# How did the ancient Greeks measure celestial angles?

I'm reading about how Hipparchus measured the earth's precession; I basically understand the theory involved—you wait for a lunar eclipse, which allows you to infer the sun's position exactly, at night when the stars are out. I understand that you measure the angle between the sun and a nearby identifiable star, and if you check those angles a century later, you'll find that they've shifted.

What I don't know about are the practicalities of:

1. What tools one uses to perform these measurements,
2. How those tools are built and calibrated,
3. How the user aligns with the proper coordinate system
4. And how one arranges the lighting so that one can take notes while still looking at the stars.

(Basically, the sorts of things I would need to know if I wanted to re-enact Hipparchus's measurements using no modern equipment.) I'm curious about the answers to these questions, and especially about references that I could use to learn more in depth about the practicalities of these measurements.

From Wikipedia:

Hipparchus gave an account of his discovery in On the Displacement of the Solsticial and Equinoctial Points (described in Almagest III.1 and VII.2). He measured the ecliptic longitude of the star Spica during lunar eclipses and found that it was about 6° west of the autumnal equinox. By comparing his own measurements with those of Timocharis of Alexandria (a contemporary of Euclid, who worked with Aristillus early in the 3rd century BC), he found that Spica's longitude had decreased by about 2° in the meantime.

• You may be interested in History of Science and Mathematics.SE Commented Dec 13, 2023 at 0:46
• @NilayGhosh Thanks for the pointer! I'll check it out. Commented Dec 13, 2023 at 9:12

In his Mathematical Syntaxis (better known as the Almagest), Ptolemy details the construction of three instruments: the plinth, the parallactic instrument, and another which he calls “astrolabe” but is now known as an armillary sphere.

While Ptolemy lived ≈ 300 years after Hipparchus, it is reasonable to think that similar instruments were available and in use back then.

The plinth (above) is simply a quarter of a circle drawn on a brick or piece of wood—we would nowadays call it a quadrant. A plumb bob helps level the instrument for observation. It is divided from 0° to 90° in increments of 1°, or better if the instrument is large enough.

The parallactic instrument (above), also known as the triquetrum in the Latin Middle Ages, is made up of two “arms” that pivot on a “mast,” one at the top, the other one at the bottom. The bottom part would slide on the top one until the celestial object was being pointed, and the position of intersection would be noted. The instrument would then be folded, and the angle would be read from the (previous) point of intersection on the vertical ruling. Such an instrument was used as late as by Copernicus.

The third instrument is the armillary sphere, although Ptolemy calls it an “astrolabe” (this word relates to a wholly different instrument). Ptolemy explains how to build it, with one ring representing the celestial equator, another the ecliptic, and another one, the meridian. Pins on the side would serve as sights, and the star’s coordinates could be read on the rulings.