# How do I typeset this symbol? (possibly astronomical)

I have an old text by CF Gauss (namely Disquisitio de elementis ellipticis Palladis, 1810) in which he uses the symbol in the picture.

It looks a lot like a boldface number 7, but he uses it as a variable name. Namely (if my translation is correct), the "average sidereal movement per day"

Does anyone know this symbol? Is it a standard astronomical symbol, or was it a made-up throwaway notation by Gauss? Furthermore, is there a LaTeX package for it?

It's on p. 119 in the link (German version of Latin text).

• Can you point to some source? – egreg Dec 23 '15 at 17:30
• It seems to a symbol for the angular velocity on a per-day-base – user31729 Dec 23 '15 at 17:32
• @JumpCow: From the context it's an angular velocity, but I've never seen it this way before. – user31729 Dec 23 '15 at 17:44
• @egreg -- i don't disagree, but if you compare the digit 7 in several different contexts on the linked pages, it's obvious that this instance is considerably wider than the others. since a metal font would have been used, i'd like to identify it, and will ask a knowledgeable font friend for assistance. – barbara beeton Dec 23 '15 at 18:43
• @barbarabeeton For reference, here is the Latin version of the symbol: this. It appears several time in Carl Friedrich Gauss Werke v.6 and v.7. – Francis Dec 23 '15 at 22:41

After some research in printed sources, I think this symbol is a variant of the Greek letter tau $\tau$.

Here is a quote from Hans Jensen, Die Schrift, 3rd printing, p. 459:

 Noch in modernen Drucken finden wir die Formen ϐθϖ3ϲ7, wo andere βϑπζςτ haben.


Note: I had to fake the zeta symbol with a digit 3 and the tau symbol with a digit 7 here. In German typesetting tradition the theta symbol ϑ is the preferred form, not the straight theta θ. The "ϲ" is the so-called lunate sigma from Unicode.

EDIT: Here is a digitised version of Carl Faulmann: Das Buch der Schrift. Enthaltend die Schriftzeichen und Alphabete aller Zeiten und aller Völker des Erdkreises. Verlag der kaiserlich königlichen Staatsdruckerei. Wien 1878, 2. verm. und verb. Aufl. 1880 showing the cursive tau variants on page 171.

EDIT2: In the thread on the Unicode Mailing list (mentioned in the comments below) Raymond Mercier found that the English translation uses a usual lowercase tau in place of the 7-shaped tau symbol.

• discussion on the unicode list has almost certainly settled on the form of an italic or cursive uppercase Tau (not lowercase), now "obsolete" for mathematics owing to the "modern" form that is identical in appearance to the latin "T". (if you have access to that list, the thread is "Turned Capital letter L (pointing to the left, with serifs)".) – barbara beeton Jan 5 '16 at 16:13
• @barbarabeeton: I am active on the unicode mailing list and I have started the quoted thread there :-) I am not sure whether to classify the symbol as uppercase or lowercase, the letter forms are very similar. – jknappen Jan 5 '16 at 16:47
• aha! (not a surprise, actually.) your initial message wasn't among what was forwarded to me. should have thought of faulmann -- that's an amazing reference. (it was being "de-accessioned" from the ams library, so i have "requisitioned" it for my own use.) and there's little doubt that this is what's intended. thanks. – barbara beeton Jan 5 '16 at 18:51

The symbol appears to be the Tironian et symbol, which looks like a backwards capital gamma. There is one in Unicode (U+204A). I have no idea if this is in any of the math fonts. You could, perhaps, be able to enter it using the unicode-math package.

• @ChristianHupfer Ah, yes, I translated the text to be the sidereal motion in seconds, not thinking angular seconds. Looking at the text, this Gauss fellow seems rather loose with his units--he'd probably only get partial credit. Perhaps he might consider going into some other field. :) – Dave Dec 23 '15 at 23:46
• this suggestion is exactly the same as proposed (independently, in response to my inquiry) by my go-to font expert. i think it's extremely plausible, and have submitted the suggestion to my unicode contacts that they consider adding a math attribute to U+204A on this evidence. – barbara beeton Dec 24 '15 at 16:52
• It is certainly not a Tironian Et ⁊. That character typically has a descender, at 90° or less (but not so small an angle as that glyph has), and typically goes only up as far as x-height. The glyph used there is obviously a digit 7 taken from another font. The question is... what was the intended symbol? – Evertype Jan 4 '16 at 15:13
• @Evertype: The sample above looks like a seven, but it is not a very good representation of versions I can find, nor of the German translation in the link. If you look at an original printing you'll see the symbol on page 18. It is certainly taller than x-height. It seems to be a symbol Gauss used in multiple writings. Gauss invented many symbols that became standard that it is certainly possible that was unique to him. – Dave Jan 5 '16 at 0:17
• @Evertype -- after a rather active discussion among unicode folk, more documentation has been found that appears to point to a cursive form of capital Tau. the discussion is ongoing, but the hypothesis for a tironian "et" seems entirely incorrect. see later answer by jknappen. – barbara beeton Jan 5 '16 at 16:07

Semantically, this symbol encodes an angle, ant it looks like a nicely typeset version of ⦢ U+29A2 TURNED ANGLE which is accessible through the stix package with the \turnangle command. This symbol is usually sans sans-serif in modern texts but I think it is a glyph problem, not a character problem. It is mentioned in Florian Cajori’s History of mathematical Notations (pdf) §361 p.404 as being used in John Ward’s The Young Mathematicians’ Guide (9th ed.; London, 1752), p.301,369. In the 6th edition (1734) this symbol indeed appears, but typeset in a modern sans serif way.

Trying to typeset Francis’ example gives this code

\documentclass{article}
\usepackage{stix,amsmath}
%\usepackage{fge,graphicx,amsmath}
%\DeclareRobustCommand{\turnangle}{\text{\reflectbox{$\fgelangle$}}}
\usepackage[latin]{babel}

\newcommand{\rd}{\mathrm{d}}
\begin{document}
Si corporis coelestis massa vel negligitur vel saltem tamquam cognita
spectatur, $\turnangle$ et $a$ ab invicem dependentes erunt,
adeoque vel $\rd\turnangle$ vel $\rd a$ e formulis nostris eliminare
licebit. Scilicet quum per art. 6 habeatur
$\turnangle a^{\tfrac32}=k\surd(1+\mu)$,
erit $\displaystyle\frac{\rd \turnangle}{\turnangle}=-\tfrac32 \frac{\rd a}{a}$,
in qua formula si $\rd\turnangle$ in partibus radii experimenda est, etiam
$\turnangle$ perinde exprimere oportebit. Ita in exemplo nostro habetur

\centerline{%
\begin{tabular}{ll}
$\log\turnangle$ &2{,}91635\\
$\log 1''$ &4{,}68557\\
$\log \tfrac32$ & 0{,}17609\\
$\mathrm{C}.\log a$ & 9{,}57756\\
\hline
$\log\frac{\rd\turnangle}{\rd a}$&7{,}35557$_{n}$
\end{tabular}%
}
\end{document}


and the following output

If you want to have sa symbol which looks closer to the one used by Gauß’ typesetter, included in a TeX package and with an angle semantic, you can use the fge package, developed to typeset Fregge’s Grundgesetze der Arithmetik (1893–1903). It contain a symbol, \fgelangle which is almost a mirror image of what you want (\fgerangle does not exist). To create this symbol, you just have to uncomment the two commented lines in the above code and comment out the first usepackage. The code is a direct adaptation of this answer. It gives the following result [

• nice reference, but the meaning as shown in cajori is entirely wrong for the gauss usage cited. – barbara beeton Jan 5 '16 at 18:55

The sign apperas to be a cursive form of the capital greek tau (usually Τ), as replied by jknappen. As for typesetting, there's basically three ways to do it.

1. Use \tau or \mathcal{T}, which will give τ in two different heights. It's not the same symbol, but the same meaning.
2. Use \mathbf{7}, which unfortunately still looks like 7, not the exact letter in Gauss' work.
3. Find a vector-format image and make a command to include it. Say, \newcommand{\varTau}{\includegraphics[height=0.8em]{fig/varTau.pdf}

The latter can typeset any symbol whatever, so long as you can find an image with it. Inkscape has a nice bitmap-to-path conversion tool if, like me, you're not satisfied with a bitmap.