I think it's just a matter of practicality. The
circles are used only in regards to specific tangent
lines. It is easier to do this since the circles are
centered in the "centers" of villages. It is easier
to talk about that than to try and describe a point in
the middle of nowhere that may be where the tangent
line touches the radius and a turnpoint may be.
--- aletheiak <
aletheiak@...> wrote:
> right
> & all as previously noticed & noted
> but still no clear explanation of why the arcs or
> circumferences
> which the border doesnt follow are even mentioned in
> the
> alignments at all
>
> why such gratuitous geometrical figurations for
> reference only
> when it would have been far easier to make reference
> to some
> physical object &or straight line distance
> as they do everywhere else
>
> & we have just been calling arcs what they call
> circumferences
> so there are not really 2 different things needing
> distinction here
>
>
> so unless i have misunderstood
> you are simply restating the enigmatic texts
> but not really resolving their mysteries
>
>
> not that they absolutely need to be resolved tho
>
> the writers could have been just as confused as they
> seem to us
>
> & perhaps the only way to fully resolve the
> confusion would be to
> match all the marker positions with all the
> alignments
> & then see if we have anything left over
> hahahahaha
> but i am not suggesting we drive ourselves so crazy
> as that
>
> --- In BoundaryPoint@yahoogroups.com, Michael
> Kaufman
> <mikekaufman79@y...> wrote:
> > 36. No since the border only runs on a tangent to
> the
> > circumference and then again a straight line in
> 37.
> > It never runs along the circumference and there is
> no
> > arc. The Grand Bete circle is used for reference
> to
> > specify the turnpoint, and the border does not run
> > along this circle.
> >
> > 49. It just runs along the line that is tangent to
> the
> > Lusi 3.5 km circle, but again does not ride an arc
> of
> > the circle.
> >
> > 54. Just following the tangent from one circle to
> > another. AKA straight line segment between two
> arcs
> > (53 and 55).
> >
> > 58. Just follows tangent from Kankali circle to
> > Gusin-Sura circle without riding an arc of
> Gusin-Sura.
> >
> > 59. It follows the tangent from Gusin-Sura circle
> to
> > Daku circle from point of intersection with the
> > tangent in 58 to the circumference of the Daku
> circle
> > (an arc of which it rides in 60).
> >
> > The 5 paragraphs are describing straight line
> > segments. The three extra circles only serve as
> > references from which to draw straight lines. So
> we
> > are still at 10 arcs: Under Alignment section -
> 26,
> > 33, 35, 42, 44, 47, 53, 55, 57, 60.
> >
> > --- aletheiak <aletheiak@y...> wrote:
> >
> > > as mentioned
> > > i couldnt be sure
> > > & on closer examination i still cant
> > > because the text occasionally varies its
> formulaic
> > > description of
> > > the arcs from one example to the next
> > > & evidently incorporates several geometric
> > > conundrums as well
> > >
> > > what i can see is
> > > there are in all 13 different arcs mentioned
> > > in a total of 15 different numbered paragraphs
> > > including your mentioned 10 paragraphs plus 36
> 49 54
> > > 58 & 59
> > >
> > > which may or may not add to your count of 10
> border
> > > arcs
> > >
> > > i agree there could be as few as 10 arcs that
> the
> > > bjng border
> > > actually follows
> > >
> > > but in any case
> > > i dont see why they would even have been
> mentioned
> > > if the
> > > border isnt supposed to follow them
> > >
> > > can you perhaps positively dispose of any or all
> 3
> > > odd men out
> > > from the mentioned 13
> > >
> > > just to keep track
> > > we have in sequence the following 13 villages as
> > > centers
> > > with radii in km
> > >
> > > okuta 8 & a half
> > > guri 4
> > > yashikira 8
> > > grand bete 4
> > > kenumbe 4
> > > besi 8
> > > gauzhi 3 & a half
> > > lusi 3 & a half
> > > naganzi 4
> > > kade 4
> > > kankali 5
> > > gusin sura 4
> > > daku 5
> > >
> > >
> > >
> > > & about your map
> > > i dont know what the mapmaker was doing or
> showing
> > > there
> > >
> > > perhaps a temporary question or situation during
> > > wwii
> > >
> > > i think modern dztn is the dash & dot line
> > > not the black dash dash line
> > >
> > > & of course the other convergents
> > > lytn & dzly
> > > are shown by the crosses
> > >
> > > & i cant account for any of the other lines
> > > but assume they are irrelevant to finding the
> > > tripoint
> > >
> > > the only presently outstanding question i am
> aware
> > > of in this
> > > vicinity is probably too small to be shown on
> this
> > > map
> > > namely whether dztn meets the arc at its
> northeast
> > > terminal
> > > or subdivides the arc 2km counterclockwise from
> > > there
> > >
> >
>
http://home.worldonline.dk/jesniel/border/african_tripoints.htm#d
> > > zlytn
> > >
> > > so as i understand it
> > > only 2 possible tripoint positions are on this
> arc
> > >
> > > --- In BoundaryPoint@yahoogroups.com, Michael
> > > Kaufman
> > > <mikekaufman79@y...> wrote:
> > > > BJNG - Ok by my count I get 10:
> > > >
> > > > Under Alignment section - 26, 33, 35, 42, 44,
> 47,
> > > 53,
> > > > 55, 57, 60
> > > > Which are the other one or two?
> > > >
> > > > Also: On
> http://www.manntaylor.com/FtSaintM.jpg -
> > > The
> > > > solid green arrow almost points right to
> DZLYTN.
> > > What
> > > > boundary is the hollow green arrow pointing
> to?
> > > > Currently this must be all in DZ. And the
> line
> > > from
> > > > the south - what is this? It would divide
> > > territory
> > > > which is currently all in Libya. How many TPs
> > > > (including ghost points) can be on this one
> arc?
> > > >
> > > >
> > > > --- aletheiak <aletheiak@y...> wrote:
> > > > > please look for several insertions
> > > > >
> > > > > --- In BoundaryPoint@yahoogroups.com,
> Michael
> > > > > Kaufman
> > > > > <mikekaufman79@y...> wrote:
> > > > > > 1. DZLYTN
> > > http://www.manntaylor.com/FtSaintM.jpg
> > > > > > (this could be DZLY and LYTN or just DZLY
> as
> > > per
> > > > > msg.
> > > > > > 13465)
> > > > >
> > > > > correct & we still dont know which is true
> > > > > so you are right to keep counting it or them
> as
> > > > > either 1 or 2
> > > > > borders
> > > > > but this is apparently only a single sweep
> of
> > > arc in
> > > > > any case
> > > > >
> > > > > > 2. DZLY
> > > > > >
> > > > >
> > > >
> > >
> >
>
http://www.law.fsu.edu/library/collection/LimitsinSeas/maps/bs1
> > > > > b.php
> > > > > > 3. LYNE
> > > > > >
> > > > >
> > > >
> > >
> >
>
http://www.law.fsu.edu/library/collection/LimitsinSeas/maps/bs2.
> > > > > php
> > > > > > 4.-15. BJNG (12 of these?)
> > > > >
> > > > > i still cant be sure
> > > > > but the following text seems to indicate
> either
> > > 11
> > > > > or 12
> > > > >
> > > > >
> > > >
> > >
> >
>
http://www.law.fsu.edu/library/collection/LimitsinSeas/IBS091.pdf
> > > > > > 16. NENG
> > > > > >
> > > > >
> > > >
> > >
> >
>
http://www.law.fsu.edu/library/collection/LimitsinSeas/IBS093.pdf
> > > > > > (but not evident)
> > > > >
> > > > > it is evident in the above text
> > > > > but i think we just havent yet found a good
> > > enough
> > > > > map
> > > > >
> > > > > > 17.-??? MXUS (msg. 13937; how many are
> > > there?)
> > > > >
> > > > > unknown
> > > > > but i believe only 1 has been reported so
> far
> > > > > & suspect the 1970 mxus treaty will reveal
> all
> > > > > if there are any others
> > > > >
> > > > > > SO,
> > > > > > We can't put a firm number on it. Depends
> on
> > > 3
> > > > > > variables:
> > > > > > 1. Where DZLYTN falls. If there is a
> short
> > > LYTN
> > > > > we
> > > > > > have 18 not 17.
> > > > > > 2. Also, do we know 12 for BJNG? So it
> would
> > > be
> > > > > more
> > > > > > or less if not exactly 12.
> > > > > > 3. And how many more arcs for MXUS on the
> > > > > channelized
> > > > > > Rio Grande?
> > > > > > I am not yet counting ITVA since I think
> here
> > > we
> > > > > would
> > > > > > be talking about features (not figures)
> which
> > > can
> > > > > not
> > > > > > be perfectly geometrically true arcs.
> > > > >
> > > > > true
> > > > > & other reasons not to count any of the itva
> > > curves
> > > > > are
> > > > > that they are elliptical rather than
> circular
> > > > > & that their total number is so highly
> debatable
> > > > > amounting to either 1 or 3 or 5 or even more
> > > > > depending on point of view
> > > > >
> > > > > what a mess
> > > > > & good idea to sidestep it
> > > > > on any grounds
> > > > >
> > > > >
> > > > > so
> > > > > we have
> > > > > by this exact count
> > > > > at least 16 international border arcs
> > > > > but still perhaps as many as 18
> > > > > or more
> > > > > if more are found
> > > > >
> > > > > & they are evidently situated on 6 different
> > > borders
> > > > > & 1 tripoint
> > > > >
> > > > > thanx
> > > > >
> > > > >
> > > > >
> > > > > of course some wag will now come along to
> remind
> > > us
> > > > > that all
> > > > > small & great circle arc borders
> > > > > including every single segment between
> > > intervisible
> > > > > markers
> > > > > are technically border arcs too
> > > > >
> > > > > so we should add an extra zillion or 2
> > > > >
> > > > >
> > > > > end insertions
> > > > >
> > > > > > --- aletheiak <aletheiak@y...> wrote:
> > > > > > > arif
> > > > > > > i too believed in this arc report about
> > > > > easternmost
> > > > > > > gmsn
> > > > > > > & may even have been responsible for
> > > starting
> > > > > the
> > > > > > > rumor about it
> > > > > > > but i have been unable to substantiate
> it
> > > > > > >
> > > > > > > this border is set at a fixed distance
> from
> > > the
> > > > > > > river on both sides
> > > > > > > presumably from both its banks rather
> than
> > > from
> > > > > its
> > > > > > > thalweg
> > > > > > > just like the manh state line is offset
> from
> > > the
> > > > > > > merrimack
> > > > > > > except doubly so
> > > > > > > as you probably also realized
> > > > > > > & can see here
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
>
http://www.lib.utexas.edu/maps/africa/gambia_pol88.jpg
> > > > > > >
> > > > > > > however
> > > > > > > as beguilingly arclike as all this may
> seem
> > > > > > > such a regime would not actually
> presuppose
> > > any
> > > > > true
> > > > > > > arcs at all
> > > > > > >
> > > > > > > except
> > > > > > > i would agree
> > > > > > > conceivably a single one centered at the
> > > > > headspring
> > > > > > >
> > > > > > >
> > > > > > > however
> > > > > > > the source of the gambia river is not in
> > > gambia
> > > > > > > but in senegal
> > > > > > > as you can also see in the above map
> > > > > > > & therefore the simple offset regime
> couldnt
> > > > > project
> > > > > > > such a
> > > > > > > simple terminal arc sector
> > > > > > >
> > > > > > > only by varying the apparent regime &
> > > reducing
> > > > > it to
> > > > > > > a single
> > > > > > > offset center point in the middle of the
> > > river
> > > > > > > could such a final true arc have been
> > > produced
> > > > > > >
> > > > > > >
> > > > > > > also the map doesnt show any such
> terminal
> > > > > rounding
> > > > > > > or bulge
> > > > > > > as one would expect in such a case
> > > > > > > but quite the contrary
> > > > > > > something more like a foreshortening or
> > > > > truncation
> > > > > > > of the basic regime
> > > > > > > & indeed it makes the cutoff point look
> > > quite
> > > > > > > arbitrary & artificial
> > > > > > > & somehow distinctly at odds with the
> basic
> > > > > offset
> > > > > > > regime
> > > > > > >
> > > > > > >
> > > > > > > so at this point i think the existence
> of an
> > > arc
> > > > > on
> > > > > > > gmsn hasnt
> > > > > > > been & probably wont be demonstrated
> > > > > > > & was just a wishful thought &
> misconception
> > > in
> > > > > the
> > > > > > > first place
> > > > > > >
> > > > > > >
> > > > > > > mind you
> > > > > > > i dont actually know how the gmsn border
> > > does
> > > > > > > accomplish this
> > > > > > > remarkable turnabout at its east end if
> not
> > > in
> > > > > some
> > > > > > > approximation of an arc or arcs
> > > > > > >
> > > > > > > & i can still imagine how it might
> somehow
> > > > > involve a
> > > > > > > true arc or 2
> > > > > > > based at some known terminal cross
> section
> > > of
> > > > > the
> > > > > > > river
> > > > > > >
> > > > > > > but i dont believe there is any text
> that
> > > > > specifies
> > > > > > > to this effect
> > > > > > > nor any map that suggests it
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > meanwhile
> > > > > > > i have scoured the ghost frgb lines of
> the
> > > > > period
> > > > > > > & have discovered nothing new
> > > > > > > so our world class border arc census is
> > > again
> > > > > > > stalled
> > > > > > > at a top count of about 20 now & perhaps
> > > forever
> > > > > > >
> > > > > > > --- In BoundaryPoint@yahoogroups.com,
> Arif
> > > Samad
> > > > >
> > > > > > > <fHoiberg@y...> wrote:
> > > > > > > > Not sure, but isn't there some (at
> least
> > > one
> > > > > arc)
> > > > > > > in
> > > > > > > > the border of Senegal and Gambia. As
> far
> > > as I
> > > > > > > > thought, the Easternmost point is
> directly
> > > > > east of
> > > > > > > the
> > > > > > > > Center of the arc in that border.
> > > > > > > > Arif
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
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