- 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.

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