Tracing the history of medieval astronomy
Today’s focus was on starting to build the discs that would allow the central column to rotate.
The central column is 4.75″ square (a roughly 6.75″ diagonal), so we decided to cut an 8″ disc as well as a 9″ disc which would lay over it.
Continue reading “Instrumentation – The Great Quadrant: Day 6”
Since the solstice is only a few weeks away, I decided it might be fun to make Ptolemy’s solar angle dial we recently saw.
Continue reading “Instrumentation – Ptolemy’s Solar Angle Dial”
With the quadrant itself pretty much complete (aside from the scale), it was time to start working on something to mount it on. So today we started with the central column which was assembled from plywood to make a 5″ box that was 8′ tall.
Continue reading “Instrumentation – The Great Quadrant: Day 5”
Our next task is to demonstrate the sizes of the individual arcs cut off between the equator and the ecliptic along a great circle through the poles of the equator. As a preliminary we shall set out some short and useful theorems which will enable us to carry out most demonstrations involving spherical theorems in the simplest and most methodical way possible.
In opening the next chapter in Book 1, Ptolemy again gives us a goal to work towards, namely, the length of the chord shown in solid red below1.
But before we do that, we’re going to have to lay out some lemma2 to get us there. There’s going to be several, but for this post, I’m only going to address the first two which come from triangles, whereas the remaining involve circles and a bit of new notation that I’ll want to introduce before getting into them. Continue reading “Almagest Book I: Triangular Lemmas for Spherical Trigonometry”
As Ptolemy begins building his model of the celestial sphere, there are a few fundamental values that will need to be known. One of them is the angle between the celestial equator and the ecliptic (denoted in the below diagram as $\angle{\theta}$.
Continue reading “Almagest Book I: Angle Between Celestial Equator and Ecliptic”
The goal in the next chapter in the Almagest, Ptolemy’s goal is to is to find the angle between the celestial equator and ecliptic. These are both features on the celestial sphere which, while fundamental to astronomy, are not terms we’ve yet explored (aside from a brief mention in the first chapter of Astronomia Nova). So before continuing, we’ll explore the celestial sphere a bit. In addition, if we’re to start measuring angles on that sphere, we will need to understand the coordinate systems by which we do so. Continue reading “Introduction to the Celestial Sphere & Astronomical Coordinates”
Here displayed in all its glory is Ptolemy’s Table of Chords. Notes to follow.
Continue reading “Almagest Book I: Ptolemy’s Table of Chords”
To get at the chord length for an angle of $\frac{1}{2}$º, Ptolemy makes use of a proof from Aristarchus. It starts with this diagram:
If you’ve been following the Almagest posts, you’ll recall that we’ve done some work to derive the chord lengths of various angles. But Ptolemy’s goal is to derive the chord length for every angle between 0-180º in $\frac{1}{2}$º intervals. To do that, we’re going to have to develop some new tools using Ptolemy’s theorem on the angles we already know in order to add, subtract, and divide them. These new tools are referred to as corollaries since they come from applications of Ptolemy’s theorem.
The first one comes from the following diagram:
Continue reading “The Almagest – Book I: Corollaries to Ptolemy’s Theorem”
With the lattice finished the goal today was to put the edging and scale on and clean things up.
To start, we inserted some additional horizontal supports along the outer arms:
Continue reading “Instrumentation – The Great Quadrant: Day 4”