An obelus (plural: obeluses or obeli) is a term in
typography
Typography is the art and technique of arranging type to make written language legible, readable and appealing when displayed. The arrangement of type involves selecting typefaces, point sizes, line lengths, line-spacing ( leading), an ...
that refers to a historical mark which has resolved to three modern meanings:
*
Division sign
*
Dagger
A dagger is a fighting knife with a very sharp point and usually two sharp edges, typically designed or capable of being used as a thrusting or stabbing weapon.State v. Martin, 633 S.W.2d 80 (Mo. 1982): This is the dictionary or popular-use def ...
*
Commercial minus sign (limited geographical area of use)
The word "obelus" comes from (obelós), the
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
word for a sharpened stick, spit, or pointed pillar. This is the same root as that of the word '
obelisk
An obelisk (; from grc, ὀβελίσκος ; diminutive of ''obelos'', " spit, nail, pointed pillar") is a tall, four-sided, narrow tapering monument which ends in a pyramid-like shape or pyramidion at the top. Originally constructed by An ...
'.
In mathematics, the first symbol is mainly used in
Anglophone
Speakers of English are also known as Anglophones, and the countries where English is natively spoken by the majority of the population are termed the ''Anglosphere''. Over two billion people speak English , making English the largest language ...
countries to represent the mathematical operation of
division. In editing texts, the second symbol, also called a
dagger
A dagger is a fighting knife with a very sharp point and usually two sharp edges, typically designed or capable of being used as a thrusting or stabbing weapon.State v. Martin, 633 S.W.2d 80 (Mo. 1982): This is the dictionary or popular-use def ...
mark , is used to indicate erroneous or dubious content; or as a reference mark or
footnote indicator. 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 .
It represented an iron roasting spit, a dart, or the sharp end of a
javelin
A javelin is a light spear designed primarily to be thrown, historically as a ranged weapon, but today predominantly for sport. The javelin is almost always thrown by hand, unlike the sling, bow, and crossbow, which launch projectiles with the ...
,
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
Zenodotus ( grc-gre, Ζηνόδοτος) was a Greek grammarian, literary critic, Homeric scholar, and the first librarian of the Library of Alexandria. A native of Ephesus and a pupil of Philitas of Cos, he lived during the reigns of the fir ...
, as one of a system of editorial symbols. They marked questionable or corrupt words or passages in manuscripts of the
Homeric epics
Homer (; grc, Ὅμηρος , ''Hómēros'') (born ) was a Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Homer is considered one of the ...
.
The system was further refined by his student
Aristophanes of Byzantium
__NOTOC__
Aristophanes of Byzantium ( grc-gre, Ἀριστοφάνης ὁ Βυζάντιος ; BC) was a Hellenistic Greek scholar, critic and grammarian, particularly renowned for his work in Homeric scholarship, but also for work on other ...
, who first introduced the
asterisk
The asterisk ( ), from Late Latin , from Ancient Greek , ''asteriskos'', "little star", is a typographical symbol. It is so called because it resembles a conventional image of a heraldic star.
Computer scientists and mathematicians often voc ...
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
Aristarchian symbols are editorial marks developed during the Hellenistic period and the early Roman empire for annotating then-ancient Greek texts—mainly the works of Homer. They were used to highlight missing text, text which was discrepant b ...
".
In some commercial and financial documents, especially in Germany and Scandinavia, a variant () is used in the margins of letters to indicate an enclosure, where the upper point is sometimes replaced with the corresponding number.
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).
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
Swiss may refer to:
* the adjectival form of Switzerland
*Swiss people
Places
* Swiss, Missouri
*Swiss, North Carolina
* Swiss, West Virginia
*Swiss, Wisconsin
Other uses
* Swiss-system tournament, in various games and sports
* Swiss Internation ...
mathematician
Johann Rahn
Johann Rahn (Latinised form Rhonius) (10 March 1622 – 25 May 1676) was a Swiss mathematician who is credited with the first use of the division sign, ÷ (a repurposed obelus variant) and the therefore sign, ∴. The symbols were used in '' ...
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 in Anglophone countries, is neither universal nor recommended: the
ISO 80000-2 standard for
mathematical notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathem ...
recommends only the
solidus or
fraction bar for division, or the
colon for
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
s; it says that "should not be used" for division.
This form of the obelus was also occasionally used as a mathematical symbol for
subtraction
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...
in Northern Europe; such usage continued in some parts of Europe (including
Norway
Norway, officially the Kingdom of Norway, is a Nordic countries, Nordic country in Northern Europe, the mainland territory of which comprises the western and northernmost portion of the Scandinavian Peninsula. The remote Arctic island of ...
and, until fairly recently,
Denmark
)
, song = ( en, "King Christian stood by the lofty mast")
, song_type = National and royal anthem
, image_map = EU-Denmark.svg
, map_caption =
, subdivision_type = Sovereign state
, subdivision_name = Kingdom of Denmark
, establish ...
).
[. Reprint of 1928 edition.] In
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...
,
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
and
Russia
Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-ei ...
, this notation is sometimes used in
engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
to denote a
range of values.
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.
See also
* () used for obelism.
*
*
*
*
List of typographical symbols and punctuation marks
References
{{Wiktionary
Typographical symbols