Introduction to Quaternions

[QA257.K3]

Contents

• Preface

• Chapter I. Introductory
• Chapter II. Vector Addition and Subtraction
  Definition of a VECTOR, with conclusions immediately resulting therefrom; definition of UNIT VECTOR and TENSOR; coplanarity of three coinitial vectors, with conditions requisite for their terminating in, a straight line; mean point.
• Chapter III. Vector Multiplication and Division
  Definition of multiplication, and first principles; fundamental theorems of multiplication; definitions of DIVISION, VERSOR and QUATERNION; conjugate quaternions; interpretation of formulae.
• Chapter IV. The Straight Line and Plane
  Equations of a straight line and plane; modifications and results -- length of perpendicular on a plane -- condition that four points shall lie in the same plane, etc.
• Chapter V. The Circle and Sphere
  Equations of the circle; tangent to circle and chord of contact; equations of the sphere.
• Chapter VI. The Ellipse
  Equations of the ellipse; properties of φρ; equation of tangent; Cartesian equations; φ^-1ρ, ψρ, etc. ; properties of the ellipse.
• Chapter VII. The Parabola and Hyperbola
  Equation of the parabola in terms of φρ; equations of the parabola, ellipse and hyperbola in a form corresponding to those with Cartesian co-ordinates.
• Chapter VIII. Central Surfaces of the Second Order, Particularly the Ellipsoid and Cone
  Equation of the ellipsoid; tangent plane and perpendicular on it; polar plane; conjugate diameters and diametral planes; the cone; Pascal's hexagram.
• Chapter IX. Formulae and their Application
  Formulae; examples.
• Chapter X. Vector Equations of the First Degree

• Appendix.