694 / 1042
.69:
C.,
f.
O
1':,
lire
EC,
alf"
nD
wieh
eh~
lin"
"Fe:,
"hich ell'O"
line~
\\'I!I
~Ul
oa::
.H\Olh::r in
lome
poi~H
e :
Iha~
1$
tI'e Ccntrt!
01th:
rih
I~
requ1fC.:d :
th::n
lix!llg
o~c
p::>in' nf )'our
C~lm ·
plll;'s in
D.
:ln,j
fI"t'e¿\in~
rhe
"d",.
rr)
:\,
delCrib~
the eildc
ABDC.
",illch
wiU p.lfs rh ro' Ihe ¡hrce l'0intl
gircn.
T!\~
reaf"l\ of Ihis is [:l.lin from eor.
l .
of
~ r:.
6.}.
9. (F:g
17.) Flon! ehe poir.1
A
of ehe r,ireo line
.¡B,
to draIV ;1I101her lioe (lill1polé
1\ <')
Ihae Ihall make rllth
All
ao anglc of al\)' r,nmoer of der.rees, fnppofe
45.
RIII,.
Lel ehe gi."o liroe
AH be
l'ronnccd, rh,o
I,k~
ofi' )'our
fca[~
Ihe leoglh
of
ti!"
ehorJ úf
h"
de;¡rét<,
whieh is eq u. l lO rhe radies ,f Ihe eirele
r~e
fc;:le
was made for (by art o75.); and fwing (lne (ooe io A,
"'i:h Ihe orher fIVeep
r.(
Ihe are
Be;
ehen IVieh yo:"
eum palfes rake (rom yonr ble Ihe ehord
01'
15
Jegrces,
a~d
lel off ehal di!!anec (rom
B
lO C. LallJ)', jnin
A
and e, and Ihe lioe
p.e
is Ihal ree¡uired Fur Ihe
angl~
eAS, " hieh is mc.,(ured by ehe are Be, is ao
angle of
45
,Iegrees, as IVas
re~uir~J.
10. P.o aogle BAe (r,g. 18.)
kin~
gil'cn, lO find hOIl
many degrees il coolaios.
Rule .
Wieh )'our eOr.!?, ffcs I.lke Ihe lenglh of your
ehord of
60
from
yo~r
fcale. Theo, feniog ooe fooeof
them io
A,
\\'ie h ehe olher fll'eep Ihe are He,
I'l},ich
i,
the are eompreheoded be¡ween Ihe rwo legs AH, Ae
produeéd if oredful. Lalll)', lake IVilh you¡-
eomp~ff~s
the difiaoee Be, aod applyiog il
te
)'cur
line
o(
ehords on
Ihe f"le, )'OU will find how mao)' (!cgrees ehe are Be
eonlaios, and eonfequeotIy Ihe dcgrees of
Ih~
anglc l3.A.e
",hieh IVas requiren.
11.
Tbree lin:s
X, J',
aod
z
being gil'eo, (fig.
19
19·)
to form a Iriangle of them; bUI any IWO of thefe lines
ukeo together mu(l al"a)'s be grraler Ihan Ihe Ihird.
Rule.
M.keany one of Ihem , as
.l,
Ihe bare ; Ihen
wit h your eompaffes cake aoolher of Ihem, as z, and
fettinn one fool io ooe eod of rhe line
x,
as B, IVilh Ihe
orhe:fIVeep Ihe
ue
DE; and raking \Virh yOllr eom·
palfes Ihe lenglh of rhe other
J ,
fel Ooe fooeof ehem io
A,
Ihe orher end
01'
Ihe line
x,
and IVilh Ihe orher flVeep
the
are.EG, whieh wil! eUI the olher in e; l.fIIy, join
CA
and ell, and Ihe rriaogle
eAB
is rhal rc<}uired .
. 12.
To make a triaogle, hal'iog one
e,f
its legs of any
.Dumber of equal parls (Iuppofe 160), and oroe uf Ihe ao–
gles al Ihat leg
50
degrers, and the olher
44
degrees.
RIII_.
Draw , n indefinile line
El),
(fig.
20)
eheo
uke
011'
rhe line of
e~ual
partS wieh your eOl11palfcs,
16o
of Ihem, aod fel them
00
.he inder:niee lioe, as Be ; eheo
(hy prob
9.)
draw
BA,
makiog Ihe .ngle ABe of
50
degrm , and (by ¡he fame) dra" from
e
Ihe line Ae, Ola·
T
Y.
king the ang!"
,\Cr.
of
,} ,~
dee""es ; ',',hidl IW" lines wiri
m"u no..: .1nIJ,h('rin
.h..,
.11,, 1
du; tfl;lng lc
¡l IJC
is
lhJt
rc–
~ltlrcd.
Sc<
TRt~(\.O'H TRY.
1,.
Upon
a
git'~n
linc AIl (firi.
21 )
to m. k. a folu. r'.
r.J/~.
Up"n rhe extrco,ity .'\ of'ehe giren !ioe AH.
raile
?
p~rrtr.dieu l."
Ae
(ul'
probo
4');
Ihen tak, Ae
er¡lI,1
tu
AB,
nnd IViti! Ih.•1 l'x:cnl, fming ooe fvtl!
01'
Ihe romlll{fcs in
e,
flVeep wilh Ihe oeher foor Ihe are
CH ; d·.,nl'Iilh Ihe faOle eX lent. aod one fool in D, wilh
rhe o'her fIVeer Ihe are
EF,
whieh wil!
mee!
the former
io fome poio¡ D; lallly, joio e aod D, D aod
13,
~nd
ehe C:31¡rc AB De wil! be Ihe fquare required.
l.). On a giwn line A13 (fig.
22. )
eo draw a rhnm!>
rhae {hal! have ooe of its anbles equal
10
any oUlllbcr
of
dcgrec;,
f~~pofe
Go
degrees.
R:d, .
hOn! Ihe poinl A of Ihe giren line An, draIV
the line Ae, making Ihe angle eAIl of
60
degrees,
(hy
probo
Q.)
¡h~o
lake Ae rqual 1.0
AB,
aod wirh ehal ex·
lenr, bxingone fool of Ihe eom?JIf<s in
n,
wilh Ihe
o.
lher deferibe Ihe are
CH;
and ae
I~e f~.me
eXlenr, r,xin.
one (ooe of ehe tompaffes io e, wilh Ihe orher
dcrcrib~
:he are
EF
cutti og Ihe former io D;
l.aly,
join
CD
and DH. and Ihe figure AeDll is rhal required.
15 .
Civeo IIVO lioes
x
aod
z,
of Ihefe IWO lOmake
a
reélangle.
R"I,
Draw a line, as
A13,
(fig.
23. 23 ..)
equal in lengll>
lOone of Ihe gi!'enlines
x;
.od on rheeXlremiry Aof Ih. 1
line, raife a perpendicular AC, on whiel> lake Ae equal
lO
ehe olher lioe
z;
Ihen tale wirh your eompalfts Ihe
length of ehe lioe AB, and al Ihal eXlent, fixiog one
fool of ehem in e, IVith rhe olher flVeep Ihe are
El:' ;
and alfo laking wilh your eompalfes rhe eXlent of Ihe
lioe Ae,
r.x
one
Fool
of them in B, and wilh Ihe olher
fweep rhe are CH, whieh IVil! meel the for".,er in D ;
la(lly, join e D and BD, and Ihe figure A13 De will be
Ihal required.
16.
Two lioes
x
and
z
being gireo, of rhefe lO form
a
rhomboides rhaeOJal! have one of il! aogles any Dumber
of
de~rees .
fuppofe
50.
RIlIe.
Draw a line AB
(fig.
24 . 24.)
equal in leoglh
ro
ooeof th: lioes. as
x;
rhen dr,IV the lioe Ae, making IVilh
Ihe former rhe angle BAe equal ro lhepropofed, fuppo(e
50
degrm,
~nd
on thal lioe take Ae equal eo Ihe given
lioe z, Ihen \Virh yOllr eumpaffes lúe Ihe lengrh of AD,
and fiXing ooe fool in e, fweep rhe are
EF;
alfo, laklOC
rhe length of AC, and (elliog ooe (oor io
13,
wilh Ihe
orher ;"eep the are
CH,
"hieh IVil! ellt Ihe former iD
D ; Ih,o join e D and DB, (o Ihe figure Ae DB Wtl! be
Ihal tellllirtJ.
P AR
T
JI.
TI rE
APPLICATlO ~~
OF
TliF.
FOf\EGOTNG
PIU:-.rCTPLES 1'0 TIIE J\lDiSURATIO.
OF
SU1~FACES,
SOLIDS,
&c.
O/
¡¡ir
!;1;I1¡, ..
ration o{
¡.il/O
t!nd
AII..
:{(J.
A
Line. or len¡:tll, o he meafllrtd, "huher ie he di ·
.
1I,,,,'c,
hLlg}¡r, ',r.1< pth, is med(ur,tI
l.,
;1 hll' ler,
ti." .it.
\\'nh
L¡
lhe 1,••11 01'. fure "f
l. ;~th
11
a~
Ir.dlnOI Ihal IVe meafll ,e no :ioe
lef~
.han il, hm hecauf< we
do nOI ufe rhe
n~01e
of any
m~.Ifure
bcllllv rhJr 01 an
ineh;
( ~rrcnio~
leO"r meafures
by
rI,e f'd,qjulI'
,,1'
.In
ineh: and 'o this I«"tir" \Ve ufe d<cilllal ("tliun! " ehe
e.lid!. Twrhc ioch" m .•ke a fvor; Ihr,e
f,~r
.•
0.
1 "1