Tracing the history of medieval astronomy
Now that we’ve done a bit of preliminary theory, we’re ready to jump into an example problem. As with before, Ptolemy selects Rhodes at a latitude of 36º. Since we’ve been seeing several of the same diagrams here, I’m going to forego the buildup and give a mostly completed diagram:
Continue reading “Almagest Book II: Calculation of Rising Times at Sphaera Obliqua”
This weekend was Crucible at the Crossroads here in my home Barony of Three Rivers. I taught two classes, one on a general overview of medieval astronomy, and one introducing practical observational astronomy. In addition, it was the autumnal equinox on Saturday, so some minor adjustments were made to the quadrant to allow for solar angle observations. Lastly, I was called up in court for a few awards related to the project.
More on all of that beneath the fold. Continue reading “Data: Stellar Quadrant Observations – 9/22/18 (Crucible at the Crossroads)”
In this next chapter, Ptolemy’s goal is to
show how to calculate, for each latitude, the arcs of the equator… which rise together with [given] arcs of the ecliptic.
To do this, we’ll do a bit of convenient math, breaking the full ecliptic into its traditional 12 parts. However, since these signs are not of equal size, Ptolemy takes an even 30º for each sign, beginning with Aries, then Taurus, etc…
The first goal will be to prove that
arcs of the ecliptic which are equidistant from the same equinox always rise with equal arcs of the equator.
First off, what’s a gnomon?
Apparently it’s the part of a sundial that casts shadows. Now you know.
To start this next chapter, Ptolemy dives straight into a new figure, but I want to take a moment to justify it first. To begin, let’s start with a simple diagram. Just a side view of the meridian, the horizon, and the north celestial pole. The zenith is also marked (A).
Continue reading “Almagest Book II: Ratio of Gnomon Equinoctial and Solsticial Shadows”
The fourth chapter in book two is a very short one. In fact, it’s a single paragraph so I almost didn’t dedicate an entire post to it but ultimately decided to as it didn’t really fit with either the previous or next chapter.
In this, Ptolemy says,
it is a straighforward computation to determine for what regions, when, and how often the sun reaches the zenith. For it is immediately obvious that for those beneath a parallel which is farther away from the equator than the 23;51,20º (approximately), which represents the distance of the summer solstice, the sun never reaches the zenith at all, while for those beneath the parallel which is exactly that distance, it reaches the zenith once a year, precisely at the summer solstice.