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History of the Symbol for "Therefore"

Date: 11/14/2005 at 20:23:24
From: Em
Subject: The symbol for therefore?

Why is it that the symbol for "therefore" is a centered dot with two 
lower dots?  Where did that symbol come from?  Our math teacher uses
it but doesn't know why either.



Date: 11/14/2005 at 23:21:46
From: Doctor Peterson
Subject: Re: The symbol for therefore!?

Hi, Em.

I've never found a clear statement of the reason for the symbol.  I
just looked in the usual source (which I probably didn't have last
time I researched this), Cajori's History of Mathematical Notations,
and here's part of what he says:

  It should be noted that with Rahn [1659] and with many writers of
  the eighteenth century the three dots were used especially in
  connection with the process of finding the products of means and
  extremes of a proportion.  Thus, Thomas Walter [A New Mathematical
  Dictionary] says: "[dots pointing down] Therefore; signifying the
  product of the two extremes is equal to that of the means."

Before this, he said that in early books the symbol was printed both as
   .             . .
  . .   and as    .

so the positions of the dots must not have been important (as if, say,
the dots suggested a completed pile), which I had previously thought.

Nothing is said of the reason for the symbol.  If it was specifically
used with reference to proportions, I'm wondering if it might be
connected with the "rule of three" that was considered an important
part of solving proportions.  That term refers to the three terms in a
proportion that you must know in order to solve it; no mention was
made above to that specific rule, but who knows?

All in all, the answer is that I still haven't found a definite answer
to the question!

See this page for a brief quote from the same source:

  Earliest Uses of Symbols of Set Theory and Logic
    http://jeff560.tripod.com/set.html 

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


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Definitions
High School Logic

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