Saturday, September 24, 2011

Opus Arithmetica of Honoratus

An illustration from an unpublished 16th century manuscript, Opus Arithmetica D. Honorati veneti monachj coenobij S. Lauretij. Honoratus was a Venetian monk, and the manuscript was written in the second half of the 16th century. But the manuscript was copied by a pupil, probably also a monk, who also did the illustrations.

The above illustration depicts the compound operation necessary to solve a given problem. The multiplication of 16299 by 613 resulting in the product 9991287 can be discerned in the central configuration. In the lower left corner is another galley division.

Saturday, September 17, 2011

Qadi Zada al-Rumi's Geometry

This is a page from the Geometry (1412) of Qadi Zada al-Rumi (1364-1436). Al-Rumi's book was a commentary on the Fundamental Theorems, written by al-Samarqandi (1250-1310), where he discusses twenty-five of Euclid's propositions in detail. The book shown in the image is a later copy of al-Rumi's work, probably written in the sixteenth century. At the top of the page is a discussion of Euclid's Proposition I-5, the "Bridge of Asses" proposition that the base angles of an isosceles triangle are equal. At the bottom, there is a discussion of I-6, the converse of I-5. Al-Rumi was an astronomer and mathematician in the court of Ulugh Beg (1393-1449) in Samarkand. He and his colleagues compiled the first complete star catlogue since the time of Ptolemy.

Saturday, September 10, 2011

Saturday, September 3, 2011

Omar Khayyam's Algebra

This is a page from a manuscript of the Algebra (Maqalah fi al-jabra wa-al muqabalah) of Omar Khayyam (1048-1131). This work is known for its solution of the various cases of the cubic equation by finding the intersections of appropriately chosen conic sections. On this page, Omar is discussing the case "a cube, sides and numbers are equal to squares", or, in modern notation, x3 + cx + d = bx2. Read more about Omar Khayyam's Algebra.