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Topic: math query
Replies: 10   Last Post: Oct 26, 1995 6:40 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: math query
Posted: Oct 26, 1995 6:40 PM
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I quote:

> There is another puzzle: about the Latin words for 18 and 19 - duodeviginti
> (two from twenty) and undeviginti (one from twenty), a pattern repeated
> for 28,29,38,39 etc. As far as I know this terminology long predates the
> use of subtractive notation in Roman numerals; e.g. XIX. Does this
> pattern appear in any other languages? Further also to the discussion of
> different base systems, I believe that in all Saxon languages 'hundred'
> originally had the meaning 120.
> Robert Goulding.

The same idea was used by the Romans in their names for fractions,
which are

uncia = 1/2 (giving us both "ounce" and "inch")
sextans = 1/6 (giving us "sextant")
quadrans = 1/4 ("quadrant")
triens = 1/3
quincunx = 5/12 ("quincunx" now means a certain pattern - see below)
semis = 1/2
septunx = 7/12
bes = 2/3 (from "dues partes" (= "two parts (of 3)")
dodrans = 3/4 (from "de quadrans")
dextans = 5/6 (from "de sextans")
deunx = 11/12

I was very pleased once to come across a reference to a
"dodrantal" shape in an eighteenth century book, and to understand
it! (Of course it means what's left of a disc when one quadrant is

On weights, the Romans indicated these by obvious patterns of
dots (for fractions less than 1/2), supplemented by the letter S
(for fractions greater than 1/2).

So . .
. .

meant "5/12" or "5 ounces", ie., "quincunx", which

is why this word is now used for that pattern. The
fraction 7/12 would be written "S."

All of this is taken from Menninger, who points out
that the subtractive principle in "Roman numerals" only
became widespread in medieval times. The Romans would
write VIIII rather than IX for 9.

Clocks with Roman numerals use IIII rather than IV for "4",
but this is certainly because this frees us from having to worry
which way up to put that "IV", and from confusing in with "VI".

John Conway

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