<p>In his <em>Mathematical Syntaxis</em> (better known as the <em>Almagest</em>), 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.</p>
<p>While Ptolemy lived ≈ 300 years after Hipparchus, it is reasonable to think that similar instruments were available and in use back then.</p>
<p><a href="https://i.sstatic.net/VeTIU.png" rel="noreferrer"><img src="https://i.sstatic.net/VeTIU.png" alt="Plinth" /></a></p>
<p>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.</p>
<p><a href="https://i.sstatic.net/xyCpB.png" rel="noreferrer"><img src="https://i.sstatic.net/xyCpB.png" alt="Parallactic instrument" /></a></p>
<p>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.</p>
<p><a href="https://i.sstatic.net/d07TE.png" rel="noreferrer"><img src="https://i.sstatic.net/d07TE.png" alt="armillary sphere" /></a></p>
<p>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.</p>
<p>(All images by me using Adobe Illustrator, Adobe Dimension, and Adobe Photoshop. © 2022 EcliptiQc / Pierre Paquette.)</p>

CC BY-SA 4.0
2023-12-13T22:01:13.130Z
The images are nice, however, especially the third image seems to depict an instrument that is much more modern than I would expect.  Is there any way to depict or reference a historical version of this spherical instrument?
JosephDoggie
CC BY-SA 4.0
2023-12-14T00:53:26.320Z
@JosephDoggie: It is perfectly in line with what Ptolemy explains in the Almagest. Sure, it’s most likely more polished than his version, but it is not impossible that he had one just like that. The instrument was invented by Eratosthenes (c. 276 BCE – c. 195/194 BCE).
Pierre Paquette
CC BY-SA 4.0
2023-12-14T03:57:45.557Z
@JosephDoggie Here are some simpler armillary spheres, used as sundials: http://www.johnclosesundials.co.uk/products/sundials-armillary-spheres/
PM 2Ring
CC BY-SA 4.0
2023-12-17T22:09:43.807Z
That armillary sphere looks like child's play compared to the Antikythera mechanism, which is dated to about 100 years before Ptolemy.  So, I'd say it's definitely doable, as it's just four brass rings.
Greg Miller
CC BY-SA 4.0
2023-12-18T19:28:19.227Z
@GregMiller: Well, it’s not “just four brass rings,” as they need to be perfectly orthogonal to each other, but indeed, it’s a much simpler principle than the Antikythera mechanism.
Pierre Paquette
CC BY-SA 4.0
2023-12-13T01:00:12.810Z
2023-12-13T01:00:12.810Z
Pierre Paquette
<p>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.</p>
<p>What I don't know about are the practicalities of:</p>
<ol>
<li>What tools one uses to perform these measurements,</li>
<li>How those tools are built and calibrated,</li>
<li>How the user aligns with the proper coordinate system</li>
<li>And how one arranges the lighting so that one can take notes while still looking at the stars.</li>
</ol>
<p>(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.</p>
<p>From Wikipedia:</p>
<blockquote>
<p>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.</p>
</blockquote>

CC BY-SA 4.0
2023-12-13T00:46:33.827Z
You may be interested in History of Science and Mathematics.SE
Nilay Ghosh
CC BY-SA 4.0
2023-12-13T09:12:52.677Z
@NilayGhosh Thanks for the pointer! I'll check it out.
user326210
<history><resource-request>
How did the ancient Greeks measure celestial angles?
user326210
# How did the ancient Greeks measure celestial angles?

(Asked by: username_0 on 2023-12-12)

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.

**Tags:** history, resource-request
> **Comments:**
> **username_1**: You may be interested in History of Science and Mathematics.SE  
> **username_0**: @NilayGhosh Thanks for the pointer! I'll check it out.  

---

## 1 answers

### Answer by username_2 on 2023-12-13. Score: 30 | Accepted answer

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.

[![Plinth](https://i.sstatic.net/VeTIU.png)](https://i.sstatic.net/VeTIU.png)

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.

[![Parallactic instrument](https://i.sstatic.net/xyCpB.png)](https://i.sstatic.net/xyCpB.png)

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.

[![armillary sphere](https://i.sstatic.net/d07TE.png)](https://i.sstatic.net/d07TE.png)

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.

(All images by me using Adobe Illustrator, Adobe Dimension, and Adobe Photoshop. © 2022 EcliptiQc / Pierre Paquette.)

> **Comments:**
> **username_3**: The images are nice, however, especially the third image seems to depict an instrument that is much more modern than I would expect.  Is there any way to depict or reference a historical version of this spherical instrument?  
> **username_2**: @JosephDoggie: It is perfectly in line with what Ptolemy explains in the Almagest. Sure, it’s most likely more polished than his version, but it is not impossible that he had one just like that. The instrument was invented by Eratosthenes (c. 276 BCE – c. 195/194 BCE).  
> **username_4**: @JosephDoggie Here are some simpler armillary spheres, used as sundials: http://www.johnclosesundials.co.uk/products/sundials-armillary-spheres/  
> **username_5**: That armillary sphere looks like child's play compared to the Antikythera mechanism, which is dated to about 100 years before Ptolemy.  So, I'd say it's definitely doable, as it's just four brass rings.  
> **username_2**: @GregMiller: Well, it’s not “just four brass rings,” as they need to be perfectly orthogonal to each other, but indeed, it’s a much simpler principle than the Antikythera mechanism.  

---

