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÷ † ⁒ ⸓
÷ † ⁒ ⸓
Modern forms of the obelus
In Unicode	U+00F7 ÷ DIVISION SIGN ; U+2020 † DAGGER ; U+2052 ⁒ COMMERCIAL MINUS SIGN ; U+2E13 ⸓ DOTTED OBELOS
Different from
Different from	U+0025 % PERCENT SIGN
Related
See also	U+261E ☞ WHITE RIGHT POINTING INDEX

Three variants of obelus glyphs

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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:

Division sign ÷
Dagger †
Commercial minus sign ⁒ (limited geographical area of use)

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, $\cdot \!/\!\cdot$ ) 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] The ambiguity of mathematical expressions that involve the obelus and implicit multiplication has become a subject of Internet memes.

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

^ R. E. Allen, ed. (1993). The Concise Oxford Dictionary. p. 817.
^ R. E. Allen, ed. (1993). The Concise Oxford Dictionary. p. 816.
^ Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.
^ Wolf, Friedrich August (2014). Prolegomena to Homer, 1795. Translated by Anthony Graton. Princeton University Press. pp. 63, 202–203. ISBN 9781400857692.
^ Howatson, M. C. (2013). "Obelos". The Oxford Companion to Classical Literature. Oxford University Press. ISBN 9780191073014.
^ The Chambers Dictionary. Allied Publishers. 1998. p. 1117. ISBN 9788186062258.
^ Merriam-Webster's collegiate dictionary. Merriam-Webster, Inc. 2003. p. 855. ISBN 978-0-87779-809-5. obelos.
^ William Harrison Ainsworth, ed. (1862). The New monthly magazine. Vol. 125. Chapman and Hall. p. 1.
^ ^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.
^ "Dagger (8)". The Oxford English Dictionary (D–E. 1933. p. 7.
^ Paul D. Wegner (2006). A student's guide to textual criticism of the Bible. InterVarsity Press. p. 194. ISBN 978-0-19-814747-3.
^ George Maximilian Anthony Grube (1965). The Greek and Roman critics. Hackett Publishing. p. 128. ISBN 978-0-87220-310-5.
^ "Writing Systems and Punctuation". The Unicode® Standard, Version 10.0 (PDF). Mountain View, CA: The Unicode Consortium. 2017. ISBN 978-1-936213-16-0.
^ ^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.
^ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Commercial minus.
^ "Supplemental Punctuation" (PDF). Unicode Consortium. 2014.
^ "Math Words". Math Words Alphabetical Index. p. 7. Archived from the original on August 7, 2011. Retrieved August 26, 2011.
^ "Division". www.mathsisfun.com. Retrieved 2020-08-26.
^ ISO 80000-2, Section 9 "Operations", 2-9.6
^ Cajori, Florian (1993), A history of mathematical notations (two volumes bound as one), Dover, pp. 242, 270–271, ISBN 9780486677668. Reprint of 1928 edition.
^ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Obelus.
^ 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.