tangent 
K. litrl, fiirf/fr, i', HI fur/, I'm/ fi iir/i nt. ete.J I, ii. 
Touch! MO; ; In i/eon*., touching at a ringle point: 
;is. M In II 1/1 nl line ; curves lillli/i lit In each ,,l her. 
Stationary tangent plane of a surface, s,, ../ 
liiniiirii. Tangent plane, a plane which touches a carved 
-III t:irr, :i .1 pllcre, C) lilldei . lie. 
II. H. 1. I ii /(///.: \<i i A straight line through 
lo eonseeiitive points (which see, under cini- 
xi-fiitin ) of n curve or surf.-ice. if we take th, linc 
through any two point* of the locus, and then, while one 
"i 'these points remalni fixed, coniider the other Mbroofiil 
i-\ :, continuous and not infinitely protracted motion along 
the 1,,,-iis into coincidence with the found, tin- line in its 
Una) position uill he a tangent at that point. The idea "I 
inn, uliidi appeals in this detlnition is only so far essen- 
tial that some parameter must he used in older t., ,1,-llm 
a tangent at a singular |H,int, and this parameter must be 
such as to pics, -ni no discontinuity or point-singularity at 
that point. A langenl al a dinary point of a curve or 
-'ill:.'' 1 ma\ lie doMned, without the use of any p:,lamc- 
ter, simply as a line through two |H>int Infinitely close 
together . alt hmmh. If thcdoctiineof limits Is Used to ex- 
plain away the idea of intlnit), a paiamdi I "ill l>e used 
for that purpose. A curve has only one tangent at an 
or, Unary point, or a mere line-singularity, or a cusp, but 
Tangent. The equation of the curve is.y (i -*)**=>. 
a. ordinary Um;eiit 1 . Ixll tangent : r. cuspidal tangent ; rf, indec- 
limiAl tangent. 
lilTH 
strings, ;il|,l proilnce tones. It, , lion was not like 
that of the pianotorl, -ha KI. -me, it n-mainc,i r 
lact with the si ling, and tiled the pitch of the lone I >) the 
plar, uheic il ,nmk. ll pi ,-ssed t. , hard, it raised tin- 
pitch hy inciea-in^ lln .-Ming's tension. Ac. ,,rdini.'l> the 
tne of the clavichord M:I- neecs.-arih weak. Artificial 
tangents. See artyWoi, Chief tangent, a tangent t,, 
a surface wind, I- also a tangent of the mien., , lion of the 
M h; the langcnl plane at the MOM p"inl "f tan- 
geuey. Conjugate, cotrtple, double, imaginary, in- 
flectional tangent. >,-,- the a,ij,cii\,s. Ideal tan- 
gent, a real line touching ., real inn,- at t,, imaginary 
points. Inverse method of tangents, the method ,,'f 
rinding the curve belonging to a given tangent. Method 
Of tangents. () A method of obtaining Hie ,|iiadrnturc 
"f a curve by means of an evaluation of the tangent I., it, 
due to Hoherval. (ti) Any method of drawing a tangent 
to a curve. - Multiple tangent, s, , ,,,,,lii,j:. Nat- 
ural tangents, tangents expressed by natural nuiulwrs. 
Principal tangent, a tangent bisect Ing the angle be- 
tween the chief tangentH at the point of 
tnngcncy Principal tangent conic. 
.See conic. Stationary tangent of a 
curve. Sec Ktatwnary. Tangent bal- 
ance, a balance in which no weights 
an used, hut the position of the beam, 
as Indicated by a pointer moving over 
a graduated scale, shows the weight : 
chiefly used tor weighing letters. Also 
called bent-leeer balance. Tangent Tangent Hiiincc 
galvanometer. See galmnomrier. 
Tangent sailing. Same as middle-latitude failing. See 
latitude. Tangent scale, In onlnance. a notched piece 
of metal titled to slide circumferen- 
tially on the breech of a piece of ar- 
tillery, the notches being at stated 
distances from the axis of the gun. 
In sighting, the scale is turned till 
one of its- notches corresponding to 
Tangent Stale. " the desired elevation or range is 
brought into internet-lion with the 
plane of the trajectory. Tangent screw, a screw at- 
tached to or fonn ing part of a clamp, and serving to move 
pieces clamped together relatively to one another with a 
.low motion. TO fly or go off at a tangent, to pass 
suddenly from one line of action or train of thought to 
another diverging widely from the first. 
tangle 
l.'iiiieil from the fruit ,,! :, tree o| 
I i I-IH i-ii I'lini/liin ('I'liiii/liiinii ri in iiit'i i-ii); 
the tree itself. I h, t,.. l,,;,,s -inooll, "I d aliceo] at ,- 
,-iowded toward tin- end of the hiaiich, s. fi..m th, 
midst of which rise ,\m, , ,,t -mall Mow. i -. I he fiuit i 
\cllow , containing a III. Ions mil. of which the kernel is the 
polBonoii- pair \l-" ipelled tanffuin. Trial by tan- 
ghlD, a kind , if ordeal fornierl) practised in Madagascar 
to -lei ei mine the guilt r in no,, -used person. 
- ,-il was pounded an, I a small piece swallowed hy each 
pel son to he Iried 1 1 t he accused I clamed t h, p 
the system death quickly resulted a proof of guilt-, if 
the Stomach ! ejected the do.se little ha I III si 1 pel Veiled, and 
innocence, was estahl 
tangibile (tiin-jili'i-lo. . [Nl,., neut. of LL. 
tuiii/i/iilis, tangible: see limgibli-.] A taciili- 
xensation or object. 
Not only does every visihil, appear to he remote, hut il 
has a position in external space, just as a tant/ibiir appears 
lobe sliperllelal and to have a determinate position on 
the surface of the body. 
lluilfji, Critiques and Addresses, p. 309. 
tangibility (tiin-ji-bil'i-ti), . [< V. tn,,gii>inti- 
= 8p. tangibilidail, < N'L. *taiigiliililti(t-)n, < LL. 
ft/n</if''rYr'M, tangible: see tangible.} The property 
of being tangible, or perceptible to tin- touch 
or sense of feeling; 
has two or more tangents at a node. A surface has a 
single Infinity of tangents lying in one plane at an ordi. 
nary point; and two of these (real or Imaginary), called 
the injlectinnal tangent*, pass through three or more con- 
secutive points of the surface. On the nodal curve of a 
surface the tangents He in two or more tangent planes ; at 
a conical point they are generators of a quadrlc cone. The 
tangents of a curve in space form two sets which are all tano-pnr ( tnn'fanM r / T< fn ,,i 1 
generators of one developable. There are point* upon T 11 ?: TJ^fPJ "',_;. ** \ anaent ; ,"! 
From Dodson and r'ogg's It [his mind] tew of at a tan- 
to the very center of the history of the queer client 
Didcent, Pickwick Papers, xxli. 
The velocity is as the square of the time, and the curve 
is therefore a parabola tamjrntiny the time with Us ver- 
tex at the start of motion. 
Nystrmn, Elem. of Mechanics, p. 158. 
wime curves and surfaces'at which, according to the doc- 1)par or hold the relation of a tangent to. 
trine of limits, there are no tangents. Such is the point in 
the second figure where the two multiple tangents inter- 
sect ; for, as a second point on 
the curve moves toward this, 
the line through the two 
points will oscillate faster and tangental (tail jen-tal), a. [< In in/, n I + -nl.] 
faster, without tending toward Same as tangentiiil. Elect. Her,. (Am'er. ). XIII 2. 
any limit. In the same sense, FRore 1 
a curve may have no tangent j. 1 'jl n / 
at any point; it may be an un- tangentally (tan jen-tal-i), atlr. Same as tan- 
dulating Hue with small un- flCHtially. Elect. Kev. (Atner.). [Rare.] 
umf 'nT "ll '"'' la th e . ne *i tan *>ential (tan-jen'shal), a. and . [< tangent 
8oonn(/il"n'm'ri(ithc'ienirths ^~ ."'""'] I- "; 1. Of or pertaining to a tangent; 
and amplitudes of the undula- 
tions being duly proportioned. 
But an intelligence situated 
on such a curve might see that 
the tangent had a definite di- 
rection, for there is no logical 
absurdity in this. It is an- 
tagonistic to the principle of 
duality which rules modern 
geometry to define the tangent 
of a plane curve as the line 
through two consecutive 
points on the curve. On the 
contrary, the definition of 
Multiple Tangents. 
scribed by the parai 
n | .01 1 it, 
turning about th 
1 moving in the direction of a tangent. 
2. Figuratively, slightly connected; touch- 
and-go. [Rare.] 
Emerson had only tangential relations with the experi- 
ment [Brook Farm|. 0. W. Holmet, Emerson, p. 166. 
Simple tangential strain. See itraini. Tangential 
coordinates, displacement, force, inversion, stress 
See the nouns. Tangential plane. Same as tanjent 
jilanf (which see, under tangent). 
II. . In the i/enm. of plane cubic curves, the 
point at which the tangent from any point cuts 
the curve again. The point of intersection is 
plane curve is a locus de- called the tangential of the point of tangencv. 
larametr ic motion of a line with a point _ Conic tangential, a point at wliich the conic of ftvi 
nt slipping along the line and the line polntic contact with n given cubic curve at a nrimitive 
le point; and such a generating line Is a point meets the cubic again. 
i ,'iii'_;rii t , in like Uiiumcr. ft aiirfucc is tho locus fonntjd -*. *. _ ^ i r i * i i_ i/ j*\ .-* 
by a plane with anoint urJon It, the position of the point tangentiallty (taii-jen-slu-al 1-tl), M. [< tow- 
in the surface and the aspect of the surface about the genital + -ity.~\ The state or character of being 
; varying, the one and the other, according to MIL 
variations of the same pair of independent parameters, 
such a plane is a tangent plane, and a tangent may equally 
b, conceived as the line through two consecutive ineunt- 
point.s, or as the line of intersection of two consecutive 
tangent planes. The tam:ent piano of a spacious curve 
U a line lying in a plane and having a point upon it, the 
plane taming continuously about the line, the point 
moving along the line, and the line turning in the plane 
around the |M>int as a center. Euclid's definition of a 
tangent ( Moments," bk. ill., def. 2) as a line meeting a 
circle and not crossing it when produced does not ex- 
tend to curves having inflections. The definition of the 
tangent as the limiting case of a secant, which Is due to 
Descartes (but was perfected by Isaae. Barrow . n. ; ,n a) 
well he considered as the foundation of modem mathe- ,,,. 
"" " ( h) The length cut off upon the straight s ce orange 1 Also 
line touching a curve between the line of ab- spelled ' 
" See 
tangential ; the characteristic quality of a tan- 
gent, ritilos. Mug., 5th ser., XXVII. 335. 
tangentially (tan-jen 'shal-i), adr. Inatangen- 
tialmanner; in the direction of a tangent. 
Tangerine (tan-je-ren'), a. and . [= F. Tan- 
g<-ri>i, < Tangrr, f'angiers. See def.] I. a. Re- 
lating to Tangiers, an important seaport of 
Morocco, on the 
Strait of Gibraltar. 
II. n. I. An in- 
habitant of Tn- 
giers. 2. [/. c.] A 
Tangerine orange. 
(tang'- 
A seal. 
Imp. 
scissas Mini th,- point of laiiiioncy. 2. In In,/- tangey " 
ow., a function of an angle, being the ratio of hi*/,/ 
the length of one leg of a right triangle to that tangflsh 
of t ho other, the angle opposite the first leg be- fish), . 
ing the angle of which t lie tangent is considered [Shetland ] 
as the function, formerly the tangent was regarded Iii, t. 
as a line dependent upon an are namely, as the line tan- tancr>iam 
gent to the arc at one extremity, and intercepted by the tp ' lu 6n. 
produced radius wliich cuts ,,tf the. arc at the other ex- ( tall g KS m - 
tremity. Abbrevia'ed (an. . S, e t.in., 
3. In the daviclii.nl, one of the thick pins of tanghinOang'irm i. 
l.rass inserted in the back ends of the digitals M. [Malagasy.] A 
sotliat tin -lingers should press them against the deadly poison ob- 
-g"), 
Tangibility and imiwnetrahility were elsewhere made 
by him the very essence of body. 
Cudumrth, Intellectual .System, p. 77". 
tangible (tan'ji-bl), a. [< F. tangible = IV. 
Sp. tangible = Fg. tangivtl = It. tangiliile, < 
LL. /inii/ibilis. that may be touched, < L. Itui- 
II, a , touch: see tangent.} 1. Capable of being 
touched or grasped, or of affecting the sense of 
touch. 
TamriUf IxHlles have no pleasure In the consort of air. 
//(iron, Nat. Hist., | 27. 
2. Discernible or disrriminable by the touch. 
By this sense (touch) the tangible qualities of bodies 
are discerned, as hard, soft, smooth. 
Lack, Elem. of Nat 1'hllos., xi. 
3. Capable of being possessed or realized; 
such that one can lay the hand on it ; within 
reach ; real : as, tangible security. 
Direct and tangible benefits to ourselves and others. 
Sauthey. (Imp. Did.) 
Men . . . who were not such bigots as to cling to any 
views when a good tangible reason could be urged against 
them. George SIM, Felix Holt, 111. 
tangibleness (tun'ji-bl-nes), n. The state or 
character of being tangible; tangibility. 
tangibly (tnn'ji-bli), adv. In a tangible man- 
ner; so as to be perceptible to the touch. 
tangie (tang'i), n. [Appar. dim. of tang 3 . But 
the touch in the legend, " as a man covered with 
seaweed," may be due to an accidental resem- 
blance to tang*.'} A water-spirit of the Ork- 
neys, fabled to appear sometimes as a little 
horse, at other times as a man covered with sea- 
weed. KeigMleu, Fairy Mythology, p. 173. 
tangierine, n. See tangerine, 2. 
Tangier pea. SeejxYii. 
tangle 1 (tang'gl), H. [< ME. tungel,< Ice). th<in- 
gutl, seaweed, dim. of thang = Sw. tang = Dan. 
tang, > E. tang, seaweed: see ton</ 3 . Hence 
(prob.) tttngle' 2 , r.] 1. A name of various large 
species of seaweed, especially Laminaria digi- 
tta and L. saccharina. See cut under seaweed. 
Also called tant/le-trrack and hanger. 
The Alga Marina, or Hva-Tanjlr, as some call it, Sea- 
Ware. 
M. Martin, Western Islandsjed. 1718), p. 149. (Jamicton.) 
And hands so often clasp'd in mine 
Should toss with t-n, : il. and with shells. 
TVnnyson, In Memorlam, \. 
2. A tall, lank person; any long dangling thing. 
[Scotch.] Tangle tent, Inmrg., a tent made of Lami- 
naria diyitala. or tangle. (See also rote-tangle.) 
tangle- (tang'gl), r. ; pret. and pp. tangled, ppr. 
tangling. [Early mod. E. also tangell; appar. 
lit. ' twist together like seaweed,' < tanglef, n. 
But the development of such a verb from a noun 
of limited use like tangle^ is somewhat remark- 
able, and needs confirmation.] I. trail*. 1. To 
unit* or knit together confusedly; interweave 
or interlace, as threads, so as to make it diffi- 
cult to separate them ; snarl. 
His speech was like a tangled chain : nothing impaired, 
but all disordered. SAo*., M. N. D., T. 1. 126. 
London, like idl other old cities, Is a vast tangled net- 
work of streets that for the most part begin nowhere and 
end nowhere. The On/ry, iLI. 142. 
2. To catch or involve as in a snarl; entrap; 
entangle. 
NeuertheUsse we were soo tangled In among the sayde 
deserte yles that we conde not gette oute froine amonges 
them vnto the nexte daye at nyght. 
Sir R. Guylforde, Pylgrymage, p. 60. 
Look, how a bird lies tangled In a net. 
Shak., Venus and Adonis, 1. 87. 
