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Re: [HM] Not a fraction?
Posted:
Feb 6, 2006 2:50 PM


>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.chrysalisfoundation.org/origins_of_length_ratios.htm
Hans Lausch



