Seeking Old German Symbols's picture

I'm seeking a font that contains the following German symbols: dragma/numerus, radix, zensus, cubus, zensdezens, sursolidum, and zensicubus.
Anybody have suggestions/references/pointers?
Thanks in advance.
Cheers, Scott

hrant's picture

Are those really German?


George Thomas's picture

Your best bet is to contact an academic who is an expert in Algebra of the Middle Ages. I don't have my Unicode book at the moment so cannot look up the names but I'm guessing of the ones you provide, only radix might be listed.

A book referenced at Google may give you some clues as to where to look:

Michel Boyer's picture

Those words above can be found in this reference from A Brief History of Mathematics, by Karl Fink, Wooster Beman, David Smith.

Michel Boyer's picture

There are more details in History and Philosophy of the Mathematical Sciences, Gratian-Guinness ed. (starting p. 195 for Germany).

quadibloc's picture

I remember that a book on wordplay (either Language on Vacation or its sequel Beyond Language, by Dimitri Borgmann) had some related terms, and then an English-language book on mathematics that I found out about from this forum had them "in real life".

Andreas Stötzner's picture

> dragma/numerus, radix, zensus, cubus, zensdezens, sursolidum, and zensicubus

Mathematics? Monetary & weights??

– conventional signage?
– Unicodes?
– can you give a sample image?

quadibloc's picture

Page 74 of this book, a reference already cited in an English translation of a later edition, is another starting point.

Further searching has led me to learn that it was Robert Recorde's book The Whetstone of Witte that introduced the term "zenzizenic" for the eighth power, as well as introducing the equals sign. (It was also the first book in English to use the plus and minus signs.)

Michel Boyer's picture

Here is from a 1615 edition of Die Coss on Google

I thought the fonts provided by the MacTeX-2012 distribution covered virtually everything that was related to mathematics but I could find nothing appropriate for Dragma, Radix or Cubus; of course, the fraktur characters for Zensus and Sursolidum pose no (major) problem.

Andreas Stötzner's picture

thanks for that excellent find. I remember I encountered that sort of characters once, anywhere … would have to dig very deeply to unearth it.

An interesting set of characters.
The Sursolidum char. applies just the ordinary ß (00DF).
Apart from that, the rest is true original abbreviational characters which are not yet encoded (*one exception); because it is no wonder why they are not materialized in any available font so far.
Dragma – * is a graphic modificant of lowercase d, very much like the usual glyphs which have been used for d[enarius], Pfennig (20B0). Strong candidate for unification.
Radix – is basically a ‘r rotunda’ (A75B) with a swashy cross-mark attached to its leg, similar to the ‘rum’ abbreviation (A75D).
In the same manner a blackletter z and a c have been modified to stand in as characters for ‘Zensus’ and ‘Cubus’; the rest of the listing is just combinations.

Summa summarum: what we have here is definitely a proof for three characters still to be encoded (Radix, Zensus, Cubus).

Michel Boyer's picture


To my eye, Zensus looks close to what \mathfrak{z} gives me with the amsfonts package in LaTeX

as well as to the unicode character U+1D59F (grabbed from the unicode charts)

[Edit:] I just noticed that \mathfrak{z} corresponds rather to U+1D537

(grabbed again from ).

Andreas Stötzner's picture

Michel, 1D59F is but a reflection of the ordinary Fraktur z. The closing or even crossing of the loop is not a mandatory feature here. – Compare the special Zensus-sign to the average z in the word …dezens, there you have the difference (which, in this case, is meaningful).

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