View source for Obelus

{{Short description|Historical annotation mark or symbol}}
{{for|the genus of snails|Obelus (gastropod)}}
{{use British English|date=August 2020}}
[[File:Obelus variants.svg|right|thumb|upright=1.1|Three variants of obelus glyphs]]
{{infobox symbol
| mark = ÷ † ⁒ ⸓
| name= Modern forms of the obelus
|unicode={{unichar|F7|Division sign}}  <br /> {{unichar|2020|dagger}} <br /> {{unichar|2052|Commercial minus sign}} <br />{{unichar|2E13|Dotted obelos}}
| see also= {{unichar|261E|White right pointing index |nlink= Index (typography)}}
|different from={{unichar|0025|percent sign}}
}}
{{special characters}}
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]] {{char|÷}}
* [[Dagger (typography)|Dagger]] {{char|†}}
* [[Commercial minus sign]] {{char|⁒}} (limited geographical area of use)

The word "obelus" comes from {{wikt-lang|grc|ὀβελός}} (obelós), the [[Ancient Greek]] word for a sharpened stick, spit, or pointed pillar.<ref>{{cite book|title = The Concise Oxford Dictionary | page=817 | editor= R. E. Allen | date=1993}}</ref> This is the same root as that of the word '[[obelisk]]'.<ref>{{cite book|title = The Concise Oxford Dictionary | page=816 | editor= R. E. Allen | date=1993}}</ref>

In mathematics, the first symbol is mainly used in [[Anglophone]] countries to represent the mathematical operation of [[Division (mathematics)|division]] and is called an obelus.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Division|url=https://mathworld.wolfram.com/Division.html|access-date=2020-08-26|website=mathworld.wolfram.com|language=en}}</ref> In editing texts, the second symbol, also called a [[Dagger (mark)|dagger]] mark {{char|†}} is used to indicate erroneous or dubious content;<ref>{{cite book|last1 = Wolf | first1= Friedrich August | translator= Anthony Graton | title= Prolegomena to Homer, 1795 | publisher= Princeton University Press |date= 2014 | isbn= 9781400857692 | pages= 63, 202–203}}</ref><ref>{{cite book|last=Howatson | first= M. C. |chapter=Obelos | title= The Oxford Companion to Classical Literature | publisher= Oxford University Press | date= 2013 | isbn=9780191073014}}</ref> or as a reference mark or [[footnote]] indicator.<ref>{{cite book| title=The Chambers Dictionary | publisher= Allied Publishers |date=1998 | isbn=9788186062258| page = 1117}}</ref>  It also has [[Dagger (mark)#Modern usage|other uses]] in a variety of specialist contexts.

== Use in text annotation ==
{{See also|Obelism}}
{{more|Dagger (typography)}}
The modern dagger symbol originated from a variant of the obelus, originally depicted by a plain line {{char|−}}, or a line with one or two dots {{char|⨪{{nbsp}}÷}}.<ref name="merriamw">{{cite book|title =Merriam-Webster's collegiate dictionary|publisher =Merriam-Webster, Inc|year =2003|page=[https://archive.org/details/merriamwebstersc00merr_6/page/855 855]|isbn =978-0-87779-809-5|url =https://archive.org/details/merriamwebstersc00merr_6|url-access =registration|quote =obelos.}}</ref> It represented an iron roasting spit, a dart, or the sharp end of a [[javelin]],<ref name="ainsw">{{cite book|editor=William Harrison Ainsworth|title =The New monthly magazine|publisher =Chapman and Hall|volume=125|year =1862|page=1|url =https://books.google.com/books?id=PycaAQAAIAAJ&q=obelos&pg=PA1}}</ref> symbolizing the skewering or cutting out of dubious matter.<ref name="scanlin"/>

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 (typography)|dagger symbol]] {{char|†}},  also called an ''obelisk'',<ref>{{cite dictionary |dictionary = The Oxford English Dictionary (D{{ndash}}E |year=1933 |entry=Dagger (8) |page=[https://archive.org/details/the-oxford-english-dictionary-1933-all-volumes/The%20Oxford%20English%20Dictionary%20Volume%203/page/n18/mode/1up 7]}}</ref> is derived from the obelus, and continues to be used for this purpose. 

The obelus is believed to have been invented by the [[Homeric scholarship|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]].<ref name="scanlin">{{cite book|author=Harold P. Scanlin|editor=Alison Salvesen|title =Origen's Hexapla and fragments: papers presented at the Rich Seminar on the Hexapla, Oxford Centre for Hebrew and Jewish Studies, 25th-3rd August|publisher =Mohr Siebeck|year =1998|page=439|chapter=A New Edition of Origen's Hexapla: How It Might Be Done|isbn =978-3-16-146575-8|chapter-url =https://books.google.com/books?id=9xQDu27_HEIC&q=metobelos&pg=PA439}}</ref> The system was further refined by his student [[Aristophanes of Byzantium]], who first introduced the [[asterisk]] and used a symbol resembling a {{char|⊤}} for an obelus; and finally by Aristophanes' student, in turn, [[Aristarchus of Samothrace|Aristarchus]], from whom they earned the name of "[[Aristarchian symbols]]".<ref name="wegner">{{cite book|author=Paul D. Wegner|title =A student's guide to textual criticism of the Bible|publisher =InterVarsity Press|year =2006|page=194|isbn =978-0-19-814747-3|url =https://books.google.com/books?id=SIMsY6b2n2gC&q=obelos&pg=PA192}}</ref><ref name="grube">{{cite book|author=George Maximilian Anthony Grube|title =The Greek and Roman critics|publisher =Hackett Publishing|year =1965|page=128|isbn =978-0-87220-310-5|url =https://books.google.com/books?id=jerucRW8UmMC&q=obelos&pg=PA128}}</ref>

In some commercial and financial documents, especially in Germany and Scandinavia, a variant ({{unichar|2052|commercial minus sign|nlink=}}) is used in the margins of letters to indicate an enclosure, where the upper point is sometimes replaced with the corresponding number.<ref name=UC>{{Cite book|url=https://www.unicode.org/versions/Unicode10.0.0/ch06.pdf#G7935|title=The Unicode® Standard, Version 10.0|publisher=The Unicode Consortium|year=2017|isbn=978-1-936213-16-0|location=Mountain View, CA|chapter=Writing Systems and Punctuation}}</ref> In Finland, the obelus (or a slight variant, <math>\cdot \! / \! \cdot</math>) is used as a symbol for a correct response (alongside the [[check mark]], {{char|✓}}, which is used for an ''incorrect'' response).<ref name=Silli /><ref>{{cite book|url=https://www.unicode.org/versions/Unicode10.0.0/ch06.pdf#G7935 | page=280, Commercial minus | chapter = 6. Writing Systems and Punctuation | publisher= Unicode Consortium | title = The Unicode® Standard: Version 10.0 – Core Specification | date= June 2017}}</ref>

In the 7.0 release of Unicode, {{unichar|2E13|Dotted obelos}} was one of [[Obelism#Modern encoding|a group]] of "Ancient Greek textual symbols" that were added to the specification (in the block [[Supplemental Punctuation]]).<ref>{{cite web |title=Supplemental Punctuation |url=https://www.unicode.org/charts//PDF/Unicode-7.0/U70-2E00.pdf | publisher=[[Unicode Consortium]] |date=2014}}</ref>

==In mathematics==
{{main|Division sign}}
[[File:Skjermbilete 2012-11-03 kl. 02.48.36.png|thumb|Plus and minuses. The obelus{{snd}} or division sign{{snd}} used as a variant of the minus sign in an excerpt from an official Norwegian trading statement form called «Næringsoppgave 1» for the taxation year 2010.]]

The form of the obelus as a horizontal line with a dot above and a dot below, {{char|÷}}, was first used as a symbol for [[Division (mathematics)|division]] by the [[Swiss people|Swiss]] mathematician [[Johann Rahn]] in his book ''Teutsche Algebra'' in 1659. This gave rise to the modern mathematical symbol {{char|÷}}, used in anglophone countries as a [[division sign]].<ref name="math">{{cite web |url=http://www.pballew.net/arithme7.html |title=Math Words |page= 7 |publisher=Math Words Alphabetical Index |access-date=August 26, 2011 |archive-url=https://web.archive.org/web/20110807071158/http://www.pballew.net/arithme7.html |archive-date=August 7, 2011 |url-status=usurped |df=mdy-all}}</ref><ref>{{Cite web |title=Division |url=https://www.mathsisfun.com/numbers/division.html |access-date=2020-08-26 |website=www.mathsisfun.com}}</ref> This usage, though widespread in Anglophone countries, is neither universal nor recommended: the [[ISO 80000-2]] standard for [[mathematical notation]] recommends only the [[Slash (punctuation)|solidus]] {{char|/}} or [[Fraction (mathematics)#Vocabulary|fraction bar]] for division, or the [[Colon (punctuation)|colon]] {{char|:}} for [[ratio]]s; it says that {{char|÷}} "should not be used" for division.<ref>[[ISO 80000-2]], Section 9 "Operations", 2-9.6</ref> The ambiguity of mathematical expressions that involve the [[Order_of_operations#Mixed_division_and_multiplication|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]]).<ref name="Cajori">{{citation|title=A history of mathematical notations (two volumes bound as one) |publisher=Dover |year=1993|isbn=9780486677668|first=Florian|last=Cajori|author-link=Florian Cajori|pages=242, 270–271|url=https://books.google.com/books?id=fNVYTRBTIJ8C&pg=PA270}}. Reprint of 1928 edition.</ref> In [[Italy]], [[Poland]] and [[Russia]], this notation is sometimes used in [[engineering]] to denote a [[Interval (mathematics)|range of values]].<ref>{{cite book| url=https://www.unicode.org/versions/Unicode10.0.0/ch06.pdf#G7935 | page=280, Obelus | chapter = 6. Writing Systems and Punctuation | publisher= Unicode Consortium | title = The Unicode® Standard: Version 10.0 – Core Specification | date= June 2017}}</ref>

In some commercial and financial documents, especially in Germany and Scandinavia, another form of the obelus{{snd}} the [[commercial minus sign]]{{snd}} is used to signify a negative remainder of a division operation.<ref>{{cite book|title= Kaufmännische Arithmetik oder allgemeines Rechenbuch für Banquiers, Kaufleute, Manufakturisten, Fabrikanten und deren Zöglinge | author= Johann Philipp Schellenberg | page = 213| date=1825| lang=DE | trans-title= Commercial arithmetic or general arithmetic book for bankers, merchants, manufacturers, craftsmen and their pupils}}<!-- NB this is not the 1805 version available from Google Books --></ref><ref name=Silli>{{cite web |url=http://unicode.org/pipermail/unicode/2014-January/000013.html |title=Commercial minus as italic variant of division sign in German and Scandinavian context |author=Leif Halvard Silli |website=Unicode.org |access-date=2020-04-04 |archive-date=2019-06-14 |archive-url=https://web.archive.org/web/20190614233459/http://unicode.org/pipermail/unicode/2014-January/000013.html |url-status=dead }}</ref>

==See also==
* {{anli|Manicule}} ({{big| ☞ }}) used for obelism.
* {{anli|Obelisk}}
* {{anli|Obelix}}
* {{anli|Obol (coin)}}
* [[List of typographical symbols and punctuation marks]]

==References==
{{Reflist}}
{{Wiktionary}}

[[Category:Typographical symbols]]