Tracing the history of medieval astronomy
Now that we’ve worked out the basic parameters of Venus’ epicycle and eccentre, we’ll need to determine the motion about the epicycle1.
As we did for Mercury, we’ll determine the position at two points in time and then use that to calculate the speed. In this post, we’ll concentrate on determining the position for the first of these observations. Continue reading “Almagest Book X: Position of Venus About the Epicycle on Dec 15/16 138 CE”
Now that we’ve sorted out the size of the epicycle, Ptolemy next step will be to determine the point about which the eccentre rotates as he doesn’t want to assume it rotates about the center of the eccentre2. Continue reading “Almagest Book X: The Equant of Venus”
Now we’ll turn our attention to finding the size of Venus’ epicycle. Fortunately, the lack of the extra sphere that Mercury had will make this much easier. Continue reading “Almagest Book X: The Size of Venus’ Epicycle”
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 perigee3.
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”
Having laid out the model for all of the planets in the last book, Ptolemy is ready to dive right into Venus without much for exposition. However, Ptolemy immediately runs into problems. Continue reading “Almagest Book X: The Apogee of Venus”
Now that we’ve worked out the system and the position of Mercury about the epicycle on two dates, we can use this to rewind and find the state of the system at the epoch time. Continue reading “Almagest Book IX: Mercury’s Epoch Positions”
Having determined the position of Mercury about its epicycle in Ptolemy’s time, he now sets out to do the same for an ancient observation so that the can determine the rate Mercury moves about the epicycle.
Here’s the observation: Continue reading “Almagest Book IX: Position of Mercury About Epicycle 264 BCE Nov 14/15”
This post will serve as an index to posts about individual manuscripts of the Almagest that I have reviewed and included in my comparative version of the Star Catalog. Continue reading “The Almagest Star Catalog Manuscripts – Index”
One of the biggest keys to understanding the model of Mercury4, is that the eccentre which drives the main motion5, 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”
Ptolemy’s next goal will be to determine the apparent size of the epicycle when at one of its two perigees. To do so, he sets up the following diagram: Continue reading “Almagest Book IX: Apparent Size of the Epicycle”