hyperbola 
COniC hyperbola, a hyperlwln proper, defined under def. 1, 
above. Conjugate hyperbolas, two hyperbolas having 
common asymptotes, the transverse axis of either being 
the conjugate axis of the other. Cubical hyperbola. 
See cubical. Deficient or defective hyperbola, see 
deficient. Equilateral hyperbola, a hyperbola whose 
asymptotes are at right angles to one another, and \vhos-.- 
axes are consequently equal. Focal hyperbola. See 
focal. Infinite hyperbola, a hjpatou in the New- 
tonian sense. See def. 2, above. Inscribed hyperbola, 
a hyperbola which does not cross its asymptotes. Loga- 
rithmic hyperbola, the section of a right cylinder hav- 
ing a hyperbola as its base by a paraboloid. This name 
was given by Booth in 1851. Nodated hyperbola. See 
nodated. Obtuse hyperbola, a hyperbola which lies in 
the obtuse angle between its asymptotes. Pitch hyper- 
bola, a hyperbola the inverse squares of whose diameters 
are proportional to the pitch of the parallel generators of 
the cylindroid whose generators are the possible screws 
of a rigid body having two degrees of freedom. 
hyperbolaeon (hi"per-bo-le'on), n. See tetra- 
cltord. 
hyperbole (hi-per'bo-le), n. [= F. hyperbole = 
Sp. hiperbole = Pg. hyperbole = It. iperbole, < L. 
hyperbole, < Gr. imepflohr/, excess, overstrained 
phrase, etc. : see hyperbola, the same word with 
accom. L. termination.] In rhet., an obvious 
exaggeration ; an extravagant statement or as- 
sertion not intended to be understood liter- 
ally. 
When we speake in the superlatiue and beyond the 
limites of credit, that is by the figure which the Greeks 
call Hiperbole. Puttenham, Arte of Eng. Poesie, p. 159. 
Three-pil'd hyperboles, spruce affectation, 
Figures pedantical. Shalt., L. L. L., v. 2. 
No city brings better home to us than Ragusa the East- 
ern hyperbole of cities great and fenced up to heaven. 
E. A. Freeman, Venice, p. 226. 
= Syn. See exaggeration. 
hyperbolic (hl-per-bol'ik), . [= P. hyper- 
bolique = Sp. hiperbolico = Pg. hyperbolico = It. 
iperbolico, < L. hyperbolicus, < Gr. {>irfp/3o/locof, 
extravagant, < i-trfpfio^i/, hyperbole : see hyper- 
bole. In mod. use the adj. goes also with hy- 
perbola.] 1. Pertaining to or of the nature 
of hyperbole ; obviously exaggerating or exag- 
gerated. 
Among the Zulus the hyperbolic compliment to the 
king, "Thou who art as high as the mountains," passes 
from the form of simile into the form of metaphor when 
he is addressed as "You Mountain." 
//. Spencer, Prin. of Soclol., 401. 
2. Pertaining to or of the nature of the hyper- 
bola. 3. Having a pair of real points at in- 
finity. Thus, hyperbolic space is so called because in it 
every right line has two real points at infinity ; so hy- 
perbolic transformation, mbstitution, etc. Hyperbolic 
amplitude of any quantity. See amplitude. ~ Hyper- 
bolic arc, an arc of the hyperiiola. Hyperbolic conoid. 
See conoidi, 1 (o). Hyperbolic curvature, function, 
geometry, etc. See the nouns Hyperbolic cylin- 
droid, a solid generated by the rotation of a hyperbola 
about its conjugate axis. SirC. Wren. Hyperbolic leg 
or branch of a curve, a leg or branch having an asymp- 
tote or asymptotes. Hyperbolic logarithm, a natural 
logarithm, or one whose base is 2.7182818. See loga- 
rithm. Hyperbolic singularity of a function, an essen- 
tial singularity : so called because such singularities of a 
theta Fuchsian function are connected with hyperbolic 
substitutions of the fundamental Fuchsian group. Hy- 
perbolic space, a space in which the sum of the three 
angles of a triangle would be less than two right angles. 
Hyperbolic spiral, a spiral curve the law of which is 
thai the distance from the pole to the generatrix varies 
inversely as the distance swept over. 
hyperbolical (hi-per-bol'i-kal), a. [< hyper- 
bolic + -al.] 1. Same as hyperbolic, 1. 
You shout me forth 
In acclamations hyperbolical, 
As if I loved my little should be dieted 
In praises sauced with lies. Shalt., Cor., i. 9. 
The shewes in our Lady street being so hyperbolical in 
pomp that day that it exceeded the rest by many degrees. 
Coryat, Crudities, I. 38. 
I have a hyperbolical tongue ; it catches fire as it goes. 
George Eliot, Middlemarch, I. 243. 
2. Same as hyperbolic, 2. [Rare.] 
hyperbolically (hl-per-bol'i-kal-i), adv. 1. 
In a hyperbolic manner; with obvious exag- 
geration ; in a manner to express more or less 
than the truth. 
Scylla is ... hyperbolically described by Homer as in- 
accessible. Broome. 
Created natures allow of swelling hyperboles ; nothing 
can be said hyperbolically of God. 
Sir T. Browne, Christ. Mor., lit 2. 
2. In the form of a hyperbola. 
hyperboliform (hi-per-bol'i-f&rm), a. [= F. 
hyperboliforme ; as hyperbola + -form.] Hav- 
ing the form of a hyperbola of a higher kind. 
hyperbolise, c. See hyperbolize. 
hyperbolism 1 (hl-per'b6-lizm), n. [< hyperbo- 
la + -ism.] In geom., a curve the equation of 
which is derived from that of another curve by 
writing xy for y. 
hyperbolism 2 (hl-per'bo-lizm), . [= F. Iiy- 
perbolisme; as hyperbole + -ism.] The use of 
2948 
hyperbole; the character of being hyperboli- 
cal. 
The hyperbolizing of the oriental style. 
Hartley, Works, I. v. 
hyperbolist (hl-per'bo-list), n. [= Pg. hiiiH-r- 
holistn; as hyperbole + -ist.] One who uses hy- 
perbole. 
hyperbolize (hi-per'bo-liz), r. ; pret. and pp. 
hyiH'i-liulizcil, ppr. hyperbolizing. [= F. liypcr- 
boliser = Sp. hiperbolisar ; as hyperliole + -ize.] 
I. intrans. To use hyperbole; speak or write 
with obvious exaggeration. 
The Spanish traveller . . . was so habituated to hyper- 
bolize . . . and relate wonders that he became ridiculous. 
Ilowell, Forreine Travell, xiv. 
II. trims. To exaggerate ; represent or speak 
of in a hyperbolical manner. 
Vain people hyperbolizing his fact, ... he grew by 
their flattery into that madness of conceit. 
Fotherliy, Atheomastix, p. 203. 
[< Gr. 
Also spelled hyperbolise. 
hyperbolograph (hi-per-bol'o-graf), n. 
vKeppo/.r/, hyperbola, + ypdipeiv, write.] An in- 
strument for the description or drawing of hy- 
perbolas. 
hyperboloid (hl-per'bo-loid), n. [< Gr. intp- 
po/.ii, hyperbola, + fMoj, form.] 1. A quadric 
surface having a center not at infinity, and 
some of its plane sections hyperbolas. There 
are two kinds of hyperboloid, those of one and of two 
sheets. The hyperboloid of one sheet has a real inter- 
section with every plane in space; that of two sheets 
has only imaginary intersections with some planes. In 
either case all the plane sections perpendicular to one of 
the axes are ellipses, and those perpendicular to either of 
the others are hyperbolas. 
2. A hyperbola of a higher order, 
hyperboloidal (hi-per-bo-loi'dal), o. [< hyper- 
boloid + -al.] Pertaining to or of the nature 
of a hyperboloid. 
The crests of the teeth of a skew-bevel wheel are paral- 
lel to the generating straight line of the hyiierboloidal 
pitch-surface. W. J. M. Rankine, Encyc. Brit., XV. 759. 
hyperborean (hl-per-bo're-an), o. and n. [= 
P. hyperboreen, < LL. Hyperooreanus, < L. hyper- 
boretts, adj. (>It. iperboreo = Pg. hyperboreo = 
Sp. hiperbdreo = F. hyperboree), Hyperborei, n. 
pl.,< Gr. i'TTcpftopeoc., inrepjUpftof, adj., beyond the 
north wind, "fTrep/)6peoi, n. pi., the Hyperbore- 
ans, an imaginary people in the extreme north, 
< inrfp, over, beyond, + flopcaf, the north wind 
(perhaps orig. the 'mountain' wind, 'Tirepf)6- 
pco/, the people 'beyond the (Rhipsean) moun- 
tains'): see hyper-, Boreas, and oread.] I. a. 
1 . Situated in or inhabiting the far north : as, 
the hyperborean regions; a hyperborean race; 
the hyperborean phalarope. 
From hyperborean^ skies, 
Embodied dark, what clouds of Vandals rise ! 
Pope, Dunciad, iii. 85. 
Hence 2. Very cold; frigid. 
The more chilly and pinching hyperborean atmosphere 
in which they have grown up and been formed. 
Crailt, Hist Eng. Lit., I. 6. 
3. [cap.] Of or pertaining to the imaginary 
race of Hyperboreans. 4. Arctic. 
The first, or Hyperborean group (of the Native Races of 
the Pacific States), comprises the tribes of Alaska and a 
part of British America, and includes races perfectly dis- 
tinct from one another. N. A. Jtec., CXX. 37. 
H. n. [cap.] 1. An inhabitant of the most 
northern region of the earth. In early Greek legend 
the Hyperboreans were a people who lived beyond the 
north wind, and were not exposed to its blasts, but enjoyed 
a land of perpetual sunshine and abundant fruits. They 
were free from disease, violence, and war. Their natural 
life lasted 1,000 years, and was spent in the worship of 
Apollo. In later times the Greeks gave the name to the 
inhabitants of northern countries generally. 
2. pi. In ethiiol., a group of arctic races, 
hyperbrachycephaiic (hl-per-brak'i-se-farik 
or hi-per-brak-i-sef'a-lik), a. [As hyperbrachy- 
cephal-y + -ic.] Extremely brachycephalic ; ex- 
hibiting hyperbrachycepnaly. 
hyperbrachycephaly (hi-per-brak-i-sef'a-li), 
n. [< hyper- + brachyeephaly.] In craniom., 
extreme brachyeephaly; the character of a 
skull of which the cranial index is over 85. 
See craniometry. 
hyperbranchial (M-per-brang'ki-al), a. [< Gr. 
r~?p, over, + Bpayxia, gills.] Situated over the 
gills or branchiae : as, the hyperbranchial groove 
of the pharynx of a lancelet. 
hyper-Calvinist (hl-per-kal'vin-ist), n. See 
<'/i I rin int. 
hypercardia (hi-per-kar'di-a), n. [NL., < Gr. 
vmp, over, + KapSia, heart.] Inpathol., hyper- 
trophy of the heart. Dunglison. 
hypercatalectic (hl-per-kat-a-lek'tik), a. [< 
L. hypercatalecticus, equiv. to hypercatalectus, < 
hypercriticize 
Gr. iVf/iKnrn/7/KTOf, < i'~fp, over, beyond, + Kara- 
fyKTOf, stopping off: see catalcctic.] In jiros., 
having an additional syllable or half-foot (the- 
sis or arsis) after the last complete dipody: as, 
a liypercntalectic colon or verse. The epithet hy- 
percatalectic, like brachycatalectic, is applicable to those 
meters only which arc scanned by dipodies that is, to 
iambic-, trochaic, anapestic, and occasionally and excep- 
tionally to dactylic meters. 
hypercatalexis(lii-per-kat-a-lek'sis), n. [NL., 
\ Gr. inr/), over, beyond, + sard/iyf <f, an ending, 
termination, catalexis: see catalexis.] Ingres., 
excess of a final syllable or half -foot after the 
last measure in a series or line measured by 
dipodies. In classical poetry hypercatalexis is found 
as the apparent excess of an arsis (metrically unaccented 
part of a foot) at the end of one colon or series, the arsis 
at the beginning of the next being wanting ; so that, if 
such an arsis be reckoned to the second colon, all the 
measures would be complete : thus, w w |w w | 
w || w | w s, _. 
hypercatharsis (hi // per-ka-thar'sis), n. [NL., 
< Gr. vvepnattapaif, excessive purging, < mepKa- 
0aipea6at, be purged Sxcessively, < inrep, over, 4- 
Kaffaipeiv, cleanse, purge, > KaSapat^, a purging : 
see catharsis, cathartic.] In meil., an excessive 
purging ; action of the bowels excited by a vio- 
lent cathartic. 
hypercathartic (hi"per-ka-thar'tik), n. and . 
[s Gr. iirip, over, 4- KadapriKof, purging (see 
cathartic), after hypercatharsis.] I. a. Per- 
taining to or of the nature of hypercatharsis. 
II. n. A medicine which produces excessive 
purging. 
hyperchloric (hi-per-klo'rik), a. [< hyper- + 
chloric.] Same &s perchloric. 
hyperchromasia (hiper-kro-ma'si-a), . [< Gr. 
rfff p, over, + ;fp<j//a, color.] A pathological con- 
dition marked by excess of pigment. 
hyperchromatism (hl-per-kro'ma-tizm), n. [< 
Gr. iifip, over, + ^/)u,ua(T-), color, + -ism.] A 
state of unusually heightened or intensified col- 
oration, as that of melanism or erythrism, in an 
animal. 
hypercinesia, hypercinesis, etc. See hyper- 
kinesis, etc. 
hypercomplex (hi-per-kom'pleks), a. [< hy- 
per- + complex.] Composed of a number of 
imaginaries or complex quantities. Thus, a quan- 
tity at -I- bj +, etc., where a> b, etc., are complex scalars, 
while t, j, etc., are peculiar units, having their proper 
multiplication-table, is a hypercomplex quantity. 
hyperconic (hi-per-kon'ik), a. [< hyper- + 
conic.] In math., relating to the intersection 
of two surfaces of the second order. 
hypercoracoid (hi-per-kor'a-koid), n. [< Gr. 
vxtp, over, + E. coracoid.] "The upper of the 
two bones of typical fishes interposed between 
the actinosts or fin-bearing elements and the 
proscapula or principal bone of the scapular 
arch. Called by Cuvier radial, by Owen ulna, 
and by later naturalists scapula. See cut under 
scap ulo-coracoid. 
hypercritic (hi-per-krit'ik), n. [= F. hypcr- 
critiqve = It. ipercritico; as hyper- + critic.] 
One who is critical beyond measure or reason ; 
an over-rigid critic ; a captious censor. 
hypercritical (hi-per-krit'i-kal), a. [< hyper- 
+ critical. Cf. hypercritic.] 1. Excessively 
or captiously critical ; judging adversely from 
trivial or irrelevant considerations ; unduly fin- 
ical or unjustly severe in judgment. 
Such hypercritical readers will consider my business 
was to make a body of refined sayings, only taking care to 
produce them in the most natural manner. Swi/t. 
I take the official oath to-day with no mental reserva- 
tions, and with no purpose to construe the Constitution 
or laws by any hypercritical rules. 
A. Lincoln, First Inaugural Address. 
2. Excessively exacting or scrupulous. [Rare.] 
We are yet far from imposing . . . these nice and h;i- 
percritical punctilios, which some astrologers . . . oblige 
our Gard'ners to. Evelyn, Calendarium Horteuse, Int. 
hypercritically (hi-per-krit'i-kal-i), adv. In 
a hypercritical manner; with excessive criti- 
cism. 
We cannot afford to speak contemptuously of any sort 
of knowledge, and God forbid that we should speak con- 
temptuously or hypercritically of any honest worker. 
Stutbe, Medieval and Modern Hist., p. 13. 
hypercriticise, r. t. See hypercriticize. 
hypercriticism (hi-per-krit'i-sizm), . [< ///- 
per- + criticism.] Excessively minute or se- 
vere criticism. 
To insist on points like these is mere hypercrtiicism. 
Scotsman (newspaper). 
hypercriticize, hypercriticise (M-per-krit'i- 
siz), v. t.; pret. and pp. hypercriticised, hij- 
pt-rcriticised, ppr. hypercriticiying, hypercriti- 
