This work is a printed edition of Kitāb taḥrīr uṣūl li-Uqlīdus (The recension of Euclid's Elements) by one of the intellectual luminaries of the Islamic world, the Persian polymath Naṣīr al-Dīn Muḥammad ibn Muḥammad al-Ṭūsī (1201–74). After his death al-Ṭūsī was referred to as al-muʿallim al-thālith (the third teacher, with Aristotle and Fārābī referred to as the first and second teachers, respectively). An extraordinarily prolific author, al-Ṭūsī made notable contributions to most of the intellectual fields of his era, writing on theology, mysticism, logic, astrology, astronomy, geomancy, mathematics, physics, mineralogy, medicine, and jurisprudence. The structure of his recension on Elements follows that of the book on which it is based. It consists of 13 chapters: the first six on plane geometry, the next four on arithmetic and the theory of numbers, and the final three on solid geometry. It was completed near the end of 1248, several years after another of his extremely influential mathematical works: his critical revision of Ptolemy's Almagest. Al-Ṭūsī's mathematical works also include recensions, commentaries, or elaborations of the mathematical works of Autolycos, Aristarchus, Apollonius, Archimedes, Hypsicles, Theodosius, and Menelaus. In many cases al-Ṭūsī's recensions supplanted in their popularity the original texts that he set out to edit, i.e., the Arabic translations of these authors. The present version of this work was printed by the Medici Oriental Press in Rome, in 1594, making it among the earliest books printed in Arabic. It includes many woodcut diagrams embedded in the text. The last page of the book contains the text of a royal decree in Ottoman Turkish issued by Sultan Murad III (reigned 1574–95) in October 1588. It concerns the shipments of “a certain number of authoritative books in Arabic, Persian, and Turkish” into the Ottoman domains by Anton and Horatio Bandini, and it stipulates that henceforth these merchants should be allowed to bring their wares into the Ottoman domains without molestation or disturbance. The decree indicates Ottoman Turkey as the nominal destination for this volume of al-Ṭūsī's work.