By Arthur S. Hathaway
Illustrated, together with a variety of Examples - Chapters: Definitions And Theorems - heart Of Gravity - Curve Tracing, Tangents - Parallel Projection - Step Projection - Definitions And Theorems Of Rotation - Definitions Of flip And Arc Steps - Quaternions - Powers And Roots - illustration Of Vectors - formulation - Equations Of First measure - Scalar Equations, airplane And directly Line - Nonions - Linear Homogeneous pressure - Finite And Null lines - Derived Moduli, Latent Roots - Latent strains And Planes - Conjugate Nonions - Self-Conjugate Nonions - Etc., and so forth.
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Additional info for A Primer of Quaternions - Illustrated
Sample text
B) The three planes parallel to a line. (c) The three planes meet in a common line. (d) The three planes parallel. (e) The three planes coincide. CHAPTER 4. EQUATIONS OF FIRST DEGREE 53 Derived Moduli of φ 82. The ratio in which the nonion φ + g dilates volume is, mod (φ + g) = S(φα + gα)(φβ + gβ)(φγ + gγ)/Sαβγ. This is independent of the values of the non-coplanar vectors α, β, γ in terms of which it is expressed. If g is a scalar, this modulus is an ordinary cubic in g, whose coefficients will therefore depend only upon φ.
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4. If two steps be multiplied by reciprocal numbers, then corresponding products and multiplicands are reciprocally proportional. 5. Construct the following products, where OA is a unit step to the right in the plane of the paper, and determine the functions of each multiplier that are defined in Art. 33. (a) 2 ·√ OA = OL, (4, 60◦ ) · OA√= OB, (4, −60◦ ) · OA = OB , (2 3, 90◦ ) · OA = OM, (2 3, −90◦ ) · OA = OM , (1, 60◦ ) · OA = OB1 , (1, −60◦ ) · OA = OB1 , (1, 90◦ ) · OA = OM1 , (1, −90◦ ) · OA = OM1 .