I have trouble interpreting the following excerpt:

“Against the first of these three positions militate the following arguments. If we imagined [the earth] removed towards the zenith or the nadir of some observer, then, if he were at sphaera recta, he would never experience equinox, since the horizon would always divide the heavens into two unequal parts, one above and one below the earth…”

For context, when Ptolemy is speaking about “the first of these three positions…” he’s speaking about the position that holds that the Earth is equidistant from both poles of the celestial sphere, but is not on the axis spanning between both poles.

He states that he’s arguing against the first proposition, and suggests that if an observer were at sphaera recta (which I’ve taken to mean that the observer is at the equator with direction/horizon being perpendicular to the equator,) then he would never experience equinox because his “horizon would always divide the heavens into two unequal parts, one above and one below the earth…”

I assume that in this case, while the Earth is displaced from the center of the celestial sphere, the Sun is still orbiting the true center. However, if it was equinox, and the Sun was orbiting on the same plane as the true center. Wouldn’t this observer still experience equinox because the Earth is still on the same plane as the true center?

Here’s the link to my source (page 41, chapter 6:) https://isidore.co/calibre/get/pdf/Ptolemy%26%2339%3Bs%20Almagest%20-%20Ptolemy%2C%20Claudius%20%26amp%3B%20Toomer%2C%20G.%20J__5114.pdf

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    $\begingroup$ Just fyi, there is also a History of Science and Mathematics Stackexchange site hsm.stackexchange.com $\endgroup$
    – uhoh
    Dec 18, 2017 at 3:52
  • $\begingroup$ It does not simply means that Earth axis is tilted? The meaning of .....could not be displaced from .... is unclear to me but perhaps sphera recta means rotating about the axis joining the celestial poles $\endgroup$
    – Alchimista
    Dec 18, 2017 at 9:31

1 Answer 1


When I can’t understand a written statement, I try to picture it. I have thus created an animation which shows why Ptolemy’s statement is true. It is at https://ecliptiqc.ca/notlr.php (sorry, since it’s not a GIF, I can’t seem to be able to paste it here).

You understood properly that sphera recta means the equator. So, Ptolemy’s statement supposes that the Earth is moved “left or right” along the equatorial plane of the celestial sphere—in my animation, Earth is right of center. You will see that the Sun (moving white disk) spends more time in the left part of the graph than in the right part: night would be longer than day for an observer located at the yellow dot.


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    $\begingroup$ FWIW, you can post SVG here. It can even use SMIL animation (eg chat.stackexchange.com/transcript/message/57685856#57685856 ), but not JavaScript. You can't upload SVG to Imgur, so you have to host it yourself (or put it on Github, etc). $\endgroup$
    – PM 2Ring
    Jun 15, 2023 at 7:09
  • $\begingroup$ Good to know, thank you! I have yet to master SVG animation for nonlinear movements, so I did it with JavaScript for now, but I’ll know for next time. $\endgroup$ Jun 15, 2023 at 15:43

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