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Re: [HM] Not a fraction?
Posted:
Feb 6, 2006 2:50 PM
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>Date: Thu, 2 Feb 2006 13:57:02 +1300
>From: Ken Pledger <ken.pledger@vuw.ac.nz>
>Subject: Re: [HM] Not a fraction?
>
>At 13:24 -0500 26/1/06, Robert Eldon Taylor wrote [of the Greeks]:
>
>
>>....
>>they seem to be very reluctant to use a fraction equal to or greater
>>than the whole. If I say I have a number of quarters in my pocket, you
>>will not be surprised to know there are four or five or more, because a
>>quarter is thought of as a distinct unit and not just a fourth of a
>>dollar. So if Archimedes or others were thinking of third or fifth as
>>new units, as you suggest, it seems they would speak also of four of
>>those thirds or five of those fifths. But they never seem to do this....
>>
>>
>
>
> I may have just happened upon an example in Archimedes, "On
>Conoids and Spheroids" 21 & 22. In the enunciation Heath says
>"half as large again," but in the proof he uses "3/2". At the
>same step, the 1970 French translation by Charles Mugler uses "les
>trois demis". From my ignorant viewing of the Greek text, the
>crucial word appears to be "hemiolios". Can any Greek reader shed
>some light on this please?
>
> Ken Pledger.
>
>
Here is a reference:
http://www.chrysalis-foundation.org/origins_of_length_ratios.htm
Hans Lausch
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