805 / 868
T R
904
T R
TRtDENT,.•n a!tribule of Neptune, bcing • kind of TRtFOLIUM, in hOlany, a
g.nu.oflhe diaddphia de-
(ceptre wh!ch lhe
palmers
and poets put
,In,a
lhe hands of
,candrla elotCs. Tbe lIowers are
fubcapi(3red;
the pod
Ihu god,
Inform
ofa fpear, orfork, wlth three tceth;
IS
hardly longerthao thecalix, anddeciduous. Thercare
whence lhe worct.
43 fpecies, 16 ofthem
Dativcs
of Britain.
1·R.IEI\-~[MERlS,
a
kind of
C:'erUTa
in Latin
veTfe,
whcrein TRIGA, in antiquity, denotes a kiDd of
carT,
or chariot.
after Ihe
fidl
rOOl
of the
veTfe
there rema¡os <in odd
fylla-
drawn
by
th ree
horres;
whencc the name.
lable, whieh help.
10
Olake up Ihe nexI foot.
TRIGLA, in iehlhyologr., ,cenu. of 1í0,e., bdonging lO
TRIENNIAL, an epilhel applied ehiefiy lO ofliees or cm_
lhe order of lhoraeicre. ,The head is lorie.ted wilh rough
ploymenu which JaU ror threee years.
Jines,
anJthere
are [even rays in
lhe
rnc:mbraneofthc:gill¡ .
TRIENS.
in
aruiquiry,
a
copper mooc:y of the value of
There are nioe fpecics.
'
one lhird of . n
as,
whieh on ooe fide bore a
J
anus', head, TR IGLOCHIN . in bonny, a genus of Ihe hexandri.
tri-
and on the othcr
a
water-rar.
gyoia claC,. The calix confins of three leave!!. and Ihe
TRIENTALIS, in bOlany, a genus of lhe heptandria mo-
eorolla of lhree pe:als; aod it has DO flylus . There are
nogyoia clars. The calix coo{jHt of Cevcn lea ves, and
two fpecies, u(.oth nalives of Britaio,
v;z.
the pal urt re,
the coroIJa of Ceven equ:d plane Cegmenu;
and
lhe berry
or arrow headed
grafs;
aod the
maritimum, or
fea
rpik~
is dryiCh . There are t\Vo fpecie5, Rone of Ihem na{ives
gT~r!.
of Hritain.
TRIGLYPHS,
in architet111re,
a
Cort of orlJaments repeat-
TRIERS,
or
TREVES,
the capital
of
the e1d lorate
of
ed
iU
equal ¡nterrals
in
lhe Dor;c freeze.
Triers in G a mlny, fitu ated on ,he
ri.erMurdle,
lix',Y
TRIGONE LLA, iD bonñy, a genu, of lhe diad<iphi.
miles fomh of Cologne:
E
loog.
6°
10' ,
N. hu . 49° 55 .
decandria clafs. The vexillum and alz are nearlyequal,
TRI ES fE.
a pl)rt·rowo
ofl(lria,
firuated on the gulph of
opeo, <lnd
in
the form of
a
corolla, with three pe{:l!to
Ven ice,
fixly miles nortb-eafl
of
(hat cilY.
l°herc are
10
Cpecies, naDe
of
tht:m natives
of
Brilaio ..
T
R
1
G
o
N
r[RIGOl'JOMETRY i, lh.. pHI of geometry whieh
te"ches
how
to meaCure the »des and angles of
tri_
oogles.
Prrigooometry is eilher plane or CphericaJ, according
as
the tri,tngle! are
PLAN
E
or
SP .:E R1CA.L
i
of cach whereof
we
{hall
lreat in order.
PLANE
TRIGONOMETRY.
P«~NE
Trigonometry, or that which teachcs tbe menrl.l_
ralioDof plane tr¡angles, is commoDly divided
iota
rlflallgu–
'tlr.
and
obliqu(·auglllar.
Of
RECTANGULAR PLANE TRIGONOMETRV.
lF
in any righl.aogled triaogle, ABC, (Plale CLIX.
lig.
1.
nO
t.)
,he hypolhenure be made Ihe r.di.s, and Wilh
,hat a circle be defcribed on the one eod, A, as a centre;
lhen, it is plain, that BC wiJl be lhe fine of ,he angle BAC;
and
i(
with ,he Citme diHance, and on Ihe cnd H as a centre,
a cirele be defcribed, it i5 plaiD. that AC
wiJI
be the fine
of lhe angle ABC : Iherefore, in gene..I, if lhe hypolhe–
nllre o( a right_angJed triangle be made ,he radius, the two
¡egs will be ,he fines of lheir oppofi le angle, .
Again, if in
a
righl-angled triangle DE
F
(ibid.
nO
2. )
one of Ihe
J~gs,
as DF, be made the radius, and on the ex·
tremlty D (4t one of the abltque angles,
viz .
Ih4t which
i. formed by lhe hypolhenufe and lhe leg mad< radius)
as
a
centre,
3
cireJe be defcribed; it is plain, tnat the othcr leg,
E
F. will be lhe tancenl of Ihe ancle
al
D, and ,he hypo.
thenuCe DE will be lhe
fec.nlof the rame ancle. The rame
\Yzy.
rnlking the )eg EF the radius. and on the center E
deCcribing a cirele, lhe other Jeg DF will become the can–
ecnl of lhe angle al E, and Ihe hypolheoure D E lhe recanl
of lhe Came.
.
Toe chord, line, tangeol,
&c.
of any arch, or angle,
iD
o
IV!
E
T
R ·Y.
ane circJe, 'is proportionabJe to the chord,
Gne.
tangent, (-¡¡;.
of {he
fame arch
in
any other circle: from
which,
aod
what
h::ts beeo
(;lid
above, the foJulion! of the feveral cafes of
reéhngul<lr trigonome.lry nat\lrally follow.
Since trigonom'etry conúfb
in
detcrmining angles and
Gde3
(rom othcrs git'en, there arife varions cal! !; which being
fe
ven in
reétanguJar. trigonometry, are as· fOlJolV.
CA S E
I.
·The angles, .od one
01'
lhe leg., of
a
rigbt–
angled "iangle being given, I? 6nd lhe olher leg.
EX.>1PLS . In Ihe " iangle ABC
(ibid.
nO
3.)
righl–
angled at
B,
CuppoCe ,he leg AB=86 ..qual parts, " fe.. ,
yards. miles,
&~.
and lhe angle
A
=
33°
40'; requ,red
the other
leg
Be,
in tbe
~\me
Fans
Wilh AB.
l.
G,,,,u/ricoJIj :
Dr.w .'\B=8 6. 'rom any line of
e–
qua) paru; upoo the point B. c:retl tbe perpendi'cllhr
Be;
and, lafUy, r, om Ihe poinl A, draw lhe line AC, mal:tng
",ilh AB ao angle of
33°
40'; and ,ha! line produCtd will
rneel B C in
e,
and fo conHirute Ihe triangle. The l.eDglh
. f B C may be found by laking it
10
your eomp,lf"s, .nd
.pplying il
10
the fame lioe of equal pa", lhal A l!
was
ta–
ken
(rolll.
H .
B.J calcula/ion:
Firll, by making ,he hypolhenure
A C raJiu5. the olher tY.'O Jet! will be lhe fines of thcir
O?pOfile 'angles,
.-iz.
A
II
.he ltoe of C, aod C B lhe fone
of A . Now lince 1he fice, tangent, (:¡, . of any areh in
'one c;rile
j,
proportion.bJe
to
the fine, rangeDt.
6,
o(' rhe
Cil.mearch
iD
aoy other circle, it is plain rhe fintl of the
anel.. A and C in lhe eirele dereribed by lhe radius A
e,
ml,n be proportiooal
to
the fine o( the COlme arches or angles,
in lhe circle
J
that lhe table o( artifici¡l¡incs,
Oc.
was cal·
culated for
i
fo the propa rtíoo for 6mJlng B C wll1 be
S,
C : AB :: S, A : BC
j .
l .
;¡,s lhe fi ne of lhe angJc:
e
in
lhe tables,
il
to the
lenctl, of AB (or fine of C in lhe eirele whore raJllls i. AC)
ro i, lhe fioe of·the anglo
A
iD
lhe labl..,
ID
the
len~lh
of
BC