Re: measuring systems (was: Selenites)

At 7:03 pm -0400 28/9/98, Nik Taylor wrote:
......
>True, but with fractions, the base doesn't really matter, now does it?
>So as far as a "basal notation", duodecimal is easier with common
>fractions, while with fractions both are equally easy.
Yep - although the ancient Romans counted in tens, they used the duodecimal
system for fractions, based on 'uncia' = 1/12.  Hence the Roman foot was
divided into 12 unciae (uncia = 1/12) which gives the modern word "inch",
coming to us via Old English.

Similarly the Roman pound weight, libra, was divided into 12 unciae, which
gives us "ounce" coming to us via Old French.  The Roman ounce was similar
to the modern ounce & the pound to the 'Troy pound' of goldsmiths &
silversmiths, not the 16 ounce Averdupois one.

>P.S., how did the Romans do multiplication with Roman numerals?  I can't
>imagine trying to multiply XXIII by XIV without converting into Arabic
>numberals.
It can be done.  I have worked out a 'pencil & paper' method for doing
addition, subtraction & multiplication using just Roman numerals.  However,
multiplication in particular is long winded & the Romans in practice use
the abacus, which also made division somewhat easier.

To go into details I'd have to look out my abacus notes, but it did make
life a lot easier.

I have not been able to work out a 'pencil & paper' method for division
other than using continual subtraction.
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Then at 7:06 pm -0400 28/9/98, Nik Taylor wrote:
>Pablo Flores wrote:
>> BTW, what's the origin of the English names of measures ("yard", "pound",
>> "gallon", "inch")? Does "mile" have something to do with the Latin root
>> for Spanish _mil_ "one thousand"?
>
>Yes.  The word "mile" was borrowed by the ancestors of the Anglo-Saxons
>while they were still on the Continent.  The Roman mile was equal to
>1,000 paces - I think it was about 3000 feet, it was definitely shorter
>than the modern mile.
It was.  10 old Roman miles is approx.11 modern AngloAmerican miles.  the
Roman miles was indeed 1000 "paces", but the "paces" (passus) was a double
step, i.e. 'left, right', and was regularized as 5 Roman feet, therefore, 1
Roman mile was 5000 Roman feet.

The Roman mile was approx. 1.5 kilometers & the foot slightly shorter than
the AngloAmerican foot.
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At 6:54 pm -0500 28/9/98, Carlos Thompson wrote:
>De: Nik Taylor <fortytwo@...>
>Fecha: Lunes 28 de Septiembre de 1998 18:09
>>
>>P.S., how did the Romans do multiplication with Roman numerals?  I can't
>>imagine trying to multiply XXIII by XIV without converting into Arabic
>>numberals.
>>
>I guess they just added...
No - far too impractical, except for small amounts.  See above.

>I remember I once read about numerical systems
>and how people performed simple math with them an I don't remember how they
>did but I know when seriuos arithmetic was neaded Europeans adopted the
>Arabic numberals wich had been around already.
No. Arabic numerals certainly made mathematics a whole lot easier, but the
ancient Greeks, for example, were doing pretty serious arithmetic centuries
before their introduction.  And Roman engineering also needed some quite
serious mathematics!

Ray.