Obelus

÷ † ⁒ ⸓
÷ † ⁒ ⸓
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

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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]

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.
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[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.

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[19] ISO 80000-2, Section 9 "Operations", 2-9.6

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Use in text annotation

In mathematics

See also

References