# Obelus

÷ † ⁒ ⸓
Modern forms of the obelus
In UnicodeU+00F7 ÷ DIVISION SIGN
U+2020 DAGGER
U+2052 COMMERCIAL MINUS SIGN
U+2E13 DOTTED OBELOS
Different from
Different fromU+0025 % PERCENT SIGN
Related

An obelus (plural: obeluses or obeli) is a term in codicology and latterly in typography that refers to a historical annotation mark which has resolved to three modern meanings:

The word "obelus" comes from ὀβελός (obelós), the Ancient Greek word for a sharpened stick, spit, or pointed pillar.[1] This is the same root as that of the word 'obelisk'.[2]

In mathematics, the first symbol is mainly used in Anglophone countries to represent the mathematical operation of division and is called an obelus.[3] In editing texts, the second symbol, also called a dagger mark is used to indicate erroneous or dubious content;[4][5] or as a reference mark or footnote indicator.[6] It also has other uses in a variety of specialist contexts.

## Use in text annotation

The modern dagger symbol originated from a variant of the obelus, originally depicted by a plain line , or a line with one or two dots  ÷.[7] It represented an iron roasting spit, a dart, or the sharp end of a javelin,[8] symbolizing the skewering or cutting out of dubious matter.[9]

Originally, one of these marks (or a plain line) was used in ancient manuscripts to mark passages that were suspected of being corrupted or spurious; the practice of adding such marginal notes became known as obelism. The dagger symbol , also called an obelisk,[10] is derived from the obelus, and continues to be used for this purpose.

The obelus is believed to have been invented by the Homeric scholar Zenodotus, as one of a system of editorial symbols. They marked questionable or corrupt words or passages in manuscripts of the Homeric epics.[9] The system was further refined by his student Aristophanes of Byzantium, who first introduced the asterisk and used a symbol resembling a for an obelus; and finally by Aristophanes' student, in turn, Aristarchus, from whom they earned the name of "Aristarchian symbols".[11][12]

In some commercial and financial documents, especially in Germany and Scandinavia, a variant (U+2052 COMMERCIAL MINUS SIGN) is used in the margins of letters to indicate an enclosure, where the upper point is sometimes replaced with the corresponding number.[13] In Finland, the obelus (or a slight variant, ${\displaystyle \cdot \!/\!\cdot }$) is used as a symbol for a correct response (alongside the check mark, , which is used for an incorrect response).[14][15]

In the 7.0 release of Unicode, U+2E13 DOTTED OBELOS was one of a group of "Ancient Greek textual symbols" that were added to the specification (in the block Supplemental Punctuation).[16]

## In mathematics

The form of the obelus as a horizontal line with a dot above and a dot below, ÷, was first used as a symbol for division by the Swiss mathematician Johann Rahn in his book Teutsche Algebra in 1659. This gave rise to the modern mathematical symbol ÷, used in anglophone countries as a division sign.[17][18] This usage, though widespread in Anglophone countries, is neither universal nor recommended: the ISO 80000-2 standard for mathematical notation recommends only the solidus / or fraction bar for division, or the colon : for ratios; it says that ÷ "should not be used" for division.[19]

This form of the obelus was also occasionally used as a mathematical symbol for subtraction in Northern Europe; such usage continued in some parts of Europe (including Norway and, until fairly recently, Denmark).[20] In Italy, Poland and Russia, this notation is sometimes used in engineering to denote a range of values.[21]

In some commercial and financial documents, especially in Germany and Scandinavia, another form of the obelus – the commercial minus sign – is used to signify a negative remainder of a division operation.[22][14]

## References

1. ^ R. E. Allen, ed. (1993). The Concise Oxford Dictionary. p. 817.
2. ^ R. E. Allen, ed. (1993). The Concise Oxford Dictionary. p. 816.
3. ^ Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.
4. ^ Wolf, Friedrich August (2014). Prolegomena to Homer, 1795. Translated by Anthony Graton. Princeton University Press. pp. 63, 202–203. ISBN 9781400857692.
5. ^ Howatson, M. C. (2013). "Obelos". The Oxford Companion to Classical Literature. Oxford University Press. ISBN 9780191073014.
6. ^ The Chambers Dictionary. Allied Publishers. 1998. p. 1117. ISBN 9788186062258.
7. ^ Merriam-Webster's collegiate dictionary. Merriam-Webster, Inc. 2003. p. 855. ISBN 978-0-87779-809-5. obelos.
8. ^ William Harrison Ainsworth, ed. (1862). The New monthly magazine. Vol. 125. Chapman and Hall. p. 1.
9. ^ a b Harold P. Scanlin (1998). "A New Edition of Origen's Hexapla: How It Might Be Done". In Alison Salvesen (ed.). Origen's Hexapla and fragments: papers presented at the Rich Seminar on the Hexapla, Oxford Centre for Hebrew and Jewish Studies, 25th-3rd August. Mohr Siebeck. p. 439. ISBN 978-3-16-146575-8.
10. ^ "Dagger (8)". The Oxford English Dictionary (D–E. 1933. p. 7.
11. ^ Paul D. Wegner (2006). A student's guide to textual criticism of the Bible. InterVarsity Press. p. 194. ISBN 978-0-19-814747-3.
12. ^ George Maximilian Anthony Grube (1965). The Greek and Roman critics. Hackett Publishing. p. 128. ISBN 978-0-87220-310-5.
13. ^ "Writing Systems and Punctuation". The Unicode® Standard, Version 10.0 (PDF). Mountain View, CA: The Unicode Consortium. 2017. ISBN 978-1-936213-16-0.
14. ^ a b Leif Halvard Silli. "Commercial minus as italic variant of division sign in German and Scandinavian context". Unicode.org. Archived from the original on 2019-06-14. Retrieved 2020-04-04.
15. ^ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Commercial minus.
16. ^ "Supplemental Punctuation" (PDF). Unicode Consortium. 2014.
17. ^ "Math Words". Math Words Alphabetical Index. p. 7. Archived from the original on August 7, 2011. Retrieved August 26, 2011.
18. ^ "Division". www.mathsisfun.com. Retrieved 2020-08-26.
19. ^ ISO 80000-2, Section 9 "Operations", 2-9.6
20. ^ Cajori, Florian (1993), A history of mathematical notations (two volumes bound as one), Dover, pp. 242, 270–271, ISBN 9780486677668. Reprint of 1928 edition.
21. ^ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Obelus.
22. ^ Johann Philipp Schellenberg (1825). Kaufmännische Arithmetik oder allgemeines Rechenbuch für Banquiers, Kaufleute, Manufakturisten, Fabrikanten und deren Zöglinge [Commercial arithmetic or general arithmetic book for bankers, merchants, manufacturers, craftsmen and their pupils] (in German). p. 213.