Kelland P., Tait P.G. Introduction to quaternions, with numerous examples

2nd edition. — London: MacMillan and Co., 1882. — 244 p.Introductory
Vector Addition and Subtraction
Definition of a vector, with conclusions immediately resulting therefrom
Examples
Definition of unit vector and tensor, with examples
Coplanarity of three coinitial vectors, with conditions requisite for their terminating in a straight line, and examples
Mean point
Addition examples
Vector Multiplication and Division
Definition of multiplication, and first principles
Fundamental theorems of multiplication
Examples
Definitions of division, versor and quatenion
Examples
Conjugate quaternions
Interpretation of formulæ
Addition examples
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
Examples
Addition examples
The Circle and Sphere
Equations of the circle, with examples
Tangent to circle and chord of contact
Examples
Equations of the sphere, with examples
Addition examples
The Ellipse
Equations of the ellipse
Properties of φ𝛒
Equation of tangent
Cartesian equations
Properties of the ellipse, with examples
Addition examples
The parabola and hyperbola
Equation of the parabola in terms of φ𝛒, with examples
Equations of the parabola, ellipse and hyperbola in a form corresponding to those with Cartesian co-ordinates, with examples
Addition examples
Central surfaces of the second order
Equation of the ellipsoid
Tangent plane and perpendicular on it
Polar plane
Conjugate diameters and diametral planes, with examples
The cone
Examples on central surfaces
Pascal's hexagram
Addition examples
Formulæ and their Application
Formulæ
Examples
Addition examples
Vector Equations of the First Degree
Appendix