reciprocantn.

Brit.

/rᵻˈsɪprək(ə)nt/, U.S.

/rəˈsɪprək(ə)nt/,

/riˈsɪprək(ə)nt/

Origin: A borrowing from Latin. Etymons: Latin reciprocant-, reciprocāns.

Etymology: < classical Latin reciprocant-, reciprocāns, present participle of reciprocāre reciprocate v.

Mathematics.

1. = polar reciprocal n. at polar adj. and n. Compounds. Now disused.

ΚΠ

1852 J. J. Sylvester in Cambr. & Dubl. Math. Jrnl. 7 180 Calling r the resultant of (x, y)⁴, R the resultant of (x, y, z)³, ρ the polar reciprocal, or, more briefly, the reciprocant of (x, y, z)⁴..we have the following equations [etc.].

1913 E. B. Elliott Introd. Algebra Quantics (ed. 2) xvi. 400 Such a contravariant has been called the reciprocant of a ternary quantic.

2. An expression involving derivatives of a function y with respect to a variable x which has the same form (up to multiplication by a factor) when expressed with derivatives of x considered as a function of y. Now historical.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > invariant

resultant1842

invariant1851

catalecticant1852

sextinvariant1852

reciprocant1886

1886 J. J. Sylvester in Amer. Jrnl. Math. 8 199 We are..led..by prosecuting this inquiry to lay the foundations of the theory of Reciprocation or Reciprocants.

1936 Amer. Math. Monthly 43 285 The left member of this equation furnished him with the first instance on record of a multinomial projective reciprocant.

1997 Notes & Rec. Royal Soc. 51 255 He [sc. Sylvester] gave an inaugural lecture entitled ‘On the Method of Reciprocants’, embellished with some characteristic verse.

Derivatives

† reciprocantive adj. Obsolete rare of or relating to a reciprocant (sense 2).

ΚΠ

1886 J. J. Sylvester in Nature 7 Jan. 225/1 A pure reciprocant, by virtue of its reciprocantive character, must remain unaltered save as to the immaterial fact of its acquiring a factor containing merely the constants of substitution.

This entry has been updated (OED Third Edition, June 2009; most recently modified version published online March 2022).

单词	reciprocant
释义	reciprocantn. Brit. /rᵻˈsɪprək(ə)nt/, U.S. /rəˈsɪprək(ə)nt/, /riˈsɪprək(ə)nt/ Origin: A borrowing from Latin. Etymons: Latin reciprocant-, reciprocāns. Etymology: < classical Latin reciprocant-, reciprocāns, present participle of reciprocāre reciprocate v. Mathematics. 1. = polar reciprocal n. at polar adj. and n. Compounds. Now disused. ΚΠ 1852 J. J. Sylvester in Cambr. & Dubl. Math. Jrnl. 7 180 Calling r the resultant of (x, y)⁴, R the resultant of (x, y, z)³, ρ the polar reciprocal, or, more briefly, the reciprocant of (x, y, z)⁴..we have the following equations [etc.]. 1913 E. B. Elliott Introd. Algebra Quantics (ed. 2) xvi. 400 Such a contravariant has been called the reciprocant of a ternary quantic. 2. An expression involving derivatives of a function y with respect to a variable x which has the same form (up to multiplication by a factor) when expressed with derivatives of x considered as a function of y. Now historical. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > invariant resultant1842 invariant1851 catalecticant1852 sextinvariant1852 reciprocant1886 1886 J. J. Sylvester in Amer. Jrnl. Math. 8 199 We are..led..by prosecuting this inquiry to lay the foundations of the theory of Reciprocation or Reciprocants. 1936 Amer. Math. Monthly 43 285 The left member of this equation furnished him with the first instance on record of a multinomial projective reciprocant. 1997 Notes & Rec. Royal Soc. 51 255 He [sc. Sylvester] gave an inaugural lecture entitled ‘On the Method of Reciprocants’, embellished with some characteristic verse. Derivatives † reciprocantive adj. Obsolete rare of or relating to a reciprocant (sense 2). ΚΠ 1886 J. J. Sylvester in Nature 7 Jan. 225/1 A pure reciprocant, by virtue of its reciprocantive character, must remain unaltered save as to the immaterial fact of its acquiring a factor containing merely the constants of substitution. This entry has been updated (OED Third Edition, June 2009; most recently modified version published online March 2022). < n.1852
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