Obelus

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Three variants of obelus glyphs
÷ † ⁒
Modern forms of the obelus
In UnicodeU+00F7 ÷ DIVISION SIGN
U+2020 DAGGER
U+2052 COMMERCIAL MINUS SIGN
Related
See alsoU+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:

The word "obelus" comes from ὀβελός (obelós), the Ancient Greek word for a sharpened stick, spit, or pointed pillar.[3] This is the same root as that of the word 'obelisk'.[4]

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. It is often used to indicate a footnote.[5][6][7]

Use in text annotation[edit]

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  ÷.[8] It represented an iron roasting spit, a dart, or the sharp end of a javelin,[9] symbolizing the skewering or cutting out of dubious matter.[10]

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.[10] 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, ) is used as a symbol for a correct response (alongside the check mark, , which is used for an incorrect response).[14][15]

In mathematics[edit]

Plus and minuses. The obelus – or division sign – 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, ÷, 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.[16][17] 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.[18]

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).[19] In Italy, Poland and Russia, this notation is sometimes used in engineering to denote a range of values.[20]

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.[21][14]

See also[edit]

References[edit]

  1. ^ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-26.
  2. ^ Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.
  3. ^ R. E. Allen, ed. (1993). The Concise Oxford Dictionary. p. 817.
  4. ^ R. E. Allen, ed. (1993). The Concise Oxford Dictionary. p. 816.
  5. ^ Wolf, Friedrich August (2014). Prolegomena to Homer, 1795. Translated by Anthony Graton. Princeton University Press. pp. 63, 202–203. ISBN 9781400857692.
  6. ^ Howatson, M. C. (2013). "Obelos". The Oxford Companion to Classical Literature. Oxford University Press. ISBN 9780191073014.
  7. ^ The Chambers Dictionary. Allied Publishers. 1998. p. 1117. ISBN 9788186062258.
  8. ^ Merriam-Webster's collegiate dictionary. Merriam-Webster, Inc. 2003. p. 855. ISBN 978-0-87779-809-5. obelos.
  9. ^ William Harrison Ainsworth, ed. (1862). The New monthly magazine. 125. Chapman and Hall. p. 1.
  10. ^ 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.
  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.
  15. ^ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Commercial minus.
  16. ^ "Math Words, pg 7". Math Words Alphabetical Index. Archived from the original on August 7, 2011. Retrieved August 26, 2011.
  17. ^ "Division". www.mathsisfun.com. Retrieved 2020-08-26.
  18. ^ ISO 80000-2, Section 9 "Operations", 2-9.6
  19. ^ Cajori, Florian (1993), A history of mathematical notations (two volumes bound as one), Dover, pp. 242, 270–271, ISBN 9780486677668. Reprint of 1928 edition.
  20. ^ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Obelus.
  21. ^ 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.