No Earlier Parans?

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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
Message 1 of 11 , Sep 3, 2006
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
• 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 2 of 11 , Sep 3, 2006
Dear Arthyr!
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.
> the
> > >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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• 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 3 of 11 , Sep 3, 2006
Dear Arthyr!
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.
> the
> > >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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• 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 4 of 11 , Sep 3, 2006
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.
>> >
• 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 5 of 11 , Sep 4, 2006
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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• 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 6 of 11 , Sep 4, 2006
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
• 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 7 of 11 , Sep 4, 2006
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
>
>
>
>
>
>
>
>
>
>
>
>
>
• 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 8 of 11 , Sep 4, 2006
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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