Secretum secretorum - De Mirabilibus Mundi - Cosmos

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The most widely used astronomical instrument of the Middle Ages, the astrolabe is a hand-held device for measuring the height of the sun or a star above the horizon. This is combined with a series of movable plates that can be used for solving graphically otherwise complex geometrical problems of astronomy or astrology. The astrolabe ordinarily consists of a brass body into which are inserted a number of circular brass plates. A decorative extension at the top connects with a suspension for holding the device, and on the back of the instrument a movable sighting bar called an alidade is pivoted on the central axis. The large variety of astrolabes makes generalizations difficult, but the great majority range between seven and thirty centimeters in diameter.

The outermost circular plate, called the *rete*
("net"), serves as a star chart; the metal is cut away to
leave an open network with a few dozen stars marked by points in
the grillwork pattern. The apparent rotation of the heavens about
the earth can be modeled by the rotation of the rete about its
center (the north celestial pole). Although the stars remain fixed
in their relative positions on the celestial sphere, turning with
it once a day, the sun moves eastward through the zodiac along the
elliptic once a year. Hence, instead of a fixed pointer for the
sun, the rete contains an eccentric circle that is the projection
of the elliptic, and the user must locate the sun on that circle by
means of a calendar relating the day of the year to the sun's
longitude along the elliptic. On some European astrolabes this
information is provided by a graph on the back of the
instrument.

Held fixed underneath the rete there is generally a horizon
tablet, on which is inscribed a series of partial or complete
circles, one within the other but not quite concentric,
representing the horizon and successive circles of equal angular
altitude (*almuncantars*), on up to the point directly
overhead (*zenith*). By rotating the rete with respect to
the horizon plate, it is possible to establish the relation of the
stars or the elliptic to the horizon for any specified moment, or
conversely, from the given positions of the sun or stars, to find
the time. Since the relation of the stars to the horizon depends on
the observer's latitude, an ordinary horizon tablet depends on
the observer's latitude, an ordinary horizon tablet works for
only a single latitude. Generally, however, three, four or five
interchangeable plates provide for a series of different latitudes,
thus making the astrolabe much less geographically restricted.

The astrolabe owes its simplicity as a mathematical instrument to the stereographic projection, whose fundamental property causes all circles on the celestial sphere to project as circles on the face on the astrolabe. This allows the instrument to serve as an analog computer for spherical astronomy. A typical astrological problem, simply soluble with an astrolabe, is: given the date, time and latitude, find the ascendant (that is, the part of the elliptic just rising).

The circumference of the astrolabe is calibrated in degrees, so that by taking a sight of the sun or other object with the alidade, it is possible to measure its angular height above the horizon (the altitude). A typical astronomical problem would be to find the time of day. The user first lines up the movable alidade with the sun and reads off its altitude from the scale on the rim of the astrolabe. Turning the device over, the user then rotates the rete until the appropriate points on the sun's position on the elliptic circle circle lies on the almuncantar corresponding to the observed altitude. The line from the center of the astrolabe through the sun's position to the of the instrument then gives the time, with noon at the top, midnight at the bottom, 6 p.m. to the right and 6 a.m. to the left.

The back side of the astrolabe includes a variety of graphical
devices for determining trigonometric functions. Islamic astrolabes
often display graphs for finding the direction of Mecca. European
astrolabes, in contrast, frequently have graphs for finding the
position o the sun, or giving the maximum altitude of the sun as a
function of season and place. Inside the astrolabe, underneath the
horizon tablets, Islamic instruments often have a gazetteer giving
latitudes and longitudes of twenty or thirty towns, and, sometimes,
azimuthal directions, or *qiblas*, for Mecca.

Besides the instrument just described, there exist also a few
representatives of the universal astrolabe, which is designed to
eliminate the use of specific plates for selected latitudes. There
is also the spherical astrolabe, represented by a single complete
specimen in the Museum of the History of Science at Oxford. A large
observing instrument with multiple revolving rings was described by
Ptolemy as an "*astrolabon*" but generally today
that device is called an armillary sphere.

Although the astrolabe was presumably known in Greek antiquity, the oldest known account of its construction was written in the 6th century by John Philoponos of Alexandria, and the earliest surviving examples are Islamic astrolabes from the 10th century.

The single most comprehensive compendium on the astrolabe is
R.T. Gunter, *The Astrolabes of the World* (1932, repr.
1976)

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Last modified: Sun Dec 27, 1998 /
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