in manuscript form. Jordanus’ De numeris datis was the first treatise in advanced algebra composed in Western Europe, building on elementary algebra provided in twelfth-century translations from Arabic sources. It anticipates by 350 years the introduction of algebraic analysis by François Viète into Renaissance mathematics. Jordanus used a system similar to that of Viète (although couched on non-symbolic terms) of formulating the equation (setting out the problem in terms of what is known and of what is to be found), of transforming the initial given equation into a solution, and the introduction of specific numbers that fulfil the conditions set by the problem. Geometry: Liber philotegni and the De triangulis This is medieval geometry at its best. It contains propositions on such topics as the ratios of sides and angles of triangles; the division of straight lines, triangles, and quadrangles under different conditions; the ratio of arcs and plane segments in the same or in different circles; trisecting an angle; the area of triangles given the length of the sides; squaring the circle. Again there are two versions of this text: the shorter and presumably first edition (the Liber philotegni Iordani de Nemore) and a longer version (Liber de triangulis Iordani) which divides the text into books, re-arranges and expands book 2, and adds propositions 4-12 to 4-28. This latter set of 17 propositions also circulated separately. While the longer version may not be by Jordanus, it was certainly complete by the end of the thirteenth century. Stereographic projection: Demonstratio de plana spera This treatise of five propositions deals with various aspects of stereographic projection (used in planispheric astrolabes). The first and historically the most important proposition proves for all cases that circles on the surface of a sphere when projected stereographically on a plane remain circles (or a circle of infinite radius, i.e., a straight line). While this property was known long before Jordanus, it had never been proved. There are three versions of the treatise: the basic text, a second version with an introduction and a much expanded text, and a third, only slightly expanded. The introduction is sometimes found with version 1 and 3, but it was obviously written by someone else. Dubious and spurious works The De proportionibus (on ratios), the Isoperimetra (on figures with equal perimeters), the Demonstrationes pro astrolapsu (on astrolabe engraving), and the Pre-exercitamina (“a short introductory exercise”?) are dubiously ascribed to Jordanus.