Obelus

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Three variants of obelus glyphs Obelus variants.svg
Three variants of obelus glyphs
÷ † ⁒ ⸓
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 fromU+0025%PERCENT SIGN
Related
See alsoU+261E☞ WHITE RIGHT POINTING INDEX

An obelus (plural: obeluses or obeli) is a historical annotation mark in codicology that has come to have three distinct modern forms, meanings and typographical uses:

Contents

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 codicology, a (usually horizontal) obelus in the form of a dagger was used to indicate erroneous or dubious content. [3] [4] The third symbol is an obsolescent mark used in some European countries

In mathematics, the ÷ symbol is mainly used in Anglophone countries to represent the mathematical operation of division (but has other meanings elsewhere) and is called an obelus in older textbooks. [5] In modern typography, the second symbol, called a dagger mark † is used 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, ) 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

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 <<Naeringsoppgave 1>> for the taxation year 2010. Skjermbilete 2012-11-03 kl. 02.48.36.png
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. [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 (for example, "24.1÷25.6" means the range of values between 24.1 and 25.6). [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]

See also

References

  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. ↑ Wolf, Friedrich August (2014). Prolegomena to Homer, 1795. Translated by Anthony Graton. Princeton University Press. pp. 63, 202–203. ISBN   9781400857692.
  4. ↑ Howatson, M. C. (2013). "Obelos". The Oxford Companion to Classical Literature. Oxford University Press. ISBN   9780191073014.
  5. ↑ Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.
  6. ↑ The Chambers Dictionary. Allied Publishers. 1998. p. 1117. ISBN   9788186062258.
  7. ↑ Merriam-Webster's collegiate dictionary . Merriam-Webster, Inc. 2003. p.  855. ISBN   978-0-87779-809-5. obelos.
  8. ↑ William Harrison Ainsworth, ed. (1862). The New monthly magazine. Vol. 125. Chapman and Hall. p. 1.
  9. 1 2 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.
  10. ↑ "Dagger (8)". The Oxford English Dictionary (D–E. 1933. p.  7.
  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. 1 2 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.
  15. ↑ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Commercial minus.
  16. ↑ "Supplemental Punctuation" (PDF). Unicode Consortium. 2014.
  17. ↑ "Math Words". Math Words Alphabetical Index. p. 7. Archived from the original on August 7, 2011. Retrieved August 26, 2011.
  18. ↑ "Division". www.mathsisfun.com. Retrieved 2020-08-26.
  19. ↑ ISO 80000-2, Section 9 "Operations", 2-9.6
  20. ↑ Cajori, Florian (1993), A history of mathematical notations (two volumes bound as one), Dover, pp. 242, 270–271, ISBN   9780486677668 . Reprint of 1928 edition.
  21. ↑ "6. Writing Systems and Punctuation". The Unicode® Standard: Version 10.0 – Core Specification (PDF). Unicode Consortium. June 2017. p. 280, Obelus.
  22. ↑ 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.
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