the theory of determinants

a₁ absolutely convergent Afgars alternate numbers An-h array b₁ b₂ c₁ c₂ complement complementary minors conjugate contain continued fraction corresponding cubic determinant D₁ D₂ denoted deter determinant of order dx₁ e₁ elementary divisor elementary factor elements equal equations expansion follows Hence homogeneous function identical integral interchange Jacobian leading diagonal linear function m₁ matrix minant minors of order multiply notation number of inversions obtained P₁ permutation Pfaffian plane prove quadric quantities reduces rows and columns rows or columns rth row S₁ semi-normal sets shew skew symmetrical determinant spheres square subtract suffixes suppose term tetrahedron theorem of Art transformation u₁ variables write x₁ y₁ zero α₁ α₂