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Well, take the sky as seen by the observer at any one time.  As you
know, directly overhead is the point of zenith, and below this is a
hemisphere of the celestial sphere, the visible part lying above the
observer's horizon.  Between these extremes are circles of "observer
latitude":  80 degrees above the horizon is an 80 degree circle etc.  As
Deakin states, the technical name for such a circle on the Astrolabe was
an almucantar.  The observer's sphere will be tilted with respect to the
standard one and vica versa.  For an abserver at Alexandria (at around
31 degrees north latitude), the north celestial pole will be 31 degrees
above the horizon or 59 degrees below the zenith.

The projections of the almucantars were engraved onto a circular plate
known as the mater and forming one component of the astrolabe.  The rim
of the mater was usually taken to be the circle representing the Tropic
of Capricorn.  Thus almucantars which intersected this were not shown in
full, but only as circular arcs.

Also, lines of equal azimuth projected by this same means into circles,
and these too were engraved onto the mater and the various climates.  As
per the above, the pattern of lines on the mater is specific to your
particular latitude.  If the instrument was to be used elsewhere, the
mater was overlaid with the pattern for that latitude.

As well as the mater and the climates, the astrolabe had the rete, which
means 'net'.  The rete was designed to represent the various major
stars:  mostly those of the constellations of the zodiac.  These lay
about the ecliptic.

The ecliptic also projects, by the same means, into a circle and this
was molded in metal to form the principal feature of the rete.  The
various stars occupy fixed positions with respect to the ecliptic.  The
rete was a highly intricate patterned device, whose shape incorporated
the circular arc of the ecliptic and various points that represented the
major fixed stars.

The rete therefore gave the positions of the fixed stars in the
celestial sphere, and did so in a 2 dimensional format.  The rete
remained unchanged whatever the position of the observer.  The mater and
the climates, by contrast, showed those features of the situation that
depend upon the latitude of the observer.  So, when navigating, you only
needed one rete (as long as the various stars used in it remain
visible), but you needed various climates to insert to replace the mater.

The third and simplest part was the alidade, which was basically a
sighting device.  By aligning the line of sight to some major star (say
Polaris) along the alidade, and reading off the angle from a scale which
was engraved on the back of the mater, the star's angle of elevation
could be determined.  From simple observations of this type, and by the
use of rotations of the rete relative to the mater (or the appropriate
climate), as well as using the various tables that might be engraved on
the back of the mater, the astrolabe enabled the mechanical computation
of time, direction and position.  Of course, the astrolabe assumed you
knew all the stars in your night sky.  What stars you would expect to
see season by season, and approximately where they were in the sky.

How did you use the Astrolabe?  Firstly, you obtained the altitude of
the Sun or a star.  Holding the Astrolabe by a line which was attached
to the top ring, you then looked at a star through the sighting vanes of
the Alidade.  The angle is then read at the rim of the instrument.  For
example, if the star sighted was Arcturus with an elevation of 30d above
the eastern horizon, you would then turn the rete until the pointer of
Arcturus lays above the 30 degree almucantar.  The Astrolae is now set
to show the ansers to a large number of celestial problems.  With the
rete set as above, the true Azimuth direction of Arcturus can be found,
along with those other stars that are above the horizon at that time.
Their altitudes can also be found by using the rete and mater.

To find the time, you held the Astrolabe vertically and allowed the
sunlight to pass through the two small holes in the sights, which were
on either end of the Alidade.  You then measured the elevation of the
Sun's altitude on the outer degree scale (say, 40d).  You would then
find the Sun's position in the ecliptic for that date.  On the front
side of the Astrolabe, you would then move the Sun's position on the
rete to lay over the 40d Almucantar.  All the rule to pass over this
point, and read the time on the rim of the instrument.

It was portable, as Deakin states, typically only 25cm across), so it
became popular and practical.  It was used from this time (400AD), right
through to the 17th century.

Here are some of the references I've found, most of which were available
in hard copy only, I'm afraid (I had to do a lot of searching):

DEAKIN, Michael The Primary Sources for the Life and Work of Hypatia of
Alexandria 1995

DEAKIN, Michael History of Mathematics - The Astrolabe, Function "A
School Mathematics Magazine, Volume 20, Part 2 April 1996.  Mathematics
Department - Monash University".

HUTTON, Charles Philosophical and Mathematical Dictionary, Comprised
under the Heads Mathematics, Astronomy and Philosophy, Volume 1, London 1815

NEUGEBAUER O, "The Early History of the Astrolabe", Isis 40 (1949) pp
240-256.

Sorry to be so long winded, but as you can see, the history of
Astronomy/navigation is a bit of a passion of mine.

All the best,
Lisa

PS I know a man in Tasmania who builds workable Astrolabes, however this
is for the Northern Hemisphere only, so I've never been able to ever
actually use one.


Alexandre Eremenko wrote:
> Fear Lisa,
> I am glad you liked my little historical digression.
>
> On Wed, 27 Oct 2004, Lisa Fiene wrote:
>
>
>>Consider Hypatia of Alexandria (?350/379AD to 415AD)
>
>
> She was also one of the last Alexandria's mathematicians...
> She was lynched by the mob.
> Other remanining mathematicians were facing a choice:
> to quit their activities or to go to exile
> (6 of them went to exile, to Persia). The full scale
> Dark Age was beginning...
>
>
>>Most references agree that the actual origin (and inventor) of the
>>astrolabe is shrouded in mystery.  Ptolemy certainly discusses the
>>principles of stereographic projection 200 years earlier.
>
>
> I actually know very little about astrolabia.
> And its connection to streographic projection is new to me.
> Any references on this connection?
>
> Alex.
>
>


--
Kind regards
Lisa Fiene
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