|÷ † ⁒|
Modern forms of the obelus
|In Unicode||U+00F7 ÷ DIVISION SIGN |
U+2020 † DAGGER
U+2052 ⁒ COMMERCIAL MINUS SIGN
|See also||U+261E ☞ WHITE RIGHT POINTING INDEX|
An obelus (plural: obeluses or obeli) is a term in typography for an historical mark that has resolved to three modern meanings:
- Division sign ⟨÷⟩
- Dagger (typography) ⟨†⟩
- Commercial minus sign ⟨⁒⟩ (limited geographical area of use)
In mathematics, the first symbol is mainly used in Anglophone countries to represent the mathematical operation of division. In editing texts, the second symbol, also called a dagger mark ⟨†⟩, is used as a reference mark, or to indicate that a person is dead, and often used to indicate a footnote.
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 ⟨⨪ ÷⟩. It represented an iron roasting spit, a dart, or the sharp end of a javelin, symbolizing the skewering or cutting out of dubious matter.
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, 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. 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".
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. In Finland, it (or a slight variant, ) is used as a symbol for a correct response alongside the check mark as an incorrect response.
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. This usage, though widespread, 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 this symbol "should not be used" for division.
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). In Italy, Poland and Russia this form of the obelus is sometimes used to denote a range of values, in engineering context.
In some commercial and financial documents, especially in Germany and Scandinavia, another form of the obelus – the commercial minus sign form is used to signify a negative remainder of a division operation.
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- ISO 80000-2, Section 9 "Operations", 2-9.6
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- 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.