In the last Almagest post, Ptolemy explained that for the models of the superior planets, we’ll be needing to use oppositions. So with that explained, we’ll begin by working to develop the model for Mars by looking at its eccentricity and apogee. However, this isn’t going to be nearly as straightforward as it has been previously. As we’ll see, we’re missing some of the angles and arcs that would be needed for this. Thus, Ptolemy is going to use an iterative method to close in on them. Continue reading “Almagest Book X: Observations and Introduction to Iterative Calculations for Apogee and Eccentricity”
The Almagest Manuscripts – Vatican Graecus 1594
I have finished my review of the Vatican Graecus $1594$ manuscript and it is available in my Google Doc. If you’d like to view the original manuscript, it can be found here, starting on $155r$1.
Discussion of this catalog below the fold. Continue reading “The Almagest Manuscripts – Vatican Graecus 1594”
Almagest Book X: Preliminary Comments Regarding the Models for Superior Planets
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”
Almagest Book X: Venus’ Epoch Position
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”
Almagest Book X: Position of Venus About the Epicycle on Oct 10/11 271 BCE
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”
Almagest Book X: Position of Venus About the Epicycle on Dec 15/16 138 CE
Now that we’ve worked out the basic parameters of Venus’ epicycle and eccentre, we’ll need to determine the motion about the epicycle2.
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”
Almagest Book X: The Equant of Venus
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 eccentre3. Continue reading “Almagest Book X: The Equant of Venus”
Almagest Book X: The Size of Venus’ Epicycle
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”
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 perigee4.
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 X: The Apogee of Venus
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”