AB}$ about which takes place the annual revolution of the epicycle in uniform motion towards the rear with respect to the signs, and the distance from $Z$ of the centre of that eccentre which performs its revolution in advance in the same period [as the previous].

In other words, it’s time to start figuring out all the parameters to calibrate Mercury’s model. In this post, we’ll explore the various eccentricities. Ptolemy has previously told us that they’re all equal, but now he will demonstrate this. Continue reading “Almagest Book IX: The Eccentricities of Mercury”