Encyclopedia of the History of Arabic Science. Volume 2, Mathematics and the Physical Sciences pdf

perfectly aware of this fact, and one had written well before 1185: ‘Since the unknownthat one wants to determine and know in each of these polynomials is the side of the cubementioned in each, and the analysis leads to the application of a known right-angledparallelepiped to a known line, and which is surplus to the entire parallelepiped by a cube25or which is deficient by a cube; we can only do this synthese using conic sections’. ow this recourse to conic sections, explicitly intended to solve cubic equations, quicklyfollowed the first algebraic renderings of solid problems. We have mentioned in the26ninth-century al-Mأ¤hأ¤nr and the lemma of Archimedes;it was not long before otherproblems such as the trisection of an angle, the two means and the regular heptagon inparticular were translated into algebraic terms. However, confronted with the difficultymentioned above, and thus with that of solving cubic equations by radicals,mathematicians such as al-Khأ¤zin, Ibn Abu al-Jأ¼d ibn al-Layth, al-Shannr etc.27ended up translating this equation into geometrical tenns. They then found in the course