As this project has progressed, I’ve picked up a number of books related to it. So others can know what I’ve read (and have available should they be interested in reading them themselves), I’ve compiled a list of the books in my medieval astronomy library, as well as some other excellent books on historical astronomy. Continue reading “My Library”
Instrumentation – The Great Quadrant: Day 9
We’re getting very close to the end of construction, so it’s the point where it’s down to a lot of small details. To start, here’s a better picture of the axle assembly:
I’d shown a picture last time, but today, we added a brass fitting to help tighten the portion that goes through the central column, and using a pipe wrench, tightened the portion that will go through the arm so it cannot rotate, forcing the quadrant arm to rotate on it whereas during the test assembly last time, the arm caused the axle itself to turn. The cap on the end still goes on finger tight so it can easily be removed to disassemble the instrument for transport. Continue reading “Instrumentation – The Great Quadrant: Day 9”
Instrumentation – The Great Quadrant: Day 8
It’s said that a project involves blood, sweat, and tears. Today was two of the three. Somehow have managed not to get splinters till today, but got a pretty good one. It was also hot in the workshop:
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Almagest Book I: Table of Inclinations
In the last post, we derived a method to calculate the angle between the celestial equator and ecliptic and generalized it to be applicable for any angle. Here, I present the table derived from those calculations.
Almagest Book I: The Arcs Between the Equator and Ecliptic
Before going on the several post detour in developing several theorems and making extra sure we understood a few, we stated the goal was to determine the length of an arc at various points between the celestial equator and ecliptic1.
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Exploring Menelaus’ Theorem
In the last post, we used several theorems we’d developed to arrive at Menelaus’ theorem. However, at the very end Ptolemy simply mentions another version of the theorem, but does not derive it. I simply took his word that it worked, but as that alternative form is used first thing in the next chapter, I want to make sure at the very use, we know how to use it, even if we don’t go through how it’s derived.
First, let’s set up a generic Menelaus configuration on a sphere which is the intersection of the arcs of four great circles:
Instrumentation – The Great Quadrant: Day 7
With the upper portion of the base ready to hold the center column, today’s focus was on getting a socket for the center column to rest in. To start, we created a set of cross beams.
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Almagest Book I: Menelaus’ Theorem
So far in these preliminary theorems, we’ve looked at some that were based on triangles and some that were based on circles. We’ll be going one step further with this next one and work with spheres. Thus far, we’ve briefly touched on spheres in this post discussing the celestial sphere. If great circles and spherical triangles aren’t familiar to you, I suggest reading over that post.
But since this is the first time we’ve encountered math in 3D if you’ve been following along, I want to build this up more slowly2 and will be trying to add some 3D elements to make the visualization a bit easier.
[L]et us draw the following arcs of great circles on a sphere: BE and GD are drawn to meet AB and AG, and cut each other at Z. Let each of them be less than a semi-circle.
Almagest Book I: Circular Lemmas for Spherical Trigonometry
As noted in the previous Almagest post, I wanted to break this next set of lemma off because they use a new mathematical term: Crd arc.
The term is very simple. In fact, the name’s on the tin. It refers to the chord subtended by a specific arc. So let’s dive right in to the next proof and see how it’s used:
Continue reading “Almagest Book I: Circular Lemmas for Spherical Trigonometry”
Data: Summer Solstice Solar Altitude
Happy Summer Solstice everyone!
Since one of the things Ptolemy was concerned with was the angle between the ecliptic and celestial equator, I built a solar angle dial to help determine this. Given that the measurements needed to be taken on the solstices (or a solstice and equinox), I set up the instrument today to take the measurement.
