# Person: Al-Quhi, Abu Sahl Waijan ibn Rustam

Al-Quhi was an Islamic mathematician who was a leading figure in the revival and continuation of Greek geometry.

### Mathematical Profile (Excerpt):

• We can deduce from al-Quhi's name that he came from the village of Quh in Tabaristan.
• A great patron of science and the arts, 'Adud ad-Dawlah supported a number of mathematicians at his court in Baghdad, including al-Quhi, Abu'l-Wafa and al-Sijzi.
• These observations of the winter and summer solstices were made by al-Quhi, al-Sijzi and other scientists in Shiraz during 969/970.
• He continued to support mathematics and astronomy so al-Quhi remained at the court in Baghdad working for the new Caliph.
• Sharaf ad-Dawlah required al-Quhi to make observations of the seven planets and in order to do this al-Quhi had an observatory built in the garden of the palace in Baghdad.
• The instruments in the observatory were built to al-Quhi's own design and installed once the building was complete.
• Al-Quhi was made director of the observatory and it was officially opened in June 988.
• We mention later in this article correspondence between al-Quhi and al-Sabi.
• Our description of al-Quhi's life has highlighted his work in astronomy.
• The geometric problems that al-Quhi studied usually led to quadratic or cubic equations.
• If a solution exists, al-Quhi showed that it will have coordinates which lie on a particular rectangular hyperbola that he has constructed.
• Of course, al-Quhi does not express the mathematics in these modern terms but rather in the usual classical geometry of ancient Greek mathematics.
• Next al-Quhi introduces the "cone of the surface" which, after many deductions, leads to showing that the solution has coordinates lying on a parabola.
• In another treatise On the construction of an equilateral pentagon in a known square al-Quhi solves the problem given in the title again using the intersection of two conic sections, this time two hyperbolas.
• The other, which requires the solution of a quartic equation, is the one presented by al-Quhi.
• Indeed al-Quhi did consider the problem of constructing astrolabes in On the construction of the astrolabe.
• There are a number of difficult mapping problems solved by al-Quhi in this work.
• Despite the appearance of the work being of practical use in constructing an astrolabe, it would appear that al-Quhi was more interested in the mathematics for its own sake than he was in giving a practical manual.
• Finally we should mention the correspondence between al-Quhi and al-Sabi which we mentioned above.
• Perhaps the most interesting parts of the correspondence are six theorems given by al-Quhi concerning the centres of gravity of various figures.

Born about 940, Tabaristan (now Mazanderan), Persia (now Iran). Died about 1000.

View full biography at MacTutor

Ancient Arab, Astronomy, Origin Iran

Thank you to the contributors under CC BY-SA 4.0!

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non-Github:
@J-J-O'Connor
@E-F-Robertson

### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. Oâ€™Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive