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Re: [Pythagorean-L] Pythagoras and Vitruvius

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  • leslie greenhill
    Hi ab Exactly what I said. The design for the court was extracted from an ancient text. In fact, it is an archetypal design and occurs in the 3:4:5 triangle
    Message 1 of 18 , Sep 30, 2006
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      Hi ab

      Exactly what I said. The design for the court was
      extracted from an ancient text. In fact, it is an
      archetypal design and occurs in the 3:4:5 triangle
      when treated in a particular way. Are you asking me
      to name the text? We will have to know more about
      each other before we can discuss that. Good that you
      are interested. Don't take it that I am being
      difficult. I have reasons. Ask more questions and I
      will try to answer them.

      Regards
      Les Greenhill

      --- a b <ath98xyz@...> wrote:

      >
      >
      > --- leslie greenhill <neoplatonist2000@...>
      > wrote:
      >
      > >I can show that
      > > the
      > > original design occurs in a well known but seldom
      > > used
      > > book that is some two thousand years old.
      > >
      >
      > Hi les,
      >
      > To what exactly are you refering ?
      >
      > Regards,
      >
      > George
      >
      > __________________________________________________
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      >
      >
      >


      P.O. Box 314
      Mentone, Victoria 3194 Australia
      Email: neoplatonist2000@...

      __________________________________________________
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    • leslie greenhill
      Hi Eric I haven t done that before. I will send you the document as an attachment. Could you put it on the files section of the newsgroup for me? Thanks.
      Message 2 of 18 , Sep 30, 2006
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        Hi Eric

        I haven't done that before. I will send you the
        document as an attachment. Could you put it on the
        files section of the newsgroup for me? Thanks.

        Les

        --- 1746 <arehisosur@...> wrote:

        > Could you possibly upload the file to the files
        > section of the
        > yahoogroup? If not, I'd like a copy to read. I'm
        > familiar with Jon
        > Michell and ancient metrology, so your work
        > definitely sounds
        > interesting.
        >
        > Thanks in advance,
        > Eric
        > arehisosur@...
      • leslie greenhill
        Hi Michael I will prepare a longer response to your interesting reply. But as a preliminary, let me help direct you down a better road in relation to measures
        Message 3 of 18 , Sep 30, 2006
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          Hi Michael

          I will prepare a longer response to your interesting
          reply. But as a preliminary, let me help direct you
          down a better road in relation to measures connected
          with the number 252. Firstly, as a recommendation,
          don't relate the metre to ancient measures or to the
          British imperial system - that will take you astray.
          The Frenchmen who created the "metre" were almost
          certainly Freemasons who attempted to bring ancient
          material into their own cultural context. The metre
          is equivalent to 39.37 inches. How did this number
          come about? I have a clear answer. Anyone reading
          this email can check the following for themselves.

          I have already previously referred to Vitruvius. Find
          and read this passage in "The Ten Books on
          Architecture", Book 1, chapter 6, passage 9.

          The passage relates to the measure of the world. What
          is the number used in relation to ... "observing that
          an eighth part of this, occupied by a wind, is ..."?
          Write the number down and look at it.

          An inexpensive edition of the book is published by
          Dover. The translator is Morris Hicky Morgan. See
          pages 27/28. I am not giving the answer because it is
          good to discover things.

          I will follow up as soon as I can. Your response in
          the meantime would be good.

          Regards
          Les Greenhill

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

          > Thanks, Les, for the Atlantis paper.
          > 1. Yes, Francis Greenway was a Freemason, as well as
          > being a freestone mason. He designed and made the
          > first set of masonic regalia in Australia, in a
          > design
          > that still forms the basis of the current regalia.
          > 2. The number 252 may well be used in Freemasonry,
          > though it is certainly not their sole preserve. The
          > great advantage of groups such as the Freemasons is
          > that they have incorporated and preserved many
          > ancient
          > traditions. The issue we have to face in our time,
          > and as students of Pythagoras, is to determine the
          > underlying significance of these traditions. What
          > is
          > it that makes these numbers and these issues so
          > important?
          > 3. As a line of length, the number 252 reflects a
          > very
          > ancient measure which is known as the english rod,
          > with a length of 5.04metres. So 50 english rods
          > extend 252metres.
          > 4. The english rod of 2 x 2.52m is the basis of the
          > ancient english Winchester foot, measuring 305.45mm.
          >
          > It is this foot, and its inch of 25.45mm, that is
          > the
          > key to the analysis of Francis Greenway's
          > architecture
          > in Australia.
          > 5. I was not aware of the measurements of the tennis
          > court. Your analysis underscores the antiquity of
          > the
          > game. Again, the issue for us must become: why are
          > these measurements and numbers so important? what
          > meaning did the ancients ascribe to them?
          > 6. Some comment and questions about Atlantis
          > shortly.
          >
        • leslie greenhill
          Hi Michael and others I forgot that Vitruvius s Ten Books on Architecture was available on a website. Here it is:
          Message 4 of 18 , Oct 1, 2006
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            Hi Michael and others

            I forgot that Vitruvius's "Ten Books on Architecture"
            was available on a website. Here it is:

            http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus:text:1999.02.0073&query=

            And here are some answers to the points you raised.

            The number 252, as you say, was not the sole preserve
            of Freemasonry. Here is an addition to the tennis
            material. I quote from 1972 edition of the Chambers
            Twentieth Century Dictionary in relation to the word
            "tun".

            ... a large cask: an obsolete liquid measure - 216
            gallons of ale, 252 of wine ...

            Again we see the numbers used in tennis.

            You raised the question "What is it that makes these
            numbers and these issues so important?"

            Here is an answer. When you have penetrated the
            basics of certain geometry, numbers like 252 and 216
            arise is remarkable, indeed, "magical" circumstances.
            When this happens our notions of space can be deeply
            challenged. One may become inspired. (I recommend
            the book "Flatland" by Edwin Abbott in this regard.
            It sits well with Plato's Cave and Shadow myth, which
            is found in the "Republic".)

            The English rod you mention, as you know, is 16.5
            feet. Fifty such rods is 9900 inches, which is 251.46
            metres. That's too far out to be considered 252
            metres. I have analysed literally hundreds of designs
            from antiquity by great people. Never once have I
            seen approximations. Their formulations always
            produce rational, meaningful and often startling
            outcomes. I have learned not to trust approximations.
            In relation to measures, can I suggest you look into
            the background of Edmund Gunter, the so-called
            inventor of Gunter's chain. He was almost certainly a
            Freemason. And the chain and the link originated in
            the mystery schools long before his time. Below is
            another talking point.

            In cricket, the pitch is one chain long. A chain is
            66 feet or 792 inches. Law 8 in the sport deals with
            the wickets. The stumps are to be 28 inches high and
            9 inches wide. The product of 28 x 9 is 252.
            Furthermore, the quotient of 792 divided by 252 is
            22/7, the well-known fraction used to represent pi, a
            transcendental number.

            Regards
            Les



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

            > Thanks, Les, for the Atlantis paper.
            > 1. Yes, Francis Greenway was a Freemason, as well as
            > being a freestone mason. He designed and made the
            > first set of masonic regalia in Australia, in a
            > design
            > that still forms the basis of the current regalia.
            > 2. The number 252 may well be used in Freemasonry,
            > though it is certainly not their sole preserve. The
            > great advantage of groups such as the Freemasons is
            > that they have incorporated and preserved many
            > ancient
            > traditions. The issue we have to face in our time,
            > and as students of Pythagoras, is to determine the
            > underlying significance of these traditions. What
            > is
            > it that makes these numbers and these issues so
            > important?
            > 3. As a line of length, the number 252 reflects a
            > very
            > ancient measure which is known as the english rod,
            > with a length of 5.04metres. So 50 english rods
            > extend 252metres.
            > 4. The english rod of 2 x 2.52m is the basis of the
            > ancient english Winchester foot, measuring 305.45mm.
            >
            > It is this foot, and its inch of 25.45mm, that is
            > the
            > key to the analysis of Francis Greenway's
            > architecture
            > in Australia.
            > 5. I was not aware of the measurements of the tennis
            > court. Your analysis underscores the antiquity of
            > the
            > game. Again, the issue for us must become: why are
            > these measurements and numbers so important? what
            > meaning did the ancients ascribe to them?
            > 6. Some comment and questions about Atlantis
            > shortly.
          • leslie greenhill
            Thanks to Eric, members of the group can now access the paper How Plato designed Atlantis in the files section. Les ... P.O. Box 314 Mentone, Victoria 3194
            Message 5 of 18 , Oct 1, 2006
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              Thanks to Eric, members of the group can now access
              the paper "How Plato designed Atlantis" in the files
              section.

              Les

              --- 1746 <arehisosur@...> wrote:

              > Could you possibly upload the file to the files
              > section of the
              > yahoogroup? If not, I'd like a copy to read. I'm
              > familiar with Jon
              > Michell and ancient metrology, so your work
              > definitely sounds
              > interesting.
              >
              > Thanks in advance,
              > Eric
              > arehisosur@...
              >
              >
              > On 9/28/06, leslie greenhill
              > <neoplatonist2000@...> wrote:
              > > Hi Michael
              > >
              > > By all means join in. As we can't send
              > attachments
              > > via the newsgroup I will send you the Atlantis
              > paper
              > > separately. After you have read the exposition
              > let's
              > > take the matter further. For a start, the number
              > 5040
              > > is 2 times 2520. You may or may not be aware that
              > > Eratosthenes, who was interested in things
              > Platonic,
              > > says the world measures 252,000 stades. Pliny the
              > > Elder makes some witty remarks in this regard.
              > And
              > > Vitruvius suggests there is more to this than
              > meets
              > > the eye. Let me now direct you to a passage in
              > "The
              > > Histories" by Herodotus, who precedes Plato and
              > > Eratosthenes. In Book 1, passage 32, we are told
              > > about the span of a man's life: 252,000 days (360
              > x
              > > 70). Read the passage. It contains a marvellous
              > and
              > > meaningful formulation which we can later discuss.
              > If
              > > Francis Greenaway is using that number he was
              > almost
              > > certainly a Freemason. (Some years ago, a senior
              > > academic in Sydney wrote a paper on street layout
              > in
              > > early Parramatta and came to the conclusion that
              > > Freemasons were involved. The academic's name is,
              > I
              > > think, Prof. Paul Allen Johnson; he headed an
              > > architecture department in one of the
              > universities.)
              > >
              > > Now for something that I hope really makes you and
              > > others sit up. If you care to study the history
              > of
              > > tennis, you will find the hand of Freemasonry,
              > > particularly in the design of a tennis court. A
              > > notable example of a connection between tennis and
              > > Freemasonry can be readily observed: the current
              > > president of the All England Lawn Tennis and
              > Croquet
              > > Club is the Duke of Kent, who also happens to be
              > the
              > > Grand Master of the United Grand Lodge of England
              > > founded in 1813.
              > >
              > > The distance from the net to the service line is
              > 21
              > > feet (252 inches) and from the service line to the
              > > base line is 18 feet (216 inches: 216 = 6 x 6 x
              > 6).
              > > Note that the ratio 252:216 is the same as 7:6, a
              > > fairly famous ratio in a range of areas. One of
              > the
              > > topics at the back of my filing cabinet is an
              > > extensive analysis of the court. I can show that
              > the
              > > original design occurs in a well known but seldom
              > used
              > > book that is some two thousand years old.
              > >
              > > The doubles court is 36 feet wide and the singles
              > > court is 27 feet wide. The ratio 36:27 is 4:3, a
              > > ratio found in a 3:4:5 triangle. There can
              > scarcely
              > > be anyone interested in the Pythagoreans not aware
              > of
              > > their interest in that triangle. In Freemasonry,
              > the
              > > 3:4:5 triangle is known as the Past Masters'
              > Jewel.
              > > (This is not an expose of Freemasonry - the Jewel
              > is
              > > public knowledge.)
              > >
              > > You will be well aware that in Plato's "Laws" the
              > > number 60 is used in a range of ways. Note that 3
              > x 4
              > > x 5 = 60.
              > >
              > > I'm getting warmed up and had better close or this
              > > email will become a paper. The Atlantis paper is
              > on
              > > its way.
              > >
              > > Regards
              > > Les
              >
              >
              >
              >


              P.O. Box 314
              Mentone, Victoria 3194 Australia
              Email: neoplatonist2000@...

              __________________________________________________
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            • michael michael
              Good morning, Les. Taking this note and your previous together, you raise some thorny issues. It would be good to get some common ground on these. 1. I agree
              Message 6 of 18 , Oct 2, 2006
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                Good morning, Les.
                Taking this note and your previous together, you raise
                some thorny issues. It would be good to get some
                common ground on these.
                1. I agree wholeheartedly about precision in
                measurement; that the ancients were precise; that
                approximations are not to be trusted.
                2. Accordingly, it has to be said that the english rod
                is 5.04metres. This is not an approximation. So 50
                english rods extend 252m. Your calculation below
                implies a rod measuring 5.0292m; and implies an inch
                of 0.0254m. Although it is the commonly used value
                now, and has been enshrined in Statute Law (only since
                about 1965 AD), such an inch is not an accurate
                representation of the ancient measure.
                3. The french metre is indeed based upon an erroneous
                premise; and the philosophes were trying to capture an
                ancient resource. But that is not a reason to dismiss
                the metre from discourse. The ancients did have a
                metre measure; and their metre was based accurately
                and precisely in the physical world.
                4. One can be and often is led astray equally by those
                who trade in feet and inches, because they rarely
                specify the standard of measurement that they are
                using for their foot and inch. It is always a
                relevant question: whose foot? and if the answer is
                locally based, as for example, 'the english foot' or
                'the greek foot', then, which english or greek foot is
                being used as the standard? there are more than one
                such.
                5. The english rod is 5.04m and it is, as you say,
                16.5 feet. Whose feet? English feet, yes; but not
                the british imperial foot. The proper standard is the
                english Winchester foot, found for instance throughout
                the english royal city of Winchester. Such a foot is
                identical to the north german foot, and the standard
                can be traced back, without alteration, to ancient
                mesopotamia. The standard, then, for the english rod
                is a foot of 305.4545...mm; having an inch of
                25.4545mm.
                6. Once this is appreciated, it can be recognized that
                the french measurers (Picard et al) were looking in
                the wrong spot for a geodetically based standard for
                the metre. The ancient metre does arise from Earth
                measurements, and it does have neat decimal multiple
                in this respect, but Earth is not measured thereby.
                7. Which takes us to Eratosthenes, and Vitruvius. The
                experiment conducted by Eratosthenes resulted in a
                circumference of Earth of 250,000 stades; not 252,000
                stades. It is said that E. altered the result of the
                experiment to 252,000 to provide a number divisible by
                60! although I would treat such an assertion with some
                caution.
                8. I am not sure of the point you are wanting to make
                about the Vitruvius text when you say: "The metre is
                equivalent to 39.37 inches. How did this number come
                about?" I note the numerical similarity to 3,937,500
                x 8. Could you elaborate?
                Regards,
                Michael.

                --- leslie greenhill <neoplatonist2000@...>
                wrote:

                > Hi Michael and others
                >
                > I forgot that Vitruvius's "Ten Books on
                > Architecture"
                > was available on a website. Here it is:
                >
                >
                http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus:text:1999.02.0073&query=
                >
                > And here are some answers to the points you raised.
                >
                > The number 252, as you say, was not the sole
                > preserve
                > of Freemasonry. Here is an addition to the tennis
                > material. I quote from 1972 edition of the Chambers
                > Twentieth Century Dictionary in relation to the word
                > "tun".
                >
                > ... a large cask: an obsolete liquid measure - 216
                > gallons of ale, 252 of wine ...
                >
                > Again we see the numbers used in tennis.
                >
                > You raised the question "What is it that makes these
                > numbers and these issues so important?"
                >
                > Here is an answer. When you have penetrated the
                > basics of certain geometry, numbers like 252 and 216
                > arise is remarkable, indeed, "magical"
                > circumstances.
                > When this happens our notions of space can be deeply
                > challenged. One may become inspired. (I recommend
                > the book "Flatland" by Edwin Abbott in this regard.
                > It sits well with Plato's Cave and Shadow myth,
                > which
                > is found in the "Republic".)
                >
                > The English rod you mention, as you know, is 16.5
                > feet. Fifty such rods is 9900 inches, which is
                > 251.46
                > metres. That's too far out to be considered 252
                > metres. I have analysed literally hundreds of
                > designs
                > from antiquity by great people. Never once have I
                > seen approximations. Their formulations always
                > produce rational, meaningful and often startling
                > outcomes. I have learned not to trust
                > approximations.
                > In relation to measures, can I suggest you look
                > into
                > the background of Edmund Gunter, the so-called
                > inventor of Gunter's chain. He was almost certainly
                > a
                > Freemason. And the chain and the link originated in
                > the mystery schools long before his time. Below is
                > another talking point.
                >
                > In cricket, the pitch is one chain long. A chain is
                > 66 feet or 792 inches. Law 8 in the sport deals
                > with
                > the wickets. The stumps are to be 28 inches high
                > and
                > 9 inches wide. The product of 28 x 9 is 252.
                > Furthermore, the quotient of 792 divided by 252 is
                > 22/7, the well-known fraction used to represent pi,
                > a
                > transcendental number.
                >
                > Regards
                > Les
              • michael michael
                Hello Les; 1. I am looking at the Herodotus text about the span of a man s life. I don t know what I am to make of it. 2. About Atlantis; I was under the
                Message 7 of 18 , Oct 4, 2006
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                  Hello Les;
                  1. I am looking at the Herodotus text about the span
                  of a man's life. I don't know what I am to make of
                  it.
                  2. About Atlantis; I was under the impression that
                  Plato regarded the design of Atlantis as deficient;
                  and that this was the reason for its destruction.
                  Any thoughts?
                  Michael

                  --- leslie greenhill <neoplatonist2000@...>
                  wrote:

                  > Hi Michael
                  >
                  > By all means join in. As we can't send attachments
                  > via the newsgroup I will send you the Atlantis paper
                  > separately. After you have read the exposition
                  > let's
                  > take the matter further. For a start, the number
                  > 5040
                  > is 2 times 2520. You may or may not be aware that
                  > Eratosthenes, who was interested in things Platonic,
                  > says the world measures 252,000 stades. Pliny the
                  > Elder makes some witty remarks in this regard. And
                  > Vitruvius suggests there is more to this than meets
                  > the eye. Let me now direct you to a passage in "The
                  > Histories" by Herodotus, who precedes Plato and
                  > Eratosthenes. In Book 1, passage 32, we are told
                  > about the span of a man's life: 252,000 days (360 x
                  > 70). Read the passage. It contains a marvellous
                  > and
                  > meaningful formulation which we can later discuss.
                  > If
                  > Francis Greenaway is using that number he was almost
                  > certainly a Freemason. (Some years ago, a senior
                  > academic in Sydney wrote a paper on street layout in
                  > early Parramatta and came to the conclusion that
                  > Freemasons were involved. The academic's name is, I
                  > think, Prof. Paul Allen Johnson; he headed an
                  > architecture department in one of the universities.)
                  >
                  >
                  > Now for something that I hope really makes you and
                  > others sit up. If you care to study the history of
                  > tennis, you will find the hand of Freemasonry,
                  > particularly in the design of a tennis court. A
                  > notable example of a connection between tennis and
                  > Freemasonry can be readily observed: the current
                  > president of the All England Lawn Tennis and Croquet
                  > Club is the Duke of Kent, who also happens to be the
                  > Grand Master of the United Grand Lodge of England
                  > founded in 1813.
                  >
                  > The distance from the net to the service line is 21
                  > feet (252 inches) and from the service line to the
                  > base line is 18 feet (216 inches: 216 = 6 x 6 x 6).
                  >
                  > Note that the ratio 252:216 is the same as 7:6, a
                  > fairly famous ratio in a range of areas. One of the
                  > topics at the back of my filing cabinet is an
                  > extensive analysis of the court. I can show that
                  > the
                  > original design occurs in a well known but seldom
                  > used
                  > book that is some two thousand years old.
                  >
                  > The doubles court is 36 feet wide and the singles
                  > court is 27 feet wide. The ratio 36:27 is 4:3, a
                  > ratio found in a 3:4:5 triangle. There can scarcely
                  > be anyone interested in the Pythagoreans not aware
                  > of
                  > their interest in that triangle. In Freemasonry,
                  > the
                  > 3:4:5 triangle is known as the Past Masters' Jewel.
                  > (This is not an expose of Freemasonry - the Jewel is
                  > public knowledge.)
                  >
                  > You will be well aware that in Plato's "Laws" the
                  > number 60 is used in a range of ways. Note that 3 x
                  > 4
                  > x 5 = 60.
                  >
                  > I'm getting warmed up and had better close or this
                  > email will become a paper. The Atlantis paper is on
                  > its way.
                  >
                  > Regards
                  > Les
                • leslie greenhill
                  Hi Michael 1. Examine the ratio 262,500 and 252,000. Establish what that is. You need to know about the slightly controversial ratio between the Greek foot
                  Message 8 of 18 , Oct 5, 2006
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                    Hi Michael

                    1. Examine the ratio 262,500 and 252,000. Establish
                    what that is. You need to know about the slightly
                    controversial ratio between the Greek foot and Roman
                    foot, which is the same ratio. Pliny the Elder is a
                    key source of that information. Then you might ask
                    yourself: does that ratio feature in a fairly common
                    Pythagorean triple? Understand this and you are on
                    your way. Below are a few remarks on the Winchester
                    foot. It might be useful not to get too attached to
                    that measure. In the big scheme of things, it's well
                    down the list. All the great measures of antiquity
                    have special mathematical/religious functions. This
                    subject is my speciality. To get you thinking in this
                    regard, be aware that the usual Roman stade measure
                    contained 625 Roman feet. The number 625 is 25
                    squared and 25 is 5 squared. Historians of metrology
                    seldom question this curiosity. Anyway, consider this
                    about the Winchester foot.

                    It is well known that the influence of the Romans did
                    not die out after they quit the British Isles. Their
                    weights and measures system persisted. You probably
                    know that. The Roman foot measured about 296 mm. It
                    had 16 digit divisions. A digit, accordingly,
                    measured about 18.5 mm. (It is very slightly more
                    actually - and there is an exact value in British
                    imperial terms.) If you take 16.5 of these digits,
                    you have a measure of around 305.25 mm, which is a lot
                    like the Winchester foot. You can see a sense in this
                    measure. For a start, 16.5 doubles to 33 and 66. The
                    number 66 is an integral aspect of the so-called
                    British imperial system: 66 feet equals one chain.
                    Sixty-six feet divided by 22/7 yields 21 feet, which
                    is 252 inches. I can tell you a bit more about the
                    world measure of 252,000 stades. It's a trick.
                    Students in the mystery schools knew how to interpret
                    the trick. Eratosthenes was much interested in
                    Plato's work. He knew exactly what he was doing.

                    The ratio 16.5:16, that is, 33:32 is well known to me
                    and is linked to other ancient measures. Note how
                    uncomplicated this is.

                    2. ATLANTIS. Go back to the end of my exposition. I
                    demonstrate fairly clearly, I think, that Atlantis is
                    a mathematical setup for students or initiates. There
                    was no such island/continent. In work I have ready
                    prepared ("Grand Design in the works of Leonardo,
                    Vitruvius, Plato and Herodotus") I hope to end
                    speculation about the lost island. More mathematical
                    setups are unveiled, including some very remarkable
                    things. The big picture is visionary and the truth is
                    more amazing than the fanciful. It may interest you
                    to know that I have recovered one of most important
                    mathematical design features of Atlantis in an ancient
                    Egyptian text. No approximations. No loose
                    interpretations. The material precedes Plato by at
                    least one thousand years.

                    Can I suggest you read "The Art of Memory" by Frances
                    Yates, a British scholar. It has been published in
                    paperback. Her work is acknowledged as amongst the
                    best in its field. She died in 1981. She was awarded
                    honours by the Queen for her intellectual
                    contributions. It is essential to understand the use
                    in antiquity of fanciful stories as memory devices.
                    Paper and writing materials were only for the few.
                    Bear that strongly in mind. Vivid astrological
                    imagery, for instance, was often used to pass on not
                    only moral and ethical issues, but mathematical
                    information as well.

                    Cheers
                    Les

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

                    > Hello Les;
                    > 1. I am looking at the Herodotus text about the span
                    > of a man's life. I don't know what I am to make of
                    > it.
                    > 2. About Atlantis; I was under the impression that
                    > Plato regarded the design of Atlantis as deficient;
                    > and that this was the reason for its destruction.
                    > Any thoughts?
                    > Michael
                  • michael michael
                    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
                    Message 9 of 18 , Oct 5, 2006
                    • 0 Attachment
                      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.


                      --- leslie greenhill <neoplatonist2000@...>
                      wrote:

                      > Hi Michael
                      >
                      > 1. Examine the ratio 262,500 and 252,000.
                      > Establish
                      > what that is. You need to know about the slightly
                      > controversial ratio between the Greek foot and Roman
                      > foot, which is the same ratio. Pliny the Elder is a
                      > key source of that information. Then you might ask
                      > yourself: does that ratio feature in a fairly
                      > common
                      > Pythagorean triple? Understand this and you are on
                      > your way. Below are a few remarks on the Winchester
                      > foot. It might be useful not to get too attached to
                      > that measure. In the big scheme of things, it's
                      > well
                      > down the list. All the great measures of antiquity
                      > have special mathematical/religious functions. This
                      > subject is my speciality. To get you thinking in
                      > this
                      > regard, be aware that the usual Roman stade measure
                      > contained 625 Roman feet. The number 625 is 25
                      > squared and 25 is 5 squared. Historians of
                      > metrology
                      > seldom question this curiosity. Anyway, consider
                      > this
                      > about the Winchester foot.
                      >
                      > It is well known that the influence of the Romans
                      > did
                      > not die out after they quit the British Isles.
                      > Their
                      > weights and measures system persisted. You probably
                      > know that. The Roman foot measured about 296 mm.
                      > It
                      > had 16 digit divisions. A digit, accordingly,
                      > measured about 18.5 mm. (It is very slightly more
                      > actually - and there is an exact value in British
                      > imperial terms.) If you take 16.5 of these digits,
                      > you have a measure of around 305.25 mm, which is a
                      > lot
                      > like the Winchester foot. You can see a sense in
                      > this
                      > measure. For a start, 16.5 doubles to 33 and 66.
                      > The
                      > number 66 is an integral aspect of the so-called
                      > British imperial system: 66 feet equals one chain.
                      > Sixty-six feet divided by 22/7 yields 21 feet, which
                      > is 252 inches. I can tell you a bit more about the
                      > world measure of 252,000 stades. It's a trick.
                      > Students in the mystery schools knew how to
                      > interpret
                      > the trick. Eratosthenes was much interested in
                      > Plato's work. He knew exactly what he was doing.
                      >
                      > The ratio 16.5:16, that is, 33:32 is well known to
                      > me
                      > and is linked to other ancient measures. Note how
                      > uncomplicated this is.
                      >
                      > 2. ATLANTIS. Go back to the end of my exposition.
                      > I
                      > demonstrate fairly clearly, I think, that Atlantis
                      > is
                      > a mathematical setup for students or initiates.
                      > There
                      > was no such island/continent. In work I have ready
                      > prepared ("Grand Design in the works of Leonardo,
                      > Vitruvius, Plato and Herodotus") I hope to end
                      > speculation about the lost island. More
                      > mathematical
                      > setups are unveiled, including some very remarkable
                      > things. The big picture is visionary and the truth
                      > is
                      > more amazing than the fanciful. It may interest you
                      > to know that I have recovered one of most important
                      > mathematical design features of Atlantis in an
                      > ancient
                      > Egyptian text. No approximations. No loose
                      > interpretations. The material precedes Plato by at
                      > least one thousand years.
                      >
                      > Can I suggest you read "The Art of Memory" by
                      > Frances
                      > Yates, a British scholar. It has been published in
                      > paperback. Her work is acknowledged as amongst the
                      > best in its field. She died in 1981. She was
                      > awarded
                      > honours by the Queen for her intellectual
                      > contributions. It is essential to understand the
                      > use
                      > in antiquity of fanciful stories as memory devices.
                      > Paper and writing materials were only for the few.
                      > Bear that strongly in mind. Vivid astrological
                      > imagery, for instance, was often used to pass on not
                      > only moral and ethical issues, but mathematical
                      > information as well.
                      >
                      > Cheers
                      > Les
                    • 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 10 of 18 , Oct 8, 2006
                      • 0 Attachment
                        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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