It’s been awhile since I’ve posted anything on the Almagest. That’s mostly because I was at a nice stopping point and with the quadrant getting finished up and observations beginning, that stole my focus for awhile. But it’s finally time to jump into Book II. The first chapter in this book is just text. No math. So what does Ptolemy have to say?
First off, Ptolemy says the goal of this book is to
develop the more important theorems concerning sphaera obliqua.
To do that, Ptolemy starts getting into where we live on the globe. He imagines the world divided into fourths, cut in half by the equator, and then in half again by a plane passing through the poles. If that is the case, he posits that we live in one of the northern ones1. His reasoning is that shadows always point north. This implies the Sun is south of us2.
From there, Ptolemy proposes we study several places on the Earth
1. The distance of the poles of the first motion [i.e. the equator] from the horizon, or [in other words] the distance of the zenith from the equator, measured along the meridian.
2. Those regions where the Sun reaches the zenith, when and how often this occurs.
3. The ratios of the equinoctal and solstical noon shadows to the gnomon3.
4. The size of the difference of the longest and shortest day from the equinoctal day, and all other additional phenomena
5. The individual increases and decreases in the length of the days and nights
6. The arcs of the equator which rise or set with [given] arcs of the ecliptic.
7. The particulars and quantities of angles between the more important great circles.
A lot of those are mouthfuls and pretty hard to decipher. Hopefully, we’ll make more sense of them as we go through them although, looking ahead, it doesn’t look like we’ll be tackling them in order.
For those reading along with this walkthrough of the Almagest, I hope that was a nice break from the math, because we’re about to get back to it in the next chapter.
- At this point, peoples much south of Egypt were not known, so Ptolemy is certainly speaking to the Greco-Roman world.
- This reasoning is mostly true, but with an unmentioned caveat. If someone observes the Sun below the tropic of Cancer, the Sun is more northward in the Summer making the shadows point south. However, Alexandria, where Ptolemy lived, is at 31º N latitude and the tropic of Cancer is at 23.5º N, so he was safely outside this zone.
- This is the part of the sundial that casts a shadow. In practice, any object of fixed length which casts a shadow could be used.