# reciprocals

Noun

- plural form of
*reciprocal*

- As will be seen later, the fundamental i, j, k of quarternions, with their
**reciprocals**, furnish a set of six quantities which satisfy the conditions imposed by Servois. - (Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present biquaternions, as also octonions, are particular cases.) The point whose position vector is Vrq i is on the axis and may be called the centre of the bi-quaternion; it is the centre of a sphere of radius Srq i with reference to which the point and plane are in the proper quaternion sense polar
**reciprocals**, that is, the position vector of the point relative to the centre is Srg i. - If the refractive index for one colour be n, and for another and the powers, or
**reciprocals**of the focal lengths, be 4) and 4)+4, then (I) dï¿½/ 4) = dn/ (n - I) =1 /v; do is called the dispersion, and v the dispersive power of the glass. - The polar form is {(u+p) cos 26} a+{(u-p) sin 20) a = (2k)t, where p and k are the
**reciprocals**of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c =a or = oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed. - In The Case Of Negative Numbers And
**Reciprocals**, Only One Is Involved; And There Might Be Three Or More, As In The Case Of A Number Expressed By (A B)".

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