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Parans

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  • terminusen
    Dear All ! Does anyone know what are the earliest sources regarding parans besides Maternus, Manilius, Hypparchus, Ptolemy, Eudoxos. I m doing a research with
    Message 1 of 11 , Sep 2, 2006
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      Dear All !
      Does anyone know what are the earliest sources regarding parans
      besides Maternus, Manilius, Hypparchus, Ptolemy, Eudoxos. I'm doing a
      research with parans and I would like to know if there are more
      obscure source-materials on this topic; I'm thinking of some genuine
      babylonian materials, not hellenistic stuff. Bernadette might know the
      answer, Your help would be appreciated, Thanks in advance Peter
      Kecskés
    • Arthyr
      Hello Peter Kecskés, ... (Arthyr) Well, I hate to bust a bubble but I really don t think you ll find too much before Hipparchus time (BCE 150) as the early
      Message 2 of 11 , Sep 2, 2006
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        Hello Peter Kecskés,

        At 11:53 PM 9/2/2006 +0000, Peter wrote:
        > Dear All !
        > Does anyone know what are the earliest sources regarding parans
        >besides Maternus, Manilius, Hypparchus, Ptolemy, Eudoxos.

        (Arthyr) Well, I hate to bust a bubble but I really don't think you'll find
        too much before
        Hipparchus' time (BCE 150) as the early Babylonians really didnt work with
        too much planetary phenomena outside of simple mathematical "zone" style
        calculations. Their Main concern was the lunar phases, primarily the New
        Moon's return at first sighting. As parans requires the mathematical
        knowledge of latitude, which the Babylonians had a primitive understanding.
        However:

        Signs and constellations rise and set with rates that vary as a function of
        one's terrestrial latitude.

        To determine when a star or planet sets, the diurnal semi-arc of the body
        must be found, then expressed in time, between the Ascendant in question
        and the upper meridian.They would need to find the semi arc, the angle
        between the ecliptic and the local horizon and the right angle to their
        horizon.

        As you know, a planet conjoined with a star gives that planet a powerful
        influence but the mathematical requirements to predict the diurnal motions
        during the following 24-hour period
        was completely out of the Babylonian mental makeup. One could perform a
        paran style chart based purly on sunset at the place and date of birth as
        that is important, but the Chaldean astrologers were much more interested
        in the synodic periods, they devised "Zones" in their calculations that
        were by no means as sophisticated as the Hellenist's spherical
        trigonometry. This is because parans are based on examining the times when
        stars and planets are at the key moments of their diurnal movement, i.e.
        either on the Ascendant, M.C. Descendant and even the I.C - something the
        Chaldeans weren't aware of calculating.

        The formula is:
        Sine ascensional difference = (tangent declination [planet]) (tangent
        latitude [place])
        where declination is the declination of the body and latitude is the
        terrestrial latitude of the place.If the (A/D) ascentional difference is
        positive add it to 90degrees; subtract from 90degrees if negative. Having
        added the A/D as necessary, divide by 15 (15 degrees = 1 hour of time). The
        result of this division is the diurnal semi-arc of the planet or star.

        (Peter) I'm doing a research with parans and I would like to know if there
        are more
        >obscure source-materials on this topic; I'm thinking of some genuine
        >babylonian materials, not hellenistic stuff. Bernadette might know the
        >answer, Your help would be appreciated, Thanks in advance Peter
        >Kecskés

        (A) Peter, because of the math, you're already in the middle of the
        playground
        for your research. The Hellenistic sholars were the culprits in designing
        this system and I don't think you'll find anything earlier.

        Best regards and well wishes,
        Arthyr
      • msbhavens1
        what about the egyptians? Just wondering as they seemed far more into the Trig. MissB ... you ll find ... work with ... style ... the New ... understanding.
        Message 3 of 11 , Sep 3, 2006
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          what about the egyptians? Just wondering as they seemed far more into
          the Trig. MissB

          --- In thefixedstars@yahoogroups.com, Arthyr <awc99@...> wrote:
          >
          > Hello Peter Kecskés,
          >
          > At 11:53 PM 9/2/2006 +0000, Peter wrote:
          > > Dear All !
          > > Does anyone know what are the earliest sources regarding parans
          > >besides Maternus, Manilius, Hypparchus, Ptolemy, Eudoxos.
          >
          > (Arthyr) Well, I hate to bust a bubble but I really don't think
          you'll find
          > too much before
          > Hipparchus' time (BCE 150) as the early Babylonians really didnt
          work with
          > too much planetary phenomena outside of simple mathematical "zone"
          style
          > calculations. Their Main concern was the lunar phases, primarily
          the New
          > Moon's return at first sighting. As parans requires the mathematical
          > knowledge of latitude, which the Babylonians had a primitive
          understanding.
          > However:
          >
          > Signs and constellations rise and set with rates that vary as a
          function of
          > one's terrestrial latitude.
          >
          > To determine when a star or planet sets, the diurnal semi-arc of
          the body
          > must be found, then expressed in time, between the Ascendant in
          question
          > and the upper meridian.They would need to find the semi arc, the
          angle
          > between the ecliptic and the local horizon and the right angle to
          their
          > horizon.
          >
          > As you know, a planet conjoined with a star gives that planet a
          powerful
          > influence but the mathematical requirements to predict the diurnal
          motions
          > during the following 24-hour period
          > was completely out of the Babylonian mental makeup. One could
          perform a
          > paran style chart based purly on sunset at the place and date of
          birth as
          > that is important, but the Chaldean astrologers were much more
          interested
          > in the synodic periods, they devised "Zones" in their calculations
          that
          > were by no means as sophisticated as the Hellenist's spherical
          > trigonometry. This is because parans are based on examining the
          times when
          > stars and planets are at the key moments of their diurnal movement,
          i.e.
          > either on the Ascendant, M.C. Descendant and even the I.C -
          something the
          > Chaldeans weren't aware of calculating.
          >
          > The formula is:
          > Sine ascensional difference = (tangent declination [planet])
          (tangent
          > latitude [place])
          > where declination is the declination of the body and latitude is the
          > terrestrial latitude of the place.If the (A/D) ascentional
          difference is
          > positive add it to 90degrees; subtract from 90degrees if negative.
          Having
          > added the A/D as necessary, divide by 15 (15 degrees = 1 hour of
          time). The
          > result of this division is the diurnal semi-arc of the planet or
          star.
          >
          > (Peter) I'm doing a research with parans and I would like to know
          if there
          > are more
          > >obscure source-materials on this topic; I'm thinking of some
          genuine
          > >babylonian materials, not hellenistic stuff. Bernadette might know
          the
          > >answer, Your help would be appreciated, Thanks in advance Peter
          > >Kecskés
          >
          > (A) Peter, because of the math, you're already in the middle of the
          > playground
          > for your research. The Hellenistic sholars were the culprits in
          designing
          > this system and I don't think you'll find anything earlier.
          >
          > Best regards and well wishes,
          > Arthyr
          >
        • Arthyr
          Hi B You may be referring to the Rhind Papyrus circa mid 16 s B.C.E. First: Parans articulate the process of a planet, in conjunction with a star, of its
          Message 4 of 11 , Sep 3, 2006
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            Hi "B"

            You may be referring to the Rhind Papyrus circa mid 16's B.C.E.

            First:
            Parans articulate the process of a planet, in conjunction with a star,
            of its motion to the four "Angels"  or angles - Asc. MC, Desc. and the IC.

            This process is involved using sine and cosine values. The values of PI were not
            actually concieved until the late (2nd century BCE) by Archimedes of Syracuse.

            What the Egyptians and Babylonians used were called chords. In plane geometry, a chord is the line segment joining two points on a curve. And although the romance of ascribing certain principles to earlier, more ancient sources has a rich influence, the truth is clear that many Greek Mathmeticians were making a "Reference to Authority" to create substantial "evidence" of their work. This approach proved successful as such "evidence" proved that the scholar knew what he was talking about - obviously, it was aparent when one looked at earlier architecture.

            Many writers do that today with the use of footnotes in their thesis papers.

            Egyptian and Babylonian scholars alike used a repeating numbering system that was used to acquire math solutions.  If the solution of dividing 60 by 5 were required, they added (or doubled) five until the number 60 could be found therein.
            For example:
            1 number  5
            2 (fives are) 10
            4 (fives are)  20
            8 (fives are)  40

            Now if we add the column that adds up to sixty (20 + 40) we note that the
            numbers associated with  the number 20 is 4 and the number associated with
            40 is 8. So, add 8+4 = 12. Sixty divided by Five equals twelve. The same process can be used for multiplication.

            They could also do fractions using the same methodology but still, rather difficult
            for solutions requiring trigonometry.

            Arthyr,


            At 05:15 PM 9/3/2006 +0000, MS.B wrote:
            >
            >what about the egyptians? Just wondering as they seemed far more into
            >the Trig. MissB
          • PeterKecskés
            Dear Arthyr! Thanks a lot for your useful comments, I did not find anything earlier either, but I just wondering where did they get the idea of having the
            Message 5 of 11 , Sep 3, 2006
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              Dear Arthyr!
              Thanks a lot for your useful comments, I did not find
              anything earlier either, but I just wondering where
              did they get the idea of having the 24-hour parans and
              the heliacal rising, and setting, there must have been
              an earlier source; Yours Cat-CH-Keys P.AEther

              -- msbhavens1 <msbhavens1@...> wrote:

              >
              > what about the egyptians? Just wondering as they
              > seemed far more into
              > the Trig. MissB
              >
              > --- In thefixedstars@yahoogroups.com, Arthyr
              > <awc99@...> wrote:
              > >
              > > Hello Peter Kecskés,
              > >
              > > At 11:53 PM 9/2/2006 +0000, Peter wrote:
              > > > Dear All !
              > > > Does anyone know what are the earliest sources
              > regarding parans
              > > >besides Maternus, Manilius, Hypparchus, Ptolemy,
              > Eudoxos.
              > >
              > > (Arthyr) Well, I hate to bust a bubble but I
              > really don't think
              > you'll find
              > > too much before
              > > Hipparchus' time (BCE 150) as the early
              > Babylonians really didnt
              > work with
              > > too much planetary phenomena outside of simple
              > mathematical "zone"
              > style
              > > calculations. Their Main concern was the lunar
              > phases, primarily
              > the New
              > > Moon's return at first sighting. As parans
              > requires the mathematical
              > > knowledge of latitude, which the Babylonians had a
              > primitive
              > understanding.
              > > However:
              > >
              > > Signs and constellations rise and set with rates
              > that vary as a
              > function of
              > > one's terrestrial latitude.
              > >
              > > To determine when a star or planet sets, the
              > diurnal semi-arc of
              > the body
              > > must be found, then expressed in time, between the
              > Ascendant in
              > question
              > > and the upper meridian.They would need to find the
              > semi arc, the
              > angle
              > > between the ecliptic and the local horizon and the
              > right angle to
              > their
              > > horizon.
              > >
              > > As you know, a planet conjoined with a star gives
              > that planet a
              > powerful
              > > influence but the mathematical requirements to
              > predict the diurnal
              > motions
              > > during the following 24-hour period
              > > was completely out of the Babylonian mental
              > makeup. One could
              > perform a
              > > paran style chart based purly on sunset at the
              > place and date of
              > birth as
              > > that is important, but the Chaldean astrologers
              > were much more
              > interested
              > > in the synodic periods, they devised "Zones" in
              > their calculations
              > that
              > > were by no means as sophisticated as the
              > Hellenist's spherical
              > > trigonometry. This is because parans are based on
              > examining the
              > times when
              > > stars and planets are at the key moments of their
              > diurnal movement,
              > i.e.
              > > either on the Ascendant, M.C. Descendant and even
              > the I.C -
              > something the
              > > Chaldeans weren't aware of calculating.
              > >
              > > The formula is:
              > > Sine ascensional difference = (tangent declination
              > [planet])
              > (tangent
              > > latitude [place])
              > > where declination is the declination of the body
              > and latitude is the
              > > terrestrial latitude of the place.If the (A/D)
              > ascentional
              > difference is
              > > positive add it to 90degrees; subtract from
              > 90degrees if negative.
              > Having
              > > added the A/D as necessary, divide by 15 (15
              > degrees = 1 hour of
              > time). The
              > > result of this division is the diurnal semi-arc of
              > the planet or
              > star.
              > >
              > > (Peter) I'm doing a research with parans and I
              > would like to know
              > if there
              > > are more
              > > >obscure source-materials on this topic; I'm
              > thinking of some
              > genuine
              > > >babylonian materials, not hellenistic stuff.
              > Bernadette might know
              > the
              > > >answer, Your help would be appreciated, Thanks in
              > advance Peter
              > > >Kecskés
              > >
              > > (A) Peter, because of the math, you're already in
              > the middle of the
              > > playground
              > > for your research. The Hellenistic sholars were
              > the culprits in
              > designing
              > > this system and I don't think you'll find anything
              > earlier.
              > >
              > > Best regards and well wishes,
              > > Arthyr
              > >
              >
              >
              >
              >
              >
              >


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            • PeterKecskés
              Dear Arthyr! Thanks a lot for your useful comments, I did not find anything earlier either, but I just wondering where did they get the idea of having the
              Message 6 of 11 , Sep 3, 2006
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                Dear Arthyr!
                Thanks a lot for your useful comments, I did not find
                anything earlier either, but I just wondering where
                did they get the idea of having the 24-hour parans and
                the heliacal rising, and setting, there must have been
                an earlier source; Yours Cat-CH-Keys P.AEther

                -- msbhavens1 <msbhavens1@...> wrote:

                >
                > what about the egyptians? Just wondering as they
                > seemed far more into
                > the Trig. MissB
                >
                > --- In thefixedstars@yahoogroups.com, Arthyr
                > <awc99@...> wrote:
                > >
                > > Hello Peter Kecskés,
                > >
                > > At 11:53 PM 9/2/2006 +0000, Peter wrote:
                > > > Dear All !
                > > > Does anyone know what are the earliest sources
                > regarding parans
                > > >besides Maternus, Manilius, Hypparchus, Ptolemy,
                > Eudoxos.
                > >
                > > (Arthyr) Well, I hate to bust a bubble but I
                > really don't think
                > you'll find
                > > too much before
                > > Hipparchus' time (BCE 150) as the early
                > Babylonians really didnt
                > work with
                > > too much planetary phenomena outside of simple
                > mathematical "zone"
                > style
                > > calculations. Their Main concern was the lunar
                > phases, primarily
                > the New
                > > Moon's return at first sighting. As parans
                > requires the mathematical
                > > knowledge of latitude, which the Babylonians had a
                > primitive
                > understanding.
                > > However:
                > >
                > > Signs and constellations rise and set with rates
                > that vary as a
                > function of
                > > one's terrestrial latitude.
                > >
                > > To determine when a star or planet sets, the
                > diurnal semi-arc of
                > the body
                > > must be found, then expressed in time, between the
                > Ascendant in
                > question
                > > and the upper meridian.They would need to find the
                > semi arc, the
                > angle
                > > between the ecliptic and the local horizon and the
                > right angle to
                > their
                > > horizon.
                > >
                > > As you know, a planet conjoined with a star gives
                > that planet a
                > powerful
                > > influence but the mathematical requirements to
                > predict the diurnal
                > motions
                > > during the following 24-hour period
                > > was completely out of the Babylonian mental
                > makeup. One could
                > perform a
                > > paran style chart based purly on sunset at the
                > place and date of
                > birth as
                > > that is important, but the Chaldean astrologers
                > were much more
                > interested
                > > in the synodic periods, they devised "Zones" in
                > their calculations
                > that
                > > were by no means as sophisticated as the
                > Hellenist's spherical
                > > trigonometry. This is because parans are based on
                > examining the
                > times when
                > > stars and planets are at the key moments of their
                > diurnal movement,
                > i.e.
                > > either on the Ascendant, M.C. Descendant and even
                > the I.C -
                > something the
                > > Chaldeans weren't aware of calculating.
                > >
                > > The formula is:
                > > Sine ascensional difference = (tangent declination
                > [planet])
                > (tangent
                > > latitude [place])
                > > where declination is the declination of the body
                > and latitude is the
                > > terrestrial latitude of the place.If the (A/D)
                > ascentional
                > difference is
                > > positive add it to 90degrees; subtract from
                > 90degrees if negative.
                > Having
                > > added the A/D as necessary, divide by 15 (15
                > degrees = 1 hour of
                > time). The
                > > result of this division is the diurnal semi-arc of
                > the planet or
                > star.
                > >
                > > (Peter) I'm doing a research with parans and I
                > would like to know
                > if there
                > > are more
                > > >obscure source-materials on this topic; I'm
                > thinking of some
                > genuine
                > > >babylonian materials, not hellenistic stuff.
                > Bernadette might know
                > the
                > > >answer, Your help would be appreciated, Thanks in
                > advance Peter
                > > >Kecskés
                > >
                > > (A) Peter, because of the math, you're already in
                > the middle of the
                > > playground
                > > for your research. The Hellenistic sholars were
                > the culprits in
                > designing
                > > this system and I don't think you'll find anything
                > earlier.
                > >
                > > Best regards and well wishes,
                > > Arthyr
                > >
                >
                >
                >
                >
                >
                >


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              • Arthyr
                Hi Peter, Have you explored any of O. Neugebauer s works? If you are acquainted with mathematical formulae his works may be of some interests. As it stands the
                Message 7 of 11 , Sep 3, 2006
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                  Hi Peter,

                  Have you explored any of O. Neugebauer's works? If you are acquainted with
                  mathematical formulae his works may be of some interests. As it stands the
                  early date from Euclid (300BCE) leaves room for two more centuries to
                  develop ancient principles by men like Archimedes and Apollonius. By the
                  time Ptolemy (close to the end of the Hellenistic period)
                  arrives at the scene he comprised most of the astronomical achievements
                  which could be reached with the mathematical methods of antiquity.

                  Heliacal risings had to date back to the earliest observations as the stars
                  were the actual markers for the daily and yearly calendars. But "Parans"
                  were not noted as such because it may heve been a simple matter of fact.
                  Certainly not as important as the simultaneous rising and setting of the
                  Sun/Moon or perhaps two planets rising and setting at the same time.

                  Remember, the Babylonians were only interested with planetary appearances,
                  length of appearance, dissappearances and their length. . . nothing more
                  sophisticated than that. Certainly, they must have watched the evening sky
                  and noted the circular motion as the constellations rose, culminated and
                  eventually set. But to believe that they did anything more than that is
                  only conjecture and wouldn't stand any reality check.

                  Naturally, the projection of the revolution of the diurnal motion was of
                  interest long before Archimedes or even later by Hipparchus, but the tools
                  were not available to do so properly.
                  Too, it was Ptolemy (150 CE) that gave us the Ascendant or "Horoscopos"
                  that allowed astronomers a starting position to extend the "chord tables"
                  set forth by Hipparchus some 300 yeqars prior.

                  If there are any earlier sources they haven't been discovered as yet.
                  Perhaps in the future some student from the Eastern School of Antiquities
                  will delve into the resources in the British Museum. Until then, concepts
                  in vogue today and those principles that were developed during Greco-Roman
                  antiquity should not be assumed "a priori" to find counterparts in
                  Babylonian texts.

                  Arthyr


                  At 04:05 PM 9/3/2006 -0700, Peter wrote:
                  > Dear Arthyr!
                  > Thanks a lot for your useful comments, I did not find
                  >anything earlier either, but I just wondering where
                  >did they get the idea of having the 24-hour parans and
                  >the heliacal rising, and setting, there must have been
                  >an earlier source; Yours Cat-CH-Keys P.AEther
                  >
                  >-- msbhavens1 <msbhavens1@...> wrote:
                  >
                  >>
                  >> what about the egyptians? Just wondering as they
                  >> seemed far more into
                  >> the Trig. MissB
                  >>
                  >> --- In thefixedstars@yahoogroups.com, Arthyr
                  >> <awc99@...> wrote:
                  >> >
                  >> > Hello Peter Kecskés,
                  >> >
                  >> > At 11:53 PM 9/2/2006 +0000, Peter wrote:
                  >> > > Dear All !
                  >> > > Does anyone know what are the earliest sources
                  >> regarding parans
                  >> > >besides Maternus, Manilius, Hypparchus, Ptolemy,
                  >> Eudoxos.
                  >> >
                • PeterKecskés
                  Thanks again for your valuable insights; I do not have Neugebauer s books, but I have some books by hungarian egyptologists, math-historians and general
                  Message 8 of 11 , Sep 4, 2006
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                    Thanks again for your valuable insights; I do not
                    have Neugebauer's books, but I have some books by
                    hungarian egyptologists, math-historians and general
                    astro-history books in english. Fagan has some really
                    good insights regarding the heliacal phenomena; but
                    I'm still searching... Yours Peter

                    --- Arthyr <awc99@...> wrote:

                    > Hi Peter,
                    >
                    > Have you explored any of O. Neugebauer's works? If
                    > you are acquainted with
                    > mathematical formulae his works may be of some
                    > interests. As it stands the
                    > early date from Euclid (300BCE) leaves room for two
                    > more centuries to
                    > develop ancient principles by men like Archimedes
                    > and Apollonius. By the
                    > time Ptolemy (close to the end of the Hellenistic
                    > period)
                    > arrives at the scene he comprised most of the
                    > astronomical achievements
                    > which could be reached with the mathematical methods
                    > of antiquity.
                    >
                    > Heliacal risings had to date back to the earliest
                    > observations as the stars
                    > were the actual markers for the daily and yearly
                    > calendars. But "Parans"
                    > were not noted as such because it may heve been a
                    > simple matter of fact.
                    > Certainly not as important as the simultaneous
                    > rising and setting of the
                    > Sun/Moon or perhaps two planets rising and setting
                    > at the same time.
                    >
                    > Remember, the Babylonians were only interested with
                    > planetary appearances,
                    > length of appearance, dissappearances and their
                    > length. . . nothing more
                    > sophisticated than that. Certainly, they must have
                    > watched the evening sky
                    > and noted the circular motion as the constellations
                    > rose, culminated and
                    > eventually set. But to believe that they did
                    > anything more than that is
                    > only conjecture and wouldn't stand any reality
                    > check.
                    >
                    > Naturally, the projection of the revolution of the
                    > diurnal motion was of
                    > interest long before Archimedes or even later by
                    > Hipparchus, but the tools
                    > were not available to do so properly.
                    > Too, it was Ptolemy (150 CE) that gave us the
                    > Ascendant or "Horoscopos"
                    > that allowed astronomers a starting position to
                    > extend the "chord tables"
                    > set forth by Hipparchus some 300 yeqars prior.
                    >
                    > If there are any earlier sources they haven't been
                    > discovered as yet.
                    > Perhaps in the future some student from the Eastern
                    > School of Antiquities
                    > will delve into the resources in the British Museum.
                    > Until then, concepts
                    > in vogue today and those principles that were
                    > developed during Greco-Roman
                    > antiquity should not be assumed "a priori" to find
                    > counterparts in
                    > Babylonian texts.
                    >
                    > Arthyr
                    >
                    >
                    > At 04:05 PM 9/3/2006 -0700, Peter wrote:
                    > > Dear Arthyr!
                    > > Thanks a lot for your useful comments, I did not
                    > find
                    > >anything earlier either, but I just wondering where
                    > >did they get the idea of having the 24-hour parans
                    > and
                    > >the heliacal rising, and setting, there must have
                    > been
                    > >an earlier source; Yours Cat-CH-Keys P.AEther
                    > >
                    > >-- msbhavens1 <msbhavens1@...> wrote:
                    > >
                    > >>
                    > >> what about the egyptians? Just wondering as they
                    > >> seemed far more into
                    > >> the Trig. MissB
                    > >>
                    > >> --- In thefixedstars@yahoogroups.com, Arthyr
                    > >> <awc99@...> wrote:
                    > >> >
                    > >> > Hello Peter Kecskés,
                    > >> >
                    > >> > At 11:53 PM 9/2/2006 +0000, Peter wrote:
                    > >> > > Dear All !
                    > >> > > Does anyone know what are the earliest
                    > sources
                    > >> regarding parans
                    > >> > >besides Maternus, Manilius, Hypparchus,
                    > Ptolemy,
                    > >> Eudoxos.
                    > >> >
                    >


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                  • msbhavens1
                    Arthyr wrote: Egyptian and Babylonian scholars alike used a repeating numbering system that was used to acquire math solutions. If the solution of dividing
                    Message 9 of 11 , Sep 4, 2006
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                      Arthyr wrote:
                      "Egyptian and Babylonian scholars alike used a repeating numbering
                      system that was used to acquire math solutions. If the solution of
                      dividing 60 by 5 were required, they added (or doubled) five until the
                      number 60 could be found therein."

                      MissBHavens aka Beth replies:
                      I understood the Babylonian number system to be a base 60, but I
                      didn't realize that the egyptions were using the same numerical
                      system. I understand chords etc. I'm just not always familiar with who
                      did what first. some of my ancient history has gaps, some baby gaps,
                      some super gaps, but gaps none the less, Thank you,

                      MissB
                    • Arthyr
                      Hi Ms B aka Beth :-) Actually the Sumerians invented the base 60 system (our clock and compass figures for example) as well as a decimal (base 10 system)
                      Message 10 of 11 , Sep 4, 2006
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                        Hi Ms "B" aka Beth :-)

                        Actually the Sumerians invented the base 60 system
                        (our clock and compass figures for example) as well as a decimal (base 10
                        system)
                        Their ingenuity was in the use of both systems within a single math framework.

                        Clever those guys. . .

                        Arthyr

                        At 01:01 AM 9/5/2006 +0000, Ms "B" aka Beth wrote:
                        >Arthyr wrote:
                        >"Egyptian and Babylonian scholars alike used a repeating numbering
                        >system that was used to acquire math solutions. If the solution of
                        >dividing 60 by 5 were required, they added (or doubled) five until the
                        >number 60 could be found therein."
                        >
                        >MissBHavens aka Beth replies:
                        >I understood the Babylonian number system to be a base 60, but I
                        >didn't realize that the egyptions were using the same numerical
                        >system. I understand chords etc. I'm just not always familiar with who
                        >did what first. some of my ancient history has gaps, some baby gaps,
                        >some super gaps, but gaps none the less, Thank you,
                        >
                        >MissB
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        >
                        >Yahoo! Groups Links
                        >
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                        >
                        >
                        >
                      • Diana K Rosenberg
                        I am not an expert in early mathematical astronomy/astrology, but one of the best books I ever read on the subject is A History of Astronomy by A Pannekoek -
                        Message 11 of 11 , Sep 4, 2006
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                          No Earlier Parans?

                          I am not an expert in early mathematical astronomy/astrology,
                          but one of the best books I ever read on the subject is
                          "A History of Astronomy" by A Pannekoek - I believe it is still
                          available in a Dover reprint of an English translation

                          I recommend it most highly

                          Love, Diana

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