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In the middle of the 15th century, a number of manuscripts by the third-century BC Greek mathematician Archimedes began to circulate in the humanistic centers in the courts of Italy. Piero della Francesca (circa 1416–92), the Renaissance artist best known for the frescos he painted for the Vatican and for the chapels in Arezzo, transcribed a copy of a Latin translation of Archimedes’s geometry (a compilation of seven surviving treatises) and illustrated it with more than 200 drawings representing the mathematical theorems in the texts. This manuscript, long ...

This work is a printed edition of *Kita**̄b taḥri**̄r uṣu**̄l li-Uqli**̄dus* (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 ...

This work is a treatise on the construction and use of the weighing balance (*qabān*, also *qapān*). It brings together geometric, mechanical, and arithmetic knowledge needed to construct and utilize measuring devices for weighing heavy and irregularly-shaped objects. The author’s name is unknown, but excerpts from another work by an already-deceased Shaykh ‘Abd al-Majīd al-Shāmulī al-Maḥallī are quoted in the treatise. The last page of the manuscript contains a sheet of verses that describe the basics of using a weighing balance, in a form that is easy to remember ...

This copy of *Mabādi' al-handasa *(Elements of geometry) is a second edition of a work by Rifā‘ah Rāfi‘ al-Ṭahṭāwī (1801−73), a leading intellectual and a pioneer of the 19th century Egyptian enlightenment. In his introduction, the author refers to an edition of 1842−43, written for students at the Madrasa al-Ṭubjīa, the military school founded by Muḥammad ʻAlī Bāshā (1769−1849) in Ṭura, Egypt. He also mentions the celebrated 1794 geometry textbook by A.M. Legendre, *Eléments de géométrie* (Elements of geometry). Al-Ṭahṭāwī says that this new 1854 ...

This work is a comprehensive tutorial guide on arithmetic and plane geometry, in 197 folio pages. It also discusses monetary conversion. The work is composed in verse form, and is meant as a commentary on existing textbooks. The author gives the following personal account of the writing of this guide: In Rajab 827 A.H. (May 1424) he traveled from Damascus to Quds al-Sharīf (in Palestine), where he met two scholars named Ismā‘īl ibn Sharaf and Zayn al-Dīn Māhir. There he took lessons on arithmetic, using an introductory book ...

This manuscript is a work on practical astronomy and the drawing of the circle of projection and related concepts from spherical trigonometry. It is rich with geometric diagrams, tables of empirical observations, and computations based upon these observations. An interesting feature of the manuscript is the appearance on the margins of the cover, and on several pages in the manuscript, of edifying verses, proverbs, and witty remarks. One reads, for example, “It is strange to find in the world a jaundiced physician, a dim-eyed ophthalmologist, and a blind astronomer.” Most ...

This manuscript is a copy of *al-Risāla al-Fatḥīya fī al-a‘māl al-jaybīya* (The introductory epistle on sinusoidal operations) by Muḥammad ibn Muḥammad ibn Aḥmad Abu ‘Abd Allāh, Badr al-Dīn (1423–1506), known as Sibṭ al-Māridīnī or the grandson of al-Māridīnī, in honor of his mother’s father, a famous astronomer. The manuscript consists of 16 pages of 14 lines each, and includes an introduction and 20 *bābs* (chapters or articles). They range in length from a few lines to a page, and cover such topics as determination of the cardinal ...

This manuscript is a commentary on the treatise *Al-Tuffāḥa fi ‘ilm al-Misāḥa* (The apple in the science of measurement), which was written at the beginning of the 12th century by the mathematician Aḥmad ibn Muḥammad al-Ašh‘ari. The study of measures and measurement techniques (*‘ilm al-misāha*) was of great interest to Arabic mathematicians during the Middle Ages, both from theoretical and practical points of view. The ability to calculate the dimensions of landholdings was extremely important when it came to determining the correct amounts for inheritances and to calculating taxes ...

This manuscript, probably dating from the 17th century, preserves only a section of what appears to have been an extensive and complete treatise on practical geometry. The title on the second page of the manuscript in fact states that it is “the third section of the book of the General Rules in the Science of Measurement.” The larger work of which this is a part consisted of four introductory essays, five chapters, and a conclusion. The author is unknown, as the opening of the treatise where indications of authorship might ...

In 1690, Emperor Kangxi summoned two French missionaries, Zhang Cheng (Jean Francois Gerbillon, 1654–1707) and Bai Jin (Joachim Bouvet, 1656–1730), to Beijing to teach him mathematics. The missionaries initially considered using for this purpose the early 17th-century partial translation by Matteo Ricci (1552–1610) and Xu Guangqi (1562–1633) of Euclid’s great work on geometry, *Elements*, but they found it too complicated. So they decided to translate instead *Elements de geometrie* by French Jesuit Ignace Gaston Pardies (1636–73), which drew on Euclid, Archimedes, and Apollonius. They ...

Naseer al-Din (or al-Naseer) al-Tusi (1201–74 AD, 597–672 AH) was a Muslim Persian polymath. He was born in Tus, Khorasan, in present-day Iran. Al-Tusi witnessed the great invasion of the Islamic empire by the Mongols, whom he later joined. He was said to have been in the company of Hulegu Khan when the latter destroyed the Abbasid capital of Baghdad in 1258 AD. Al-Tusi, already a well-known scientist, later convinced Hulegu Khan to construct an observatory to facilitate the establishment of accurate astronomical tables for better astrological predictions ...

Abu al-Rayhan al-Biruni (also known by the Latinized version of his name, Alberonius, 973–1048 AD; 362–440 AH) was an 11th-century Muslim polymath whose works and scholarly interests spanned the physical and natural sciences, mathematics, astronomy, geography, history, chronology, and linguistics. Al-Biruni was born in Kath, Khuwarazm, in present-day Uzbekistan, and died in Ghazni, in what is today east-central Afghanistan. He wrote more than 120 works and is considered the founder of Indology for his detailed description of 11th-century India. The crater Al-Biruni on the moon is named after ...

This work is a commentary on *Ashkāl al-ta’sīs* (Forms of foundation), a geometrical tract by Shams al-Dīn Muḥammad b. Ashraf al-Ḥusaynī al-Samarqandī. The author of the commentary, Qāḍīzāda al-Rūmī (Ṣalāh al-Din Mūsā ibn Muḥammad, 1364–1436) was one of the principal astronomers at the celebrated Samarkand observatory. He was a native of Bursa, where his father Maḥmūd served as a prominent judge (hence the appellation Qāḍīzāda, which means "born to a judge" in Persian). The commentary was completed in 1412 (814 AH) and, judging from the many surviving copies ...