The pain in his chest couldn't **equate** with the pain and distress shooting through him like cold fire.

How to **equate** this foreign civilizing race from Asia with the Semitic elements in the ancient Egyptian speech we do not yet know.

Assuming then 01 to have the coefficients B1, B2,...B,, and f l the coefficients A 1, A21...A,n, we may **equate** coefficients of like powers of x in the identity, and obtain m+n homogeneous linear equations satisfied by the m+n quantities B1, 2, ...B n, A 1, A 2, ...A m.

(iii.) Another result is that we can **equate** coefficients of like powers of x in two multinomials obtained from the same expression by different methods of expansion.

To find the border curve of equilibrium between the two states, giving the saturation pressure as a function of the temperature, we have merely to **equate** the values of G and G".

It must be grounded in principles of assured certainty and must demonstrate its conclusions with the use of such middle or linking terms only as it is possible to **equate** with the real ground or cause in the object of knowledge.

If we **equate** these to zero we get the co-ordinates of the instantaneous centre.