Definition of "affine"

Now, let P, Q, and R be three noncollinear points that are left fixed by an affine transformation T.

1986, Patrick J. Ryan, Euclidean and Non-Euclidean Geometry: An Analytic Approach, Cambridge University Press, page 44

In our example of the affine cryptosystem family, deciphering is also accomplished by an affine map, namely P ≡ a − 1 C − a − 1 b mod N {\displaystyle P\equiv a^{-1}C-a^{-1}b{\bmod {N}}} , and so the deciphering transformation uses the same algorithm as the enciphering transformation, except with a different key, namely, the pair ( a − 1 , − a − 1 b ) {\displaystyle (a^{-1},-a^{-1}b)} .

1987, Neal Koblitz, A Course in Number Theory and Cryptography, Springer, page 81

Clearly every linear functional is affine, and every affine function is both convex and concave.

2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 256

The element of personal idiosyncracy[sic] may be expected to be most marked in regard to affines (i.e. those related by marriage) and particularly with the consanguines of affines, who are linked by still more tenuous bonds. There are many possible degrees of affinal relationship here, but broadly affines separate into two main types: spouse of consanguine of Ego, and consanguine of spouse of Ego—exemplified by my brother's wife, and my wife's brother.

1970 [Routledge and Kegan Paul], Raymond Firth, Jane Hubert, Anthony Forge, Families and Their Relatives: Kinship in a Middle-Class Sector of London, 2006, Taylor & Francis (Routledge), page 135

In contrast to bonds of kaḅisu membership, which require ritual maintenance and can produce intense factional rivalries, and those of affines, which demand ongoing exchanges, unmediated relations of blood are created by nothing more than physical procreation. […] People's ability to swivel between these two rhetorical possibilities reflects the inherent tension that lies between affines, who are both others and extensions of oneself.

1997, Webb Keane, Signs of Recognition: Powers and Hazards of Representation in an Indonesian Society, University of California Press, page 51

For the Cubeo the Vekürüwá and Okómiwa were, as they say, designated to be their affines, in a manner that was calculated to emphasize their similarities rather than the formal differences that set contemporary intermarriages apart. I suspect that Cubeo themselves sense that an excessive intimacy with the contingent of affines may have been suitable for a formative period of still ambiguous distinctions, but not for the real social world.

2004, Irving Goldman, Cubeo Hehénewa Religious Thought, Columbia University Press, page 64