June 14, 2026
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R3 – Square Roots

Definition The square root of an expression in R3 is made of the roots of the individual Opposite Values with the signs remaining constant. Square of an Expression Given the generic expression (a? + bi? + cj?): Note that as a result of the Zero Rules of Rotation a??b?? + b??a?? = 0, so This […]

Axioms – Ratios

In Cecilia Hamm’s “Making Sense of Negative Numbers,” she states, “Arnauld (1612-1694) claimed that the basic principle of multiplication is that the ratio of unity to one factor is equal to the ratio of the second factor. i.e., given the product x , then x or x .” This is known as the axiom of […]