## equalities

Noun

- plural form of
*equality*

- 4.1.1 (i)
**Equalities**and Inequalities - Similarly the
**equalities**99 X I o I = 9999 = wow - I 98 X 102 = 999 6 = moo() - 4 97 X 10 3 =9991 =1 0000 - 9 lead up to (A - a) (A+a) = A 2 - a 2. - The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the
**equalities**= - I. - All this is analogous to the corresponding formulae in the barycentric calculus and in quaternions; it remains to consider the multiplication of two or more extensive quantities The binary products of the units i are taken to satisfy the
**equalities**e, 2 =o, i ej = - eeei; this reduces them to. - The five
**equalities**which stand first in the five pairs of**equalities**in ï¿½ 15 (2) may therefore be taken as the main types of a simple statement of equality.

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