History of the Fraction Bar

Date: 09/01/2005 at 14:39:44
From: Don
Subject: The Fraction Bar in Fractions

What is the original name of the fraction bar?  I know it is called
the vinculum, but was that the original name?  If not, what was it
originally called?

Date: 09/01/2005 at 19:43:34
From: Doctor Peterson
Subject: Re: The Fraction Bar in Fractions

Hi, Don.

In what language?  I believe it was first used by Arabs, and I might 
be able to research the Arabic term they would have used, but I'd 
need to know that's what you want!

See this page for the history:

    http://jeff560.tripod.com/fractions.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 09/01/2005 at 20:05:08
From: Don
Subject: The Fraction Bar in Fractions

I do not know the language, my professor just asked me to research 
the original name of the fraction bar whatever it may be.  So I'm not 
sure what language he is talking about.  Was there a common name for 
the "fraction bar" at any time?

Date: 09/01/2005 at 23:06:12
From: Doctor Peterson
Subject: Re: The Fraction Bar in Fractions

Hi, Don.

So the question is not clearly stated in the first place.  That's
typical of real life; often when you have a good question, you have to
decide in the course of your research how to interpret the question.
Do we need to find what it was first called by whoever invented it,
whatever language they spoke, or is it more important to find what it
was first called in English?  That's apparently up to you to decide,
based on what you learn about the origin of the symbol.

My best source (which is also a major source of the site I referred
you to) is Cajori's History of Mathematical Notations, which you may
be able to find.  He gives the history of notations for fractions, but
I don't see any footnotes (which he often gives when it is 
interesting) about what the symbol was called by its early users.  He
himself just calls it "the fractional line" or "the horizontal bar".
He shows various Hindu writers who wrote fractions without the bar at
all, and identifies al-Hassar, a twelfth century Arab, as using the
line, followed by Leonardo of Pisa (Fibonacci).  What did they call 
it? al-Hassar says

  Write the denominator below a [horizontal] line and over each of
  them the parts belonging to it; for example, if you are told to
  write three-fifths and a third of a fifth, write thus,
     3  1
     ----
     5  3

It's not quite our modern notation, and he just calls it a "line".

Cajori then quotes Fibonacci in Latin, where he uses "uirgula"; though
Cajori translates that as "line", it means "little rod" or "twig" or
"wand" in Latin, and is the source of the modern word "virgule", which
means the symbol "/" instead.  (Cajori calls that symbol a solidus,
which is probably its original name.)

So you might be able to say that the original term was "virgule",
though that has since changed its meaning, and perhaps was never used
this way in English.

Cajori says the fractional line came into common use in the sixteenth
century, but says very little about that usage and nothing about what
it was called--which in my mind probably means it didn't have a 
special name. (See sections 235, 272.)

I find no evidence, by the way, that it has ever properly been called
a vinculum, which is a bar OVER an expression and serves to group it
as parentheses do today.  The fraction bar has something in common 
with that, but not enough in my opinion to justify the usage.  With 
both vinculum and virgule used for other things, I just call it a 
fraction bar and am perfectly happy with that term!


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/