Of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)ï¿½x4; and it can be shown that 0, x, 1P are the three conjugate quadratic factors of t above mentioned.
The Leiden copy of ~Omar Khayygms work on algebra was noticed as far back as i 742 by Gerald Meerman in the preface to his Specimen calculi fluxionalis; further notices of the same work by Sdillot appeared in the Nouv.
Of the Notices et extraits des MSS.
Articles on Omars life and works are found in Reinauds Geographie dAboulfeda, pref., p. 101; Notices et extraits, ix.
This would fix the date of his death in 738; and, as Alcuin tells us he was eighty-one years old when he died, it may be inferred that he was born in 657 - a theory on which all the dates given above are based, though it must be added that they are substantially confirmed by the incidental notices of Bede.