1000000031

r rom C

dr.IV

lhe NNE line CR, aod from 11 dra

AB pa,.!lel to lhe NEhE ll oe CO. whieh \ViII meet CB

-io l:! tne place ofthe e"pe, aod CB will be lhe clillaoee of

il from Ihe Il\lp in i" 6rfl lIalioo, and AB lhe dlllance

10 lhe

(econd

1TTd

which,

CA'1.CULA TIO N;

In the triangle Al:!C are given AC. equ.1 to 20 miles ;

the angle ACB, equal lO 78°

4)',

lhe di!lance belween

the NNE and NWb\'1lineo ; alf. lhe

.n~le

ABC, equ,tl

to BCD , equallo

33°

4)',

Ihe dillanee belween ,heNNE

and NBbE lines; and confequently the angle

equallo

67° 30'.

H en.:e for CB, lbe din.nce of the cape from the fh ip

in her firn nation, i, \Viii ue (by obliq.e trigonometry)

S. ABC : AC : : S . BAC : CB,

i .

t .

As Ihe fine of the angle B

33° 45

9·

74473

is lO lhe dillance run AC

20 -

1. 3°1°3

fois .thefine ofBAC

67, 30 9 . 96562

to CB

33.26

1.52191

the di llanee of the cape from the fh ip at the firfl Ilation.

Then for AB, it \ViII be, by oblique trigonometry,

S . ABC : AC : : S. ACB : AB.

i .

•.

As the fine of-8

33°,45' 9. 74474

istoAC

1.30 t03

fo i..he (jne of C

78 - 45

9.99157

to Al:!

J5.31

1.54726

the diflaoee of the fhip from lhe cape at her feeond !la–

tioo .

P ROB o

JI.

CoaOing aloog the fhore,

faw two head·

lands; the 6rO bore from me NEhE t 7 miles, the other

SSW miles. Required the bearing aod di llanee of,hefe

headlaods from one. another.

GE OM ETR l

LLY . H avingdrawn the compafs NWSE

(No. 23 . ) let C reprefeo< tbe place of the IllÍp; fet off

Hpon the NEhE lioe CA '7 mil.. r,om C to A ••nd upon

the SSW line CB 20 miles from C

B, and join AB :

~hen

A will be lhe (¡rfl headland, and B the feeond ; alfo

AB will he their dillanee. and the angle

will be the

~earing

from the N EhN line: lO find whieh

CALCULATION;

In lhe triangle ÁCB are given, AC '7, CB 20. and

the angle ACB equal to 101 °

15 ',

the dlflaoee belween

.he NEbE and SSW line,. Henee (by oblique angular

trigonometry) il will be

A, the fum of the fid.. AC and CB

is la

their difference

fo i. the tango of.{ the fum

ofthe.nglesA aodB

.39°,22';' 9 .9

4'7

to the ..ng of half their diff.

,4Q

8 .8 23°9

onfequently the angle A w,1I he

1t', and the angle

,5°

34';

alfo the bearing of B from A \ViII be

49 wellerly, and the bearing of A from B will be

NbE

49' e.lIerly,

Then for the dillanee AB,

will he, byohlique· angular

trigoDomeuy

S: A : CB :: S. C : AB.

t .

the fine of A

43°, 11'

is to CB

foiSlheGne ofC

IOt,15

to AR

28 .67

¿he dJClall'e helwceDlhe lWO hcadlallds.

9. 8

3507

1·3°'°3

9.99

1·45733

PROB o

rrI.

Co.lling along the n,nre.

r.,..

til'O head–

l.ocls; ,be firfl bore (rom me NW

bN,

and the f<colld

NNE ; then flnnding '\\Iay

EbN

no"herly 2"> miles,

fouod the fi

III

bore from me WN\Y .;. w<lterly, aod

the feeond

N hW

.¡.

wellerly. R equirt d the hearing aod

dillanee of ,hefe tWO heodl.nds.

G. OM ETR leALLY . Hovingdrawo

theeomp~fsNWSE

(No. 24 ) lel C repref"ol ¡he firll place of the fhip; from

whieb dr.w Ihe

N\VhN

line CH, aod the NNE line CO,

,Ifo the

EhN

N line CA, whieh make equal to 20.

From Adraw AB paralld to the \VNW

.¡.

W lioe, aOO

AO parallel

the

NbW

.;.

W meeting the two /idllio..

in the points B and O ; theo B will be the firll aod D

the feeood headlands _ J oio the poiots B aod O,-and BD

will be Ihe diflanee het",eeo them, aod the angle

coa

the bearing from tite NNE lioe: to 6nd whieh

By CALCULAT I O;';

1. In the triangle

<'\

BC are given the aogle BCA, ._

qual lO 104° 04', the dillanee between ¡he

NWhN

liDe,

",nd .he

ENE~E

line; the angle BAC. _qual to 36°

34',

the diflaoee between the

WSW~W

line and the WNW

.}W lioe; the angle ABC equal tO 39° 22, the diflaoee

hetweeo the ESE{.E line; aod the

SWhS

lioe, alfL the

fiJ e CA equal to 20 miles: whence for CB, it will be (by

oblique trigonometry)

As Ihe fine ofCBA -- 39°,2 2' -

9.80228

is tO AC

20 -- 1.3°103

.fo is the fioeofCAB --

36°.34'

9.77507

tO CB

-- -- 18 ·79 -

1.77382

the diflaoce between the 6rn headlaod and ,he fhip iD

b..,

firflltation.

2. In the triangle ACO, are giveo the angle ACO,

<–

qual

47° 49' . the diltanee betweeo the

EN.E~E lin~

and the NNE line ; the angle CAD, equal to 92°

49',

lhe rliflance between the WSW{W line; and the

N¿W~

W line, the angle CD A equal lO' 39° 22', the dillanee

betweeo the SSW lioe aod ,he

ShE'¡'E

lioe ; alfo lhe leg

CA equal to 20.

Hence for CO, i. will h. (by. oblique trigooometry)

A, the fine CAD

-- 39°,22' -

9.80228

i, to AC

20 -- 1.3°1°3

fo i, the fine ofCAO -- 92°,34' -

9 '99960

to CO

31. 5

1.49835

the dillanee belweeo the fecond headlaod aod the fhip io

her firn nalioD.

3· lo the triangle BCD are .eiven BC 18 ,79;

31.5,

aod ,heangle BCD equal to

56°

15', thed,naoce

bet. een the

NWbN

line aod the NNE liDe.

HeDee fo r the angle COB, it will be (by oblique tri,.

gonometry)

A, the' fum of the fides -

the difFerence of fide',

fo is tangent of {- Cum"2

oftheunknowoangle,

5 -

50.29

1'7014!1

12.7 1

°4

6 , °, 5" -

10.27189

to tango of half their diff. 25, ,8

9. 6 74 58

eonfequently the angle CBO i, 87 ° 10', aod the aogle

COB 36°

35'.

H enee the beariog of the firll headlaod

from the feeoDd will he S 59° 8',

or SWhW'¡'W

nearlYI and for the dinanee hel",eeo them, il will be,

As the fioe of BO C

36°,

35'

9. i7S2~

to BC

18·79

1.2738,.

.fa.