Means and Extremes of a ProportionDate: 09/16/2004 at 17:27:43 From: Kathy Subject: means and extremes In the proportion a/b = c/d, why are the a and the d called the extremes and the b and c called the means of the proportion? Date: 09/16/2004 at 18:09:31 From: Doctor Schwa Subject: Re: means and extremes Hi Kathy - In the old days, instead of writing 1/2 = 3/6, people would write 1:2 = 3:6 and conventionally they would be written in that order so that the "middle" numbers, the means, are actually in the middle, and the "extreme" numbers are the ones way out on the ends. At least, that's as much as I know about it! Then I tried the Oxford English Dictionary, and found: 1570 BILLINGSLEY Euclid 153b, A right line is sayd to be deuided by an extreme and meane proportion, when the whole is to the greater part, as the greater part is to the lesser. That is, originally "extremes" were the whole thing and the small piece, while the "means" were two EQUAL numbers in the middle of the proportion, like 9:6 = 6:4. Now it makes sense: in fact, 6 is called the "geometric mean" in that case, and 9 and 4 are reasonable "extremes" around the "mean" of 6. I guess it was later that the same terms were used when the middle parts were unequal! - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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