But most astonishing it is, that an arithmetic by the same author completely excludes the Hindoo numerals. It is constructed wholly after Greek pattern. Abul Wefa also, in the second half of the tenth century, wrote an arithmetic in which Hindoo numerals find no place. This practice is the very opposite to that of other Arabian authors. The question, why the Hindoo numerals were ignored by so eminent authors, is certainly a puzzle. Cantor suggests that at one time there may have been rival schools, of which one followed almost exclusively Greek mathematics, the other Indian.
The Arabs were familiar with geometric solutions of quadratic equations. Attempts were now made to solve cubic equations geometrically. They were led to such solutions by the study of questions like the Archimedean problem, demanding the section of a sphere by a plane so that the two segments shall be in a prescribed ratio. The first to state this problem in form of a cubic equation was Al Mahani of Bagdad, while Abu Gafar Al Hazin was the first Arab to solve the equation by conic sections. Solutions were given also by Al Kuhi, Al Hasan ben Al Haitam, and others.[20] Another difficult problem, to determine the side of a regular heptagon, required the construction of the side from the equation . It was attempted by many and at last solved by Abul Gud.
The one who did most to elevate to a method the solution of algebraic equations by intersecting conics, was Omar al Hayyami of Chorassan, about 1079 A.D. He divides cubics into two classes, the trinomial and quadrinomial, and each class into families and species. Each species is treated separately but according to a general plan. He believed that cubics could not be solved by calculation, nor bi-quadratics by geometry. He rejected negative roots and often failed to discover all the positive ones. Attempts at bi-quadratic equations
