November 8, 2011

Jabir ibn Hayyan

Jabir ibn Hayyan (also known by the Latinized version of his name, Geber, 721–815 AD, 103–200 AH) was a Muslim polymath, philosopher, and alchemist. He was probably born in Tus, Khorasan, in present-day Iran, although some sources claim that he was born and grew up in Kufa, Iraq. Some aspects of the life of Jabir ibn Hayyan as well as the authenticity of tens, if not hundreds, of the titles of his vast body of work have been questioned. More than 3,000 treatises or books are attributed to him in one way or another, covering fields that include cosmology, music, medicine, magic, biology (including the artificial generation of living beings), chemical technology, geometry, grammar, metaphysics, and logic. This work is a biography of Jabir ibn Hayyan by Zaki Naguib Mahmoud (1905–93), who was an Egyptian writer, academic, and philosophy professor. He was an encyclopedic writer who was known for his ability to simplify complex ideas, and for taking philosophy out of its “ivory tower” and into the public domain.

A Treatise on Drawing Chords in a Circle

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 him. Risālah fī Istikhrāj al-awtār fī al-dāʼirah (A treatise on drawing chords in a circle) is, as its title suggests, a treatise on geometry that deals with circles.

Cosmographical Map or Universal Description of the World with the Actual Path of the Winds

This world map, made in Dieppe, northern France, in 1570, is thought to be the only extant map by Jean Cossin (also seen as Jehan and Johan Cossin), a hydrographer from Dieppe known in his time as an excellent maker of marine maps. It is entitled Carte cosmographique ou universelle description du monde avec le vrai traict des vents (Cosmographical map or universal description of the world with the actual path of the winds). The map is framed on an original projection, known as sinusoidal, in which the meridians are sinusoids and the parallels the equidistant straight lines divided into equal parts by the meridians. After the Flemish cartographer Gerardus Mercator (1512–94), Cossin was only the second mapmaker to employ this complex projection. The map reflects its maker’s considerable knowledge of mathematics, but it was of limited practical interest or use for sailors. It shows a vast southern continent that unfurls from Tierra del Fuego, and that was hypothesized as an essential counterbalance to the lands of the northern hemisphere. The map is enclosed in a large frame that presents the signs of the zodiac along the left side and the climates along the right. In the banners that fill out the four corners between the map and the edge are listed the title, the author's name, and the date and place of production.

The Best of Arithmetic

This treatise on the art of arithmetic, completed in the late 1880s, opens a window into the early interaction between traditional and modern mathematical pedagogy in Egypt. The use of French loan words, such as million, along with some modern notation, indicates the author’s familiarity with developments in the teaching of arithmetic at the time. The work has an introduction followed by ten chapters and a conclusion. Following traditional praise for God, the Prophet Muhammad, and virtuous vanguards of learning, the treatise opens by introducing arithmetic as a useful and rigorous science, which underlies mathematics, is the cornerstone of worldly transactions, and is a source of knowledge on which many questions in Islamic law depend. In his introduction, the author offers a descriptive and operational definition of numbers and their classifications. Chapter 1 covers operations (addition, subtraction, multiplication, and division) on whole numbers. Chapter 2 deals with fractions, and their expansion, reduction, and basic operations. Chapter 3 addresses the special case of fractions based on division by 24 parts, each called a qirāt (carat), which are said to have been in wide use by the Egyptian Copts; these he calls Coptic fractions. In Chapter 5, the author turns to decimal fractions, which he introduces as being widely used in Europe. Chapter 6 discusses sexagesimal fractions used in celestial calculations, provides information on a variety of arithmetic transactions used in Egypt at the time, and discusses measurements of length, weights, scales, and exchange rates. Chapter 7 treats the extraction of square roots and cube roots, as well as operations on radicals. Chapter 8 discusses geometric, arithmetic, and musical numbers, along with operations on them. Chapter 9 is on solving equations and contains problems related to calculating zakāt (alms tax) and the division of inheritance. Chapter 10 treats the question of inheritance in more detail. The conclusion of the book introduces algebraic methods.

November 9, 2011

Book of the Alphonsine Tables

A reflection of the knowledge of astronomy of the time, these tables were produced in Spain between 1263 and 1272 under the direction of Isaac ben Sid and Judah ben Moses Cohen. The Ptolemaic belief that the planets orbited the Earth was then the predominant cosmological system, and the heliocentric model of the solar system formulated by Copernicus, who personally studied and copied the tables, was still two centuries away. Known as Alfonsine tables after King Alfonso X of Castile (reigned 1252–84), the tables are a compilation of data about the positions and movements of the planets. Alfonso was a patron of learning who employed Christian, Jewish, and Muslim scholars to translate works of Arabic science into Latin and Castilian Spanish. He assembled a team of astronomers who compiled the Alfonsine tables, based on the calculations of the Arab astronomer al-Zarqali (also known as Arzachel, 1029–87). The work was edited and printed in Venice in 1483, the only Alphonsine astrological work to make it to the printing press during the Renaissance. The manuscript is from the Cathedral of Toledo and is now in the National Library of Spain. It was the property of Cardinal Francisco Javier de Zelada in Italy, and brought to Spain by Cardinal Lorenzana in the late 18th century.

Life and Deeds of the Cunning Rogue Guzman de Alfarache

Vida y hechos del picaro Guzman de Alfarache (The life and deeds of the cunning rogue Guzman de Alfarache) is an important early example of the picareseque novel, a fictional genre that developed in Spain and that takes its name from picaro, a Spanish word meaning rogue or rascal. Written more as a moralizing discourse than for amusement, Guzman de Alfarache offers all of the features of the picaresque novel. The author, Mateo Alemán (born in Seville in 1547, died in Mexico circa 1615), developed an original personal style, not yet exploited in La vida de Lazarillo de Tormes y de sus fortunas y adversidades (The life of Lazarillo de Tormes and of his fortunes and adversities), the anonymous novella published in 1554 that served as his model. In both the first and second parts of the work, the storyline is supplemented with short tales, diversions, and anecdotes that allow the author to reflect on topics such as justice, honor, and forgiveness, even as they interrupt the main narrative by Guzman, an unscrupulous character who undertakes numerous frauds and deceptions. A feeling of sadness pervades the story, drawing the reader into the complicated realities of 16th-century Spain and Italy, and reflecting the spirit of the Counter-Reformation then underway. The first part was published in Madrid in 1599 and was a remarkable success. Publication of the second part followed in 1604. The work was enormously popular and was soon translated into English, French, German, Italian, and Latin. This edition from the National Library of Spain was printed in 1681.