Finding the Meridian Line in the 13th chapter of the second book of ʿAbd al-Jabbār al-Kharaqī’s Muntaha al-Idrāk fī Taqāsīm al-Aflāk (The Utmost Attainment on the Divisions of the Orbs)

The meridian is one of the most famous great circles imagined on both the celestial sphere and the earth. On the celestial sphere, the altitude of celestial bodies is measured along the meridian with reference to the horizontal coordinates. On the earth, the meridian also shows the local longitude. Methods for determining a meridian of reference and measuring the longitude of different locales on the earth belong to the mathematical geography topics. They have been mentioned in the astronomical works of the Islamic period. All instruments must be aligned on the meridian line of the observer’s location therefore its determination is required for the observation. For this reason, practical methods of finding the meridian line were included in the astronomical works. In hayʾa works of the Islamic astronomy, a chapter entitled “On Finding the meridian line” has been added to the mathematical geography section (hayʾa al-ʾarḍ, lit. “the configuration of the Earth”). In the Almagest, Ptolemy did not discuss finding the meridian line, although he used it in his observations. So, this presumably was an addition to the Islamic astronomical works. In most of these works, among other methods, the famous method of the “Indian circle”often introduced. In this article, the chapter on finding the meridian line from the Muntaha al-Idrāk fī Taqāsīm al-Aflāk of ʿAbd al-Jabbār al-Kharaqī (6th AH/12th AD century), early comprehensive work on ʿilm al-hayʾa, has been studied. Kharaqī discussed three methods for determining the meridian line, and described the pros and cons of each method. Almost no other work in ʿilm al-hayʾa presents this diversity of methods for finding the meridian line. By comparing Kharaqī’s methods with those of Bīrūnī (d. 440 AH/1048 AD) this article will provide evidence about the possible sources of Kharaqī’s methods.