• Sale 9819

EXCEPTIONAL SCIENTIFIC AND ENGINEERING WORKS OF ART

London, South Kensington

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8 April 2004

# A trigonometric quadrant, unsigned, dated 1321 Hijra [= 1903]

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A trigonometric quadrant, unsigned, dated 1321 Hijra [= 1903]
the astronomical markings engraved on a brass plate -- Radius: 26.9cm. (11in.); thickness: 0.3cm. ( 1/8in.); with a brass lip to the reverse -- 3.4cm. (1 5/16in.) deep

See Illustration

This is a fine example of the kind of quadrant that was common in the Islamic world from the 9th and 10th centuries to the 19th and even early 20th. The grid, resembling modern graph paper, with a cord attached at the centre bearing a movable bead (now missing) enables the mechanical solution of various problems of trigonometry and practical astronomy. Such quadrants were sometimes fitted on the backs of astrolabes, sometimes on the backs of astrolabic quadrants for a fixed latitude. This particular quadrant has no markings on the back.
One axis of the quadrant bears a pair of protruding sights each with a hole for viewing celestial objects. This first axis is labelled jayb al-sittînî, "sine to base 60", reminding us that medieval trigonometry used 60 as a base rather than 1, as we use today. The other axis is labelled jayb al-tamâm, "sine of the complement", that is, "cosine". Each axis is divided into 60 units, labelled for each 5 units, and subdivided into single units. The outer scale is divided for each 15°, subdivided for each 5°, and then for each 1° and ½°. The arguments are labelled for each 5° in both directions. In addition, each 30° interval is associated with four signs of the zodiac, to be used to find the solar declination (see below).
The grid is elegantly executed, with the markings for each 5 units slightly more pronounced that the rest. There are squares of dots along the radius at 45°, and along the diagonal joining the extremities of the axes. These dots are purely decorative. There are several other sets of markings that serve some of the standard problems in spherical astronomy. First, there are two semi-circles standing on the axes of the quadrant, labelled tajyîb awwal and tajyîb thânî, lit., "first and second (curves for) taking the sine". These provide an ingenious method of determining the sines and cosines of any arc and having the appropriate function available as the distance from the centre to the bead lying on one of the semi-circles. Second, there is a quarter-circle of radius 24 labelled dâ'irat al-mayl al-a'zam, lit., "circle of the obliquity of the ecliptic", which serves to determine the solar declination from the solar longitude scale around the rim. Third, there are two curves across the grid that start from the extremity of the second axis. These are labelled 'asr awwal and 'asr thînî, lit., first and second 'asr, and are for finding the altitude of the sun at the beginning and end of the afternoon prayer ('asr) as a function of the solar meridian altitude.
There is a signature at the end of the first axis, which translates "(From) the Hijra of the Prophet the year 1321", so that the quadrant was made in 1903. From the style of the engraving it is clear that the piece comes from somewhere in the region limited by Istanbul, Cairo and Baghdad. In each of these three cities, traditional astronomy was still being practised at the time.
All of the above markings are carefully engraved. Therefore, it comes as something of a surprise that there is no hole at the centre of the quadrant for attaching a thread with a movable bead. Rather, there are two holes near the centre, and two more at the extremity of each axis. These can serve no useful purpose.

Literature

For a list of surviving medieval Islamic instruments, arranged chronologically according to provenance, see the website:
http://www.uni-frankfurt.de/fb13/ign/instrument-catalogue.html.

On the quadrant in Islamic astronomy see the article "Rub'" [=quadrant] in the Encyclopaedia of Islam, 11 vols. to date, Leiden: E. J. Brill, 1960 to present; Charette, Mathematical Instrumentation, passim, and King, Instruments of Mass Calculation, X-6.

For some of the latest research on Islamic instruments, see François Charette, Mathematical Instrumentation in Fourteenth-Century Egypt and Syria - The Illustrated Treatise of Najm al-Dîn al-Misrî, Leiden: E. J. Brill, 2003, and David A. King, Instruments of Mass Calculation, vol. 2 of In Synchrony with the Heavens - Studies in Astronomical Timekeeping and Instrumentation in Medieval Islamic Civilization, Leiden: E. J. Brill, 2004.

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Pre-Lot Text

ISLAMIC INSTRUMENTS