Ibn al-Haytham's Universal Solution for Finding the Direction of the Qibla by Calculation

Abstract

This paper presents an edition of al-Hasan ibn al-Ḥasan ibn al-Haytham's (d. 1040) treatise, Qawl fi samt al-qibla bi-al-ḥisāb (on finding the azimuth of the Qibla by calculation) with translation and commentary. In it Ibn al-Haytham provides a universal method for finding the direction of the qibla at any location on the surface of the earth by using spherical trigonometry and accurate calculation. Ibn al-Haytham's computational solution has not been studied before, and it has often been confused with another work of his in which he uses an analemma construction to solve the problem of the qibla graphically. As a result of this confusion, contemporary scholars have mistakenly attributed the first universal solution of the qibla problem to Jamshīd al-Kāshī (15th century), some four centuries after the introduction of this method by Ibn al-Haytham. The present treatise represents an important juncture in the history of the development of mathematics of the qibla, and sheds more light on the contributions of one of the most important scientists of medieval Islam.