geometric 
orated style. See decorated. Geometric decora- 
tion, decoration by means of straight lines or curves, or 
small surfaces bounded by such lines or curves, without 
the suggestion of plant or animal forms or the like. Frets 
and meanders, zigzags, checkers, circles, anil triangles 
which frequently interlace with one another, forming 
elaborate star-shaped patterns, dog-teeth, notches of dif- 
ferent kinds, and all similar forms, whether applied to a 
flat surface or carved in greater or less relief, are included 
In geometric decoration. Geometric elevation, lo- 
cus, etc. See the nouns. Geometric style, in arch., 
that development of the Pointed medieval architecture <>t* 
England which includes the examples just previous to the 
most perfect artistic achievement of the style, or perhaps 
even the examples of highest excellence. It succeeded 
the Lancet or Early English style in the early part of the 
thirteenth century, and is characterized by the adoption 
of tracery, as yet in simple geometric forms, in broader 
windows, in place of the plain, narrow lancets of the pre- 
ceding style, together with modifications of consistent 
character in wall-decoration and other sculptured orna- 
ment. With the advance of the thirteenth century, the 
severity and geometric simplicity of line in tracery and 
ornament became less marked, and the style passed grad- 
ually into the Decorated. See cut on preceding page. 
geometrically (je-o-met'ri-kal-i), adv. In a 
geometric manner; 'according to the principles 
of geometry Geometrically irrational, transcen- 
dental : said of a curve. Geometrically rational, al- 
gebraic. 
geometrician (je-om-e-trish'an),. [(geometric 
+ -ian. Cf. arithmetician, mathematician, etc.] 
One skilled in geometry ; a geometer in sense 1. 
geometrid (je-om'e-trid), a. and n. I. a. In 
r a t<> HI., pertaining to the moths of the section 
Geometrina, whose larvae are measuring-worms. 
II. . A moth of the family Geometridce or 
section Geometrina, or its larva ; a measuring- 
worm. 
GeometricUe (je-6-met'ri-de), n. pi. [NL., < 
Geometra + -idee.] A large family of hetero- 
cerous lepidopterous insects or moths, named 
from the genus Geometra, whose larvre are mea- 
suring-worms; the geometers, geometrids, pha- 
I : i i lids, or PhalfBnidce. This group, regarded as a fam- 
ily, is divided into 26 subfamilies, named Urapterince, 
Ennomince, (Enockrominte^ Amphidaxiiwe, Boarmince, 
Boletobiince, Geometrince, Microcerinar, Palyadinas, Ephy- 
rince, Acidalince, Micronince, Eaberince, Macarince, Fido- 
niince, Hazinte, Zereninte, lAgince,Hyberniiice t Larentxince, 
Evbolinae, Sionirue, Hedylince, Erateininae, Emplocinte, 
and Hypochrosince. In some systems, as Guen^e s, these 
are all elevated to the rank of families, ending in -idee, 
and the superfamily thus constituted, called Phalcenites, 
is the Geometrina of English authors. The names Geo- 
metridce and Phal(enid<8 are exactly synonymous ; and 
the various names resulting from the changes in termina- 
tion of the two words are applied to what is practically 
an identical group of moths, rated higher or lower in the 
taxonomic scale, according to the classiflcatory views of 
different authors. See the extract, and cuts under Cidaria 
and Haplodee. 
The Geometridce or Phalcenidce form a family of great 
size, being exceeded in numbers among the Lepidoptera 
only by the noctuids and tineids, and probably equalled 
only by the pyralids and tortricids. They are . . . wide- 
ly distributed over the globe, and the caterpillars of many 
species have proved very destructive to some of our most 
important vegetable productions. The moths have rather 
long, slender bodies, the thorax without tufts or crests. 
Ocelli are present in some species, and absent in others. 
The antennae are either simple, ciliated, or pectinated. 
The fore wings are large and triangular; the outer margin 
... is nearly as long as the hinder margin. The hind 
wings are ample. ... In some [species], the females are 
wingless, or have only rudimentary wings, which are use- 
less for flight. . . . The caterpillars are slender and na- 
ked, usually with two pairs of abdominal legs, though 
rarely they have three or four pairs. This deficiency causes 
them to move along with a looping gait, and hence they 
are often called " measuring-worms," from which fact the 
family name [Geomttridas] was given. 
Stand. If at. Hist., II. 445. 
geometrient, See geometrian. 
geometriform (je-o-met'ri-f 6rm), a. [< Geome- 
tra + L. forma, form.] In entom., resembling 
in form a moth of the family Geometridce. 
Geometrina (je-om-e-tri'na), n. pi. [NL., < 
Geometra + -in'a.] In entom., a group of hete- 
rocerous lepidopterous insects ; the geometers 
or geometrid moths. 
Geometrinse (je-om-e-trl'ne), n. pi. [NL., < 
Geometra + -ince.] One of numerous restricted 
subfamilies of Geometridce, named from the ge- 
nus Geometra. 
geometrine (je-om'e-trin), a. [< Geometra + 
-inc.} Pertaining to the Geometridce. 
geometrize (je-om'e-triz), v. i. ; pret. and pp. 
geometriged, ppr. geometrizing. [< geometry + 
-ize.~] To solve geometrical problems; specu- 
late geometrically ; practise geometry. The use 
of this word originated from Plato% saying (reported by 
Plutarch) that God continually gemnetrizes. 
Nature [in crystallization] . . . confined herself to ye- 
ometrize. Boyle. 
All things were disposed, according to their nature and 
use, in number and measure, by the magnificent architect ; 
who in the one did every where geometrize as well as in 
the other. N. Grew, Cosmologia Sacra, iv. 8. 
geometry (je-om'e-tri), .; pi. geometries (-triz). 
[< ME. geometric, commonly gemetrie, gemetry, 
2495 
< OF. geometric, F. geometric = Sp. geomrlriii 
= Pg. It. geometria = I). G. geometric = Sw. 
Dan. geometri, < L. geometria, < Gr. ycu/icrpia, 
geometry, < ytufiirfnis, a land-measurer, a ge- 
ometer: see geometer.] 1. That branch of 
mathematics which deduces the properties of 
figures in space from their denning conditions, 
by means of assumed properties of space. Ab- 
breviated geom. 
Qpomttrie, 
Through which a man hath the sleight 
Of length, of brede, of depth, of height. 
Gouter, Conf. Amant, vii. 
2. A text-book of geometry Abstract geome- 
try, the general theory of the connections of more than 
two variables. Geometry, in its analytical treatment, 
appears as identical with the algebra of two or three vari- 
ables. A similar study of the connections of a number of 
variables in general is called m-dimensional geometry, 
and abstract geometry as not descending to particulars. 
Algebraic, algorithmic, analytical, Cartesian, 
coordinate, etc., geometry. See the adjectives. 
Common or elementary geometry, that treatment of 
geometry which assumes no previous knowledge of the 
subject, and is supposed to be well known in all other 
mathematical writings. This discipline remains in nearly 
the condition in which Euclid left it. See Euclidean geom- 
etry. Descriptive geometry (invented by Gaspard 
Monge, 1794), the theory of making projections of any ac- 
curately denned figure such that from them can be de- 
duced, not only its projective, but also its metrical prop- 
erties. It is highly useful in engineering. The name is 
also applied to the theory of geometry in general treated 
by means of projections. Elliptic geometry, a system 
which assumes that space, though infinite in measure- 
ment, has a real and definite boundary, separating the 
points at a real distance from points at an imaginary dis- 
tance. Enumerative or denumerative geometry, 
the theory of the number of solutions of geometrical prob- 
lems, and of the number of incidences and coincidences in 
a diagram drawn under given conditions. Euclidean ge- 
ometry, a system of geometry which adopts the assump- 
tions of Euclid with regard to space, namely, that space 
is an infinite continuum of three dimensions, that rigid 
bodies are capable of translation and rotation in all direc- 
tions in every position, and that the sum of the three an- 
gles of a plane triangle is equal to two right angles. Ge- 
ometry Of forces, the theory of congruencies and com- 
plexes of forces. Geometry of position, (a) A branch 
of geometry created by the French revolutionary states- 
man Carnot, which traces the connection between the 
changes of an equation and the changes of position of a 
locus. (&) Modern projective geometry, commonly written 
in German Geometrie der Lage, to distinguish it from (a). 
Geometry of space, geometry of three dimensions, 
geometry of figures not restricted to a plane or other sur- 
face. Geometry Of the compasses, a system of geom- 
etry in which the postulate that a right line be describa- 
ble is not admitted, but instead links turn about pivots 
and are connected together. The first important discov- 
ery in this branch of geometry was the Peaucellier cell. 
See cell. Graphical geometry. Same as projective ge- 
ometry. Higher geometry, any geometry not elemen- 
tary; especially, modern synthetic geometry. Hyper- 
bolic geometry, a system which assumes that space re- 
turns into itself, so that there are no points whose distance 
exceeds a certain finite distance. Linear or line geom- 
etry, the theory of systems of rays, congruencies, and 
complexes. Metric or quantitative geometry treats 
of the distances of points or the magnitude of angles, ares, 
surfaces, volumes, etc. Modern geometry, the syn- 
thetic geometry which has been developed in the nine- 
teenth century by Carnot (" Geometric de position," 1803), 
Brianchon (" Memoire sur les lignes du second ordre," 
1817), Poncelet ("Traite des proprietes projectives des 
figures," 1822), Mobius (" Barycentrische Calcul," 1827), 
Steiner (" Systematische Entwickelung," 1832), Chasles 
(" Geometric sup^rieure," 1852), Von Staudt (" Geometric 
der Lage," 1847), and others. Organic geometry, (a) A 
kind of geometry invented by MacLaurm (1719), in which 
more complicated curves are produced from less compli- 
cated ones. Hence (b) Higher synthetic geometry in gen- 
eral. Parabolic geometry, a system which assumes (in 
harmony with Euclidean principles) that the locus at an 
infinite distance consists of two coincident planes with an 
imaginary circle upon them. Plane geometry, the ge- 
ometry of figures all lying in one plane. Practical ge- 
ometry, (a) Surveying. (b) The art of geometrical draw- 
ing. Protective geometry, a method of investigating 
geometry by the application of the theory of projections. 
Segmentary geometry, modern synthetic geometry, 
especially when treated by means of the anharmonic ratio. 
Solid geometry, (a) The elementary geometry of solid 
bodies, (b) Geometry of three dimensions. Specula- 
tive geometry, the science of geometry proper, as dis- 
tinguished from practical geometry. Spherical geom- 
etry, the geometry of figures drawn on the surface of a 
sphere. Synthetic geometry, geometry treated not by 
means of coordinates or other algebraic devices, but by 
means chiefly of projections. Theoretical geometry. 
Same as speculative geometry. To hang by geometry! , 
to have the clothes hang angularly, out of shape, or in 
rags. , 
Look you, here's Jarvis hangs by geometry, and here's 
the gentleman. Rowley, Match at Midnight, iii. 
Transcendental geometry, all geometry not elemen- 
tary; especially, geometry treated by the calculus. 
geomorphy (je'o-m6r-n),'. [< Gr. yij, the 
earth, + ftop<j>^, form.] The theory of the fig- 
ure of the earth. 
geomyid (je-om'i-id), n. One of the Geomyidce. 
Geomyidae (je-o-mi'i-de), n. pi. [NL., < Geo- 
mys -r -idee.] A remarkable American family 
of myomorphic rodents; the pouched rats or 
pocket-gophers. They are characterized by the enor- 
mous external cheek-pouches lined with fur, not com- 
Geophilinae 
municating with the mmith, and extending In some cases 
along tile neck as far ;us the shoulders ; dental formula, 2 in- 
cisors in each up- 
perand lower half- 
jaw, no canines, 
1 premolar and 3 
molars ill each up- 
per and lower 
lialf-jaw;forefeet 
fossorial, with 
large claws ; tail 
short and stumpy; 
cars small, and 
general form ro- 
bust. The group 
corresponds to the 
Sciuroiipalacoides 
of Brandt or Geo- 
myince of Bainl, 
and consists of the 
two genera Gi'<>- 
inys and Tft"ii">- 
mys. See gopher. 
Under Side of Head of Geomys bunarius, 
} showing entrance of external cheek-pouches 
* . ..-m f and silicate superior incisors. 
n.pl. [NL., < 
Geomys + -ince.] A subfamily of Saccomyidte; 
the pouched rats. See Geomyidce. 
Geomys (je'o-mis), n. [NL., < Gr. yij, the earth, 
+ fivf E. mouse.] The typical genus of Geo- 
myidce, with grooved incisors, rudimentary ex- 
ternal ears, and enormous fore claws. There are 
several species, of North and Central America, sharing 
with those of Thoinomys the name gopher. G. bursarius 
is the common pocket-gopher of the United States, espe- 
cially in the Mississippi valley; G. tuza inhabits Georgia, 
Florida, and Alabama ; G. castanops is found in Texas and 
New Mexico ; G. meximnus is the tucan of Mexico ; and 
G. hispid-us is the quachil of Central America. 
geo-navigation (je"6-nav-i-ga'shon), n. [< Gr. 
yij, the earth, + E. navigation.] That mode of 
navigation in which the place of a ship at sea is 
determined by referring it, by the course and 
distance sailed, to some other spot on the sur- 
face of the earth. Harbord. See dead-reckon- 
ing. 
Geonoma (je-on'o-ma), n. [NL., so called in 
allusion to its rapid propagation, < Gr. ytuv6/oK, 
also yeuv6/jof, a colonist, one receiving a portion 
of distributed lands, < yij, the earth, + vipuv, 
distribute.] A genus of low, slender, graceful, 
unarmed palms, with reed-like stems, of about 
100 species, common in the forests of tropical 
America. The leaves are entire, or bifid, or more or 
less pinnately cleft, the flowers are small upon a simple 
or forked spadix, and the small one-seeded fruit is usually 
black. 
geonomic (je-o-nom'ik), a. [< geonomy + -ic.] 
Pertaining to'geonomy. 
geonomy (je-on'o-mi), n. [< Gr. yjj, the earth, 
+ v6/ioe, a law.]' The science of the physical 
laws relating to the earth, including geology 
and physical geography. 
geophagism (je-of'a-jizm), . [< geophagy + 
-ism.'] Same as geophagy. 
geophagist (je-of 'a-jisrt)* n. [< geophagy + -ist.'] 
One who practises geophagism; one who eats 
earth. 
geophagous (je-of'a-gus), a. [< NL. geophagus, 
< Gr. as if "-yea^dyof, for which yattxpayof, yaaj- 
fyayof, earth-eating, < JTJ, yala, the earth, + 0a- 
yeiv, eat.] Earth-eating: as, geophagous tribes. 
geophagy (je-of 'a-,ji), n. [< Gr. as if *yeu<j,ayia, < 
"yt-a^dyof, earth-eating: see geophagous.'] The 
act or practice of eating earth, as dirt, clay, 
chalk, etc. See dirt-eating. Also geophagism. 
Geophila (je-of'i-la), n. pi. [NL. (Menke, 
1828), neut. pi. of g'cophihis: see geophilous.] 
A group, generally ranked as a suborder, of 
terrestrial pulmonate gastropods; the land- 
snails and land-slugs, including those forms 
which have the eyes at the tips of the tenta- 
cles. The group is framed for the inoperciilate land-snails 
generally, such as the Limacidce, Helicidce, Vaginulidcs, 
and related families. Also called Stylommatop/iora and 
Nephropneusta. 
geophilian (je-o-fil'i-an), a. and . I. a. Of or 
pertaining to tie Geophila or terrestrial inoper- 
culate pulmoniferous gastropods. 
II. n. A member of this group. Compare 
gehydrophilian, hygrophilian. 
geophilid (je-of'i-lid), n. A myriapod of the 
family (Icop'liitidte. 
Geophilidae (je-o-fil'i-de), n. pi. [NL., < Geo- 
philus -f- -idee.] A family of centipeds, of the 
order Cliilopoda and class Myriapoda, contain- 
ing terrestrial forms (whence the name) which 
have numerous (30 to 200) similar flattened seg- 
ments, with short legs, 14-jointed antennae, 
single-jointed tarsi, and no eyes. There are 
several genera besides Geophilus. 
Geophilinae (je-of-i-li'ne), n. pi. [NL., < Geo- 
jiliilus + -/'.] A subfamily group of centi- 
petls. See Geophilidte. Alsowritten Geophilini. 
