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Re: [Pythagorean-L] Pythagoras and Vitruvius

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  • leslie greenhill
    Hi Michael Let s get back to the 3:4:5 triangle. It has 3 angles. Put the right angle aside and examine the other two. Subtract the smaller from the
    Message 1 of 18 , Oct 8, 2006
      Hi Michael

      Let's get back to the 3:4:5 triangle. It has 3
      angles. Put the right angle aside and examine the
      other two. Subtract the smaller from the greater.
      The remainder leads to another Pythagorean triple.
      Let me know what you find.

      Les

      --- michael michael <michael3992002@...>
      wrote:

      > Yes, Les.
      > The ratio (doubled) is that between 525,000 and
      > 504,000; and is the ratio between the egyptian royal
      > cubit and the english rod.
      > The stadion of 625 roman feet measures equally the
      > greek stadion of 600 artabic or greek feet.
      > As you say, the ratio of the greek (artabic) foot
      > and
      > the roman foot is the same: 0.308276458m :
      > 0.2959454m
      > = 1.041666...
      > The ratio, as a fraction, is 100 : 96 or 25 : 24,
      > which is how many ancient measures are related.
      > I accept that the ancient measures are indeed all
      > related; and they stand together in simple numerical
      > relationships. But...?
      > The ratio relates equally to the measures 525 and
      > 504
      > through the numeric of "the name of god" or 21.
      > The triple with pythagorean significance? are you
      > suggesting the relationship 21 - 24 - 25 as the 3 -
      > 4
      > - 5 triangle in multiples of 7 - 6 - 5 ?
      > But... I am on my way to where?
      >
      > 2. On the Winchester foot; I accept your
      > reservations, without, however, agreeing with them;
      > so
      > I will not push the point. I will simply emphasize
      > that when discussing the 504 or 252 x 2 numbers, one
      > is tying the discourse to the Winchester foot and to
      > the anglo-saxon gyrd of 16.5 such feet. Also, the
      > Winchester foot is necessary for the elucidation of
      > ancient egyptian issues (such as the number of the
      > 'souls of the dead'; issues which, in fact, underlie
      > Eratosthenes calculation of Earth dimensions.
      >
      > 3. When Strabo notes that Eratosthenes, with
      > Hipparchus, calculated Earth dimensions as 252,000
      > stadia, he is noting that the calculation is made by
      > degrees where each degree of Earth's round measures
      > 700 stadia.
      > The interesting thing is that 252,000 times 700 such
      > stadia are exactly equivalent to 252,000 stadia of
      > 600
      > feet.
      > It might be observed that 96 of the stadia that
      > comprise the degree in Eratosthenes calculation
      > extend
      > 100 Winchester feet; illustrating the
      > 96 : 100 or 24 : 25 ratio yet again.
      > Moreover, the ratio of the egyptian royal cubit and
      > that stadion is 1.65.
      >
      > 4. I would like to know more about the trick.
      >
      > Michael.
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