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Sine quadrant

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The sine quadrant (Arabic: Rubul mujayyab, الربع المجيب) was a type of quadrant used by medieval Arabic astronomers. It is also known as a "sinecal quadrant" in the English-speaking world. The instrument could be used to measure celestial angles, to tell time, to find directions, or to determine the apparent positions of any celestial object for any time. The name is derived from the Arabic "rub" meaning a quarter and "mujayyab" meaning marked with sine.[1] It was described by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad.[2]

The sine quadrant, invented by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad, was used for astronomical calculations.[3] Also known as the "Sinecal Quadrant" (the Arabic term for it is "Rubul Mujayyab"), it was used for solving trigonometric problems and taking astronomical observations. It was developed by al-Khwarizmi in the 9th century and remained prevalent until the 19th century. Its defining feature is a graph paper like grid on one side that is divided into sixty equal intervals on each axis and is also bounded by a 90 degree graduated arc. A cord was attached to the apex of the quadrant with a bead at the end of it to act as a plumb bob. They were also sometimes drawn on the back of astrolabes.[4]


File:Sighting the Pole Star.JPG
File:Taking the Measure.JPG
File:Sun Sight.JPG

The instrument is a quarter of a circle made of wood or metal (usually brass) divided on its arc side into 90 equal parts or degrees. The 90 divisions are gathered in 18 groups of five degrees each and are generally numbered both ways from the ends of the arc. That is, one set of numbers begins at the left end of the arc and goes to 90 at the right end while the other set the zero is at the right and the 90 is at the left. This double numbering enables the instrument to measure either celestial altitude or zenith distance or both simultaneously.

At the apex where the two graduated straight sides of the grid pattern meet in a right angle there is a pin hole with a cord in it and a small weight on the free end with a small bead that slides along the cord. The cord is called “Khait” and is used as a plumb line when measuring celestial altitudes. It is also used as the indicator of angles when doing calculations with the instrument. The sliding bead facilitates trigonometric calculations with the instrument.

Traditionally the line from the beginning of the arc to the apex is called “Jaibs” and the line from the end of the arc to the apex is called “Jaib tamams”. Both jaibs and jaib tamams are divided into 60 equal units and the sixty parallel lines to the jaibs are called sitheeniys or” sixtys “ and the sixty parallel lines to the jaib tamams are “juyoobul mabsootah”.

The reason for sixty divisions along the Jaibs and Jaib Tamams is that the instrument uses the Sexagesimal number system. That is it is graduated to the number base 60 and not to the base 10 or decimal system that we presently use. Time, angular measurement and geographical coordinate measurements are about the only hold overs from the Sumerian/Babylonian number system that are still in current use.

Like the arc, the Jaibs and Jaib tamams have their sixty divisions gathered into groups of five that are numbered in both directions to and from the apex. The double numbering of the arc means that the “Jaibs” and “Jaib tamams” labels are relative to the measurement being taken or to the calculation being performed at the time and the terms are not attached to one or the other of the graduated scales on the instrument.

Measuring A Celestial Altitude With The QuadrantEdit

On one of the straight edges of the quadrant there are two sight vanes which are called “Hadafatani”. Each of the vanes has a small hole or "pinnule" at its center through which one sights a celestial object. Light passing from a star through both holes to the eye guarantees that the instrument is aligned with the star and that the plumb line will indicate the true altitude of the star when the instrument is held in a vertical plane.

It has been stated by several authors that two people are required to use the instrument successfully; one to take the sight and one to read the cord position on the arc. This is not entirely true as one can see from the photograph that it is quite easy to pin the cord to the face of the instrument with a finger of the left hand once the sight vanes are perfectly aligned with the star. At that instant one simply rotates the instrument in the right hand to read the position of the cord on the arc. However, it does help to have another person to write down the scale readings as they are taken. As any navigator knows one must take multiple readings and average the result in order to have any faith in the measurement. This is why the old wood cuts showed an assistant standing next to the observer. Not to read the scale but to record the results.

The “one read the scale while the other sights the star” technique was tried by the author on a sailing yacht in relatively calm waters and was found to be vastly more difficult than having the observer read the instrument himself as described above.

Taking the altitude of the sun is a bit more difficult than sighting a star due to the blinding intensity of the solar disk. In this case one holds the instrument as one would to read the scale, that is facing the graduated face of the instrument. Then it is oriented with the hands in such a way that a ray of sunlight will pass through both sight vane pinnules and make a bright spot on the observer’s finger (see photo). As soon as the alignment is thus perfected the scale can be read by the observer at the point where it is cut by the cord.


  2. David A. King, "Islamic Astronomy", in Christopher Walker (1999), ed., Astronomy before the telescope, p. 167-168. British Museum Press. ISBN 0-7141-2733-7.
  3. (King 2002, pp. 237-238)
  4. King, David A. (1987), Islamic Astronomical Instruments, London: Variorum


  • King, David A. (2002), "A Vetustissimus Arabic Text on the Quadrans Vetus", Journal for the History of Astronomy 33: 237–255

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