homaloidn.adj.

Brit.

/ˈhɒməlɔɪd/, U.S.

/ˈhɑməˌlɔɪd/

Forms: 1800s omaloid, 1800s– homaloid, 1900s– homoloid (irregular).

Origin: A borrowing from Greek, combined with an English element. Etymons: Greek ὁμαλός , -oid suffix.

Etymology: < ancient Greek ὁμαλός (see homalographic adj.) + -oid suffix. Compare homaloidal adj.In form homoloid by association with words in homo- comb. form.

Mathematics. Now rare.

A. n.

A homaloidal or flat (Euclidean) space of any number of dimensions.

ΘΚΠ

the world > relative properties > number > geometry > surface > [noun] > plane

plaina1398

plane1604

plan1714

primitive plane1798

homaloid1850

biplane1870

1850 J. J. Sylvester in London, Edinb. & Dublin Philos. Mag. 37 368 The Homaloidal law..is a corollary to a proposition which represents analytically the indefinite extension of a property common to lines and surfaces to all loci (whether in ordinary or transcendental space) of the first order, all of which loci may, by an abstraction derived from the idea of levelness common to straight lines and planes, be called Homaloids.

1870 Philos. Trans. (Royal Soc.) 160 57 If k = m, the corresponding locus is a point; if k < m the locus is a k-fold, or (m − k)dimensional omaloid; the expression omaloid used absolutely denotes the onefold or (m − 1)dimensional omaloid.

1907 Smith College Monthly Nov. 90 Where the measure of curvature of space is zero that space conforms to Euclid's axioms and is a homaloid or surface in contrast to..curved spaces.

1955 Amer. Math. Monthly 62 532 The base of the web of homoloids consists of two twisted cubics.

2005 Chaos, Solitons & Fractals 25 517 All these lines are double..on a generic homaloid of the inverse web.

B. adj.

= homaloidal adj.

ΘΚΠ

the world > relative properties > number > geometry > surface > [adjective] > relating to plane surfaces > of nature of

plaina1398

plane1666

homaloidal1850

homaloid1876

1876 Mind 1 310 Now whenever the value of this measure of curvature in any space is everywhere zero, that space everywhere conforms to the axioms of Euclid; and it may be called a flat (homaloid) space in contradistinction to other spaces.

1879 Q. Jrnl. Pure & Appl. Math. 16 155 In space of four dimensions let a homaloid three-dimensional solid be taken touching an ellipsoid at A.

1919 Proc. Royal Soc. A. 96 355 The Minkowski four-fold continuum of space and time..may be conceived as a flat or homaloid locus in our present auxiliary five-fold continuum.

This entry has been updated (OED Third Edition, September 2011; most recently modified version published online March 2022).

单词	homaloid
释义	homaloidn.adj. Brit. /ˈhɒməlɔɪd/, U.S. /ˈhɑməˌlɔɪd/ Forms: 1800s omaloid, 1800s– homaloid, 1900s– homoloid (irregular). Origin: A borrowing from Greek, combined with an English element. Etymons: Greek ὁμαλός , -oid suffix. Etymology: < ancient Greek ὁμαλός (see homalographic adj.) + -oid suffix. Compare homaloidal adj.In form homoloid by association with words in homo- comb. form. Mathematics. Now rare. A. n. A homaloidal or flat (Euclidean) space of any number of dimensions. ΘΚΠ the world > relative properties > number > geometry > surface > [noun] > plane plaina1398 plane1604 plan1714 primitive plane1798 homaloid1850 biplane1870 1850 J. J. Sylvester in London, Edinb. & Dublin Philos. Mag. 37 368 The Homaloidal law..is a corollary to a proposition which represents analytically the indefinite extension of a property common to lines and surfaces to all loci (whether in ordinary or transcendental space) of the first order, all of which loci may, by an abstraction derived from the idea of levelness common to straight lines and planes, be called Homaloids. 1870 Philos. Trans. (Royal Soc.) 160 57 If k = m, the corresponding locus is a point; if k < m the locus is a k-fold, or (m − k)dimensional omaloid; the expression omaloid used absolutely denotes the onefold or (m − 1)dimensional omaloid. 1907 Smith College Monthly Nov. 90 Where the measure of curvature of space is zero that space conforms to Euclid's axioms and is a homaloid or surface in contrast to..curved spaces. 1955 Amer. Math. Monthly 62 532 The base of the web of homoloids consists of two twisted cubics. 2005 Chaos, Solitons & Fractals 25 517 All these lines are double..on a generic homaloid of the inverse web. B. adj. = homaloidal adj. ΘΚΠ the world > relative properties > number > geometry > surface > [adjective] > relating to plane surfaces > of nature of plaina1398 plane1666 homaloidal1850 homaloid1876 1876 Mind 1 310 Now whenever the value of this measure of curvature in any space is everywhere zero, that space everywhere conforms to the axioms of Euclid; and it may be called a flat (homaloid) space in contradistinction to other spaces. 1879 Q. Jrnl. Pure & Appl. Math. 16 155 In space of four dimensions let a homaloid three-dimensional solid be taken touching an ellipsoid at A. 1919 Proc. Royal Soc. A. 96 355 The Minkowski four-fold continuum of space and time..may be conceived as a flat or homaloid locus in our present auxiliary five-fold continuum. This entry has been updated (OED Third Edition, September 2011; most recently modified version published online March 2022). < n.adj.1850
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