Associated Topics || Dr. Math Home || Search Dr. Math

### 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!

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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search