Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī, often referred to as Al-Nayrizi, was indeed a significant Persian mathematician and astronomer from the 9th and 10th centuries. It seems that his work had considerable influence in both mathematics and astronomy during his time and subsequently. Here's a summary based on your text:
Life: Al-Nairīzī was born in Neyriz, a town in what is now Iran. Although not much is known about his personal life, he appears to have flourished in Baghdad during the reign of the Abbasid caliph, al-Mu'tadid, to whom he dedicated a book on atmospheric phenomena. Al-Nairīzī is thought to have passed away around 922 CE.
Mathematics: Al-Nairīzī wrote a commentary on Al-Ḥajjāj ibn Yūsuf ibn Maṭar's Arabic translation of Euclid's Elements. This commentary has survived and contains unique extracts from two other commentaries on the Elements, authored by Hero of Alexandria and Simplicius of Cilicia. He used the concept of "umbra versa", equivalent to the tangent, as a genuine trigonometric line and gave a proof of the Pythagorean theorem using Pythagorean tiling. Furthermore, Al-Nayrizi gave a mathematical proof of the parallel postulate, based on the assumption that parallel lines are equidistant.
Astronomy: Al-Nairīzī wrote an extensive treatise on the spherical astrolabe, an instrument used for solving problems relating to time and the positions of the stars. His work is considered one of the best Persian resources on this topic. Although his commentary on Ptolemy's Almagest and his zijes (astronomical tables) have not survived, his treatises on the spherical astrolabe and astrological conjunctions have.
Al-Nairīzī's contributions in both the fields of mathematics and astronomy are notable for their originality, depth, and influence, and he is considered a significant figure in the history of both disciplines. His work helped to shape the intellectual landscape of the Middle East during the Islamic Golden Age and has left a lasting legacy in the field of science.