Tracing the history of medieval astronomy
In our last post, I noted that Ptolemy had identified the line of apsides, but was very careful not to state which point was the apogee and which was the perigee. He’s now ready to start looking into that:
In accordance with the above, we investigated the size of the greatest elongations which occur when the mean longitude of the sun is exactly in the apogee, and again, when it is diametrically opposite that point.
Continue reading “Almagest Book IX: Mercury’s Double Perigee”
Having demonstrated the conceptual model, Ptolemy now turns to determining
in what part of the ecliptic Mercury’s apogee lies by the following method. Continue reading “Almagest Book IX: The Line of Apsides of Mercury”
Now that we’ve demonstrated that the equation of anomaly is symmetric about the line of apsides for the general model, we’ll demonstrate the same for Mercury’s model. Or, as Ptolemy puts it,
we must prove that in this situation too the angles of the equation of ecliptic anomaly [are equal].
We’ll start by producing a diagram based on Mercury’s particular model. Continue reading “Almagest Book IX: Symmetries in Mercury’s Planetary Model”
Now that we’ve laid out the models for the planets except Mercury and the special case for Mercury, Ptolemy revisits them to explore some symmetries. We’ll start with the ones for the model for the planets other than Mercury first.
To start, let’s produce a new diagram based on that model. As usual, I’ll break up Ptolemy’s description into several steps to help make it a bit more digestible. Continue reading “Almagest Book IX: Symmetries in the General Planetary Model”
The recurrent nova T CrB is likely to erupt again in the early spring of next year. This nova has an $\approx 80$ year long cycle and only lasts for about a week, making it an extremely rare event to catch. Thus, it’s no surprise that we only had reliable records for the two most recent eruptions.
But research from Dr. Bradley Schaefer indicates that there may be two historic accounts of this star during its eruption including one in a medieval chronicle.
I’ve written more about this research over at Universe Today.
Recently a series of historic astronomy papers came to my attention claiming and refuting the notion that the decline of the Hopewell Native America community in the $3^{rd}$ or $4^{th}$ century.
I’ve written a summary as an article over at Universe Today. It’s an interesting discussion so give it a read!
Now that we’ve taken the time to understand the model for the four planets other than Mercury, let’s start on the model for Mercury as that’s the focus of the remainder of this book.
Let the eccentre producing the anomaly be $ABG$ about centre $D$, and let the diameter through $D$ and centre $E$ of the ecliptic be $\overline{ADEG}$, [passing] through the apogee at $A$. Continue reading “Almagest Book IX: Model for Mercury”
Having thoroughly discussed what anomalies Ptolemy wants his model to account for as well as what hypotheses1 he intends to use for each, Ptolemy is ready to start laying out the basic models. Ultimately, there will be two models. One for the four planets other than Mercury, and a special one for Mercury.
In this post, we’ll explore the first of these models. Continue reading “Almagest Book IX: Model for Planets Other than Mercury”
Now that these [mean motions] have been tabulated, our next task is to discuss the anomalies which occur in connection with the longitudinal positions of the five planets.
Having derived the mean and anomalistic motions, Ptolemy now turns to exploring the anomalies in more depth (as there’s going to be two of them), in order to derive the parameters necessary for configuring the model’s scale. Continue reading “Almagest Book IX: Preliminary Notions”
This week I completed the addition of another manuscript of the Almagest to my collection. This is the Cambridge MS 32 manuscript. And it’s very interesting.
This manuscript doesn’t have a lot of information on it. It’s one I stumbled across when doing some other research and was not included in Peters & Knobel’s work.
The Cambridge website itself gives precious little information. The manuscript itself is a composite, written by at least two hands, most likely in the early $16^{th}$ century. However, no information is given on the lineage of this manuscript, but we’ll shed some light on this here shortly.
Continue reading “The Almagest Manuscripts – Cambridge MS 32”