analogium 
195 
analytic 
say that there is an analogy between things, and that one 
thing has analogy to or with another.] 
Intuitive perceptions in spiritual beings may, perhaps, 
hold some analogg unto vision. 
Sir T. Browne, Christ. Mor,, iii. ir>. 
That there is a real analogy between an individual or- 
assumed as true, and consequences are drawn from it until 
something conceded is reached, which if it is true involves 
the truth of the thing sought, the demonstration corre- 
sponding to the analysis ; in the latter, the construction 
sought is assumed as already known, and consequences 
are deduced from it until something given is reached. 
(6) Algebraical reasoning, in which unknown 
quantities are operated upon in order to find 
their values. Vieta. (c) The treatment of 
problems by a consideration of infinitesimals, 
or something equivalent, especially by the dif- 
ferential calculus (including the integral cal- 
thnes applied to an ambo or a pulpit. 2. The 
inclosure of the tomb of a saint. J>n I'mnji . 
Also written analogioii. 
analogize (a-ual'o-jiz), .; pret. and pp. anal- 
ogized, ppr." analogizing. [< analogy + -ize. _ _ aa 
The Gr. dvaAoyi&atiat agrees ill form, but not in ganism and a social organism, becomes undeniable when 
^iH^^^SSy"! ^SSHiEIHH5qS 
U. mttan.'i. lo make use ot analogy, rj > rf tw n { ltu . Si hut o{ two qualitative relations. 
analogous. A'(, Critique of Pure Reason (tr. by Max Miiller). 
Also spelled analogise. Specifically 3. In logic, a form of reasoning culus, the calculus of variations, etci"): often 
analogon (a-nal 9-gon), .; p 1. analoga (-ga). in wniehj from the similarity of two or more called infinitesimal analysis. This is the com- 
[< Gr. avafoyov, adj., neat, ol )of, a^ thi jn cert ain particulars, their similarity in mO n meaning of the word in modern times. 
gous:seeanato<70s.] An analogue ; something other particu i ai . 8 4 ls j n f er red. Thus, the earth and Hence (d) The discussion of a problem by 
Mars are both planets, nearly equidistant from the sun, mea ns of algebra (in the sense of a system of 
not differing ^j 1 ^,,"!,^!!"^ symbols with rules of transformation), in oppo- 
mkUty" te'nip^rat'ure.'seasons.'d'ay and night, etc.; but the Sltipn to a geometrical discussion of it, that is, 
earth also supports organic life ; hence Mars (probably) a discussion resting directly upon the imagina- 
supports organic life is an argument from analogy. See tion of space: thus, analytical geometry is the 
r?n^, conformity ; to the spirit, structure, ^^^^^^ff^l^ 
or general rules of a language L ^similarity 'as Qf a book digcourse ^ of the princi pi e8 
analogous. Coleridge. 
Even the other element of the Jewish system, the ele- 
ment of prophecy, is not without its analogon among the 
heathen. 0. P. Fisher, Begin, of Christianity, i. 
analogous (a-nal'o-gus), a. [< L. analogus, < 
Gr. dvd'Aoyoi,' according to a due Xoyof or ratio, 
proportionate, conformable, analogous, < ava, 
throughout, according to (see ana-), + Uyos, _ _ _ _ , 
ratio, proportion: see logos and logic.] 1. In respects any of the characteristics of a Ian- ^ 
sc i en ce -Analvsis of a plant an examina- 
- 
between things morphologically or structurally 
unlike : the opposite of Jtomology. Thus, there is 
an analogy between the wing of a bird and that of a butter- 
fly, both being adapted to the same physiological purpose 
of flight, but there Is no morphological relation between 
them. Analogy rests upon mere functional (that is, 
physiological) modifications ; homology is grounded upon 
erefore physiologically i 
l. Analogy of 
resemblance or proportion : sometimes loosely 
used for similar. Thus, there is something in the ex- 
ercise of the mind analogous to that of the body ; animal 
organs, as the wing of a bird and that of a bat, which per- 
form the same function, though different in structure, are 
analogous. See 4, below. 
The effect of historical reading is analogous, in many 
respects, to that produced by foreign travel. 
Macaulay, On History. 
Specifically 2. In diem., closely alike, but dif- 
fering in some degree as to each of the more 
prominent characters. 3. In bot., resembling 
in form but not in planjrf structure. fl ^ThuMhe analphabet,' analphabete (an-al'fa-bet, -bet), 
JwpaliuuAhe other a^petaL A^Gray. ' not knowing one's A B C, < dv- priv. + W^d/Si/ros, 
4. In biol., similar physiologically but not an- the ABC, alphabet: see alphabet.] I. a. Not 
atomically; like in function but not in struc- knowing the alphabet; illiterate, 
ture : the opposite of homologous. See analogy, 
5. 5. In logic, from Albertus Magnus down to 
modern writers, applied to terms which are ho- 
monymous or equivocal in a special way, name- 
ly, those in which the identity of sound is not 
accidental, but is based upon a trope or upon 
anal 
analysis, 
See the adjec- 
the detection 
of the constituents of a compound body, in distinction 
from quantitative analysis, or the determination of the 
amounts and proportions of the constituents. Spectrum 
analysis. See spectrum. =Syn. Assay, Analysis. Seefls- 
pllySlOIOglCal^ 1UOU111UHL1OIIB , llulllvlugj' la glvunnvv* ujyun Hfl,f 
structural (that is, morphological) identity or unity. Anal- all ;,'i vs * ( an ' a -list') n I" F analvste = Pg. 
ogy is the correlative of physiology, homology of morphol- anaiysp (.anaiisi;, . L--*- ^ K , 
ogy; but the two may be coincident, as when structures analysta = Sp. It. analuta : formed from the 
identical in morphology are used for the same purposes verb analyze, as if from a verb in -ize : see -ist, 
.,._,..,!.. ,_,...:,..,, A__,-^ ^ J One who analyzes or who is versed in 
analysis, in any application of that word. 
The analyst has not very many resources at his disposal 
for separating an intimate mixture of several bodies. 
Pop. Sci. Mo., XXV. 203. 
II. n. One who does not know the alphabet ; 
one who cannot read. 
As late as the census of 1861 it was found that [in Italy] 
in a population of 21,777,331 there were no less than 16,- 
ic. analytical (an-a-lit'ik, -i-kal), a. and 
) first form) . K ML. analyticus, < Gr. 
of, analytic, < ovaAurof, dissoluble, verbal 
adj. of avaf-veiv, dissolve, resolve, analyze : see 
" is.] I. a. 1. Relating to, of the nature 
some other reason. 
A term is analogous whose single signification applies 
with equal propriety to more than one object : as, the 
leg of the table, the leg of the animal. Whately. 
In all senses used with to, sometimes with. 
= Syn. Correspondent, similar, like. 
analogously (a-nal'o-gus-li), adv. In an anal- 
ogous manner. 
anal 
struction, absolutely unable to read. 
Uncyc. Brit., XIII. 460. 
Not know- 
analphabetic (an-al-fa-bet'ik), a. 
ing the alphabet ; illiterate ; unable to read. 
" i, analyse, etc. See analyzable, etc. 
i. [Also written analise, < F. ana- 
lyse^ ML. analysis: see analysis, analyze.] 
Analysis. 
The analyse of it [a tractate] may be spared, since it is 
in many hands. Bp. Hacket, Life of Abp. Williams, ii. 104. 
of, or operating by analysis: opposed to syn- 
thetic, synthetical: as, an analytic mode of 
thought. 
His [Webster's] mind was analytical rather than con- 
structive, and his restlessness of life was indicative of a 
certain instability of temper. 
H. E. Scudder, Noah Webster, tv. 
2. In the Kantian logic, explicatory ; involving 
a mere analysis or explication of knowledge, 
and not any material addition to it. 
In all judgments in which there is a relation between 
subject and predicate (I speak of affirmative judgments 
raly, the application to negative ones being easy), that re- 
The mechanical law, that action and reaction are equal, 
has its moral analogue. H. Spencer, Social Statics, p. 253. 
and though it may be very well in giving a relish to thought 
for certain palates, it cannot supply the substance of it. 
Lmvell, Study Windows, p. 137. 
Specifically 2. In pliilol., a word correspond- 
ing with another; an analogous term. 3. In 
zodl. and bot. , an animal or a plant corresponding 
in some special and essential attributes or rela- 
tions to a member of another group or region, 
so that it is a representative or counterpart. 
4. In biol., an organ in one species or group 
having the same function as an organ of differ- 
ent structure and origin in another species or 
group. The difference between homologue and analogue 
may be illustrated by the relation between the wing of a 
bird and that of a butterfly : as the two differ totally in 
anatomical structure, they cannot be said to be homo- 
logues, but they are analogues, since both serve for flight. 
See analogy, 5. 
analogy (a-nal'o-ji), n. ; pi. analogies (-jiz). [< 
F. analogic, < L. analogia, < Gr. ava/joy'ia, equal- 
ity of ratios, proportion, analogy, < ava/lojof, 
analogous: see analogous.] 1. In math., an 
equation between ratios. This use is obsolete ex- 
cept in a few phrases, as Napier's analogies, which are four 
important formulas of spherical trigonometry. 
2. An agreement, likeness, or proportion be- 
tween the relations of things to one another ; 
hence, often, agreement or likeness of things 
themselves. Analogy strictly denotes only a partial 
similarity, as in some special circumstances or effects 
pmlicable of two or more things in other respects essen- 
tially different : thus, when we say that learning enlightens 
the mind, we recognize an analogy between learning and 
light, the former being to the mind what the latter is to 
the eye, enabling it to discover things before hidden. [We 
synthetical. Analytical judgments (affirmative) are there- 
fore those in which the connection of the predicate with 
the subject is conceived through identity, while others in 
which that connection is conceived without identity may 
be called synthetical. 
Kant, Critique of Pure Reason (tr. by Max Miiller). 
'.iv, resolve into its elements, analyze, lit. 
loosen, undo, (. ava, back, + tJotiv, loosen: see 
loosen.] 1. The resolution or separation of 
anything which is compound, as a conception, 
a sentence, a material substance, or an event, 3. I n philol., deficient in inflections, and em- 
into its constituent elements or into its causes ; ploying instead particles and auxiliary words to 
decomposition. 
In the deductive syllogism we proceed by analysis 
that is, by decomposing a whole into its parts. 
Sir W. Hamilton. 
In the associationalist psychology, the analysis of an 
idea is the discovery of the different kinds of elementary 
sensations which are associated together to produce the 
idea. 
Analysis is real, as when a chemist separates two sub- 
stances. Logical, as when we consider the properties of 
the sides and angles of a triangle separately, though we 
cannot think of a triangle without sides and angles. 
Fleming, Vocab. of Phil. 
The analysis of a material object consists in breaking it 
up into those other material objects which are its elements, 
and it is only when we know something of the properties of 
these elements as they exist separately that we regard an 
analysis of the whole as satisfactory. Mind, IX. 80. 
2. The regressive scientific method of discov- 
ery; research into causes; induction. 3. In 
math. : (a) Originally, and still frequently, a 
regressive method, said to have been invented 
by Plato, which first assumes the conclusion 
and gradually leads back to the premises. The 
thirteenth book of Euclid's Elements has the following 
definition, which is not supposed to be by Euclid, but 
which is ancient, and perhaps by Eudoxus : Analysis is the 
proceeding from the thing sought, as conceded, by conse- 
quences to some conceded truth ; synthesis is the pro- 
ceeding from the conceded by consequences to the truth 
sought. According to Pappus, analysis is of two kinds : 
theoretical, so called because used in research into truth, 
and problematic, so called because used in the solution of 
problems. In the former, the proposition to be proved is 
express modifications of meaning and to show 
the relations of words in a sentence : as, an 
analytic language Analytical chemistry, a meth- 
od of physical research in which compound substances are 
resolved into their elements. Analytical definition. 
See definition. Analytical geometry, geometry treated 
e the i,y meang o f ordinary algebra, with a reference, direct or 
M ill. indirect, to a system of coordinates. See coordinate. In 
ordinary rectangular coordinates, for example, there is 
just one point of space for every set of values of the three 
variables, x, y, z. If, now, an equation is assumed be- 
tween these variables, some of the sets of otherwise pos- 
sible values will be excluded, and thus some of the points 
of space will be debarred to us, and we shall be restricted 
to a certain "locus" or place; and since the number of 
independent variables is, in consequence of the equation, 
reduced by one, the number of dimensions of the locus 
at any one point will be one less than that of space, so 
that the locus will be a surface. By the use of such equa- 
tions of loci every problem of geometry is reduced to a 
problem of algebra, and the whole doctrine of geometry 
is mathematically identified with the algebra of three 
variables. Thus, to discover that, when four equations 
subsist between three unknown quantities, they can be 
satisfied simultaneously, amounts to discovering that, 
when a certain geometrical relation subsists between four 
surfaces, they meet in a common point. The idea of ana- 
lytical geometry is exclusively due to the genius of Des- 
cartes (1596-1650), who published his Grometrie, contain- 
ing illustrations of the new method, in 1636. Analyti- 
cal jurisprudence, a theory and system of jurisprudence 
wrought out neither by inquiring for ethical principles 
or the dictates of the sentiment of justice, nor for the 
rules which may be actually in force, but by analyzing, 
classifying, and comparing various legal conceptions. The 
best known of the analytical jurist* are Bentham and 
