† orthomorphosisn.

Origin: Probably formed within English, by compounding. Etymons: ortho- comb. form, metamorphosis n.

Etymology: Probably < ortho- comb. form + -morphosis (in metamorphosis n.), after orthomorphic adj. (see quot. 1885).

Mathematics. Obsolete. rare.

A. Cayley's term for: an orthomorphic transformation (see orthomorphic adj. 2).

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements

inclusion1870

orthomorphosis1885

isomorphism1892

identity1910

homoeomorphism1918

homomorphism1935

topological mapping or transformation1939

isometry1941

Möbius transformation1941

injection map(ping)1950

monomorphism1954

bijection1963

surjection1964

1885 A. Cayley in Q. Jrnl. Math. 20 220 (title) On the orthomorphosis of the circle into the parabola.

1891 A. Cayley Wks. XIII. 191 The author [sc. Schwartz] considers the orthomorphic transformation (or, as I call it, the orthomorphosis) of a square into the infinite half-plane, or into a circle.

1891 A. Cayley Wks. XIII. 191 It is easy to deduce the orthomorphosis of the rectangle into a circle.

This entry has been updated (OED Third Edition, September 2004; most recently modified version published online June 2018).

单词	orthomorphosis
释义	† orthomorphosisn. Origin: Probably formed within English, by compounding. Etymons: ortho- comb. form, metamorphosis n. Etymology: Probably < ortho- comb. form + -morphosis (in metamorphosis n.), after orthomorphic adj. (see quot. 1885). Mathematics. Obsolete. rare. A. Cayley's term for: an orthomorphic transformation (see orthomorphic adj. 2). ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements inclusion1870 orthomorphosis1885 isomorphism1892 identity1910 homoeomorphism1918 homomorphism1935 topological mapping or transformation1939 isometry1941 Möbius transformation1941 injection map(ping)1950 monomorphism1954 bijection1963 surjection1964 1885 A. Cayley in Q. Jrnl. Math. 20 220 (title) On the orthomorphosis of the circle into the parabola. 1891 A. Cayley Wks. XIII. 191 The author [sc. Schwartz] considers the orthomorphic transformation (or, as I call it, the orthomorphosis) of a square into the infinite half-plane, or into a circle. 1891 A. Cayley Wks. XIII. 191 It is easy to deduce the orthomorphosis of the rectangle into a circle. This entry has been updated (OED Third Edition, September 2004; most recently modified version published online June 2018). < n.1885
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