Tracing the history of medieval astronomy
Having gotten our preliminary estimate for the eccentricity and position of apogee
let us investigate the differences which can be derived from them in the ecliptic arcs which we week to determine at each of the oppositions [in turn].
In this post, we’ll cover Ptolemy’s method for the first opposition. Continue reading “Almagest Book X: Correction for Equant – First Opposition”
In the last post, we began the process of determining Mars’ eccentricity and the position of apogee. The technique is fundamentally similar to the three eclipse method used for the moon, but the presence of the equant is throwing a wrench in things. Specifically, in that previous post we showed that an line extended through the observer from one of the observations did not have a length of $120^p$ which affirmed that the observer was still off center.
So in this post, we’ll use that information to determine how far off center so that we can complete the task we set about. Continue reading “Almagest Book X: Preliminary determination of Mars’ Apogee & Eccentricity – Part 2”
Having completed the preliminary models for the inferior planets, Mercury and Venus, Ptolemy now turns his attention towards the superior ones: Mars, Jupiter, and Saturn. Continue reading “Almagest Book X: Preliminary Comments Regarding the Models for Superior Planets”
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. Continue reading “Almagest Book X: Venus’ Epoch Position”
Continuing with our process of finding the position of Venus about the epicycle at two widely discrepant points in time, we’ll now look at one from Timocharis. Continue reading “Almagest Book X: Position of Venus About the Epicycle on Oct 10/11 271 BCE”
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 eccentre1. 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 perigee1.
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”