CONTENTS XV 32.Quaternions,Vectors,and Linear Associative Algebras,722 I I'he Foundation of Algebra on Permanence of Form,772 2.The Search for a Three-Dimensional"Complex Number,"776 3.The Nature of Quaternions,779 4 Grassman's Calculus of Extension,782 5 From Quaternions to Vectors,785 6 Linear Associate Algebras,791 33.Determinants and Matrices,795 I Introduction,795 2 Some New Uses of Determinants,795 3.Determinants and Ouadratic Forms.799 4 Matrices.804 List of Abbreviations Index