1000000030

·,.,

J .

I:#/r

nlin~

{I'cn rhcc Illht 1'lIf,o 111C1 ;.llan, an.l

J....

u':

in.te'

lO Ih,

l~i\ ::o

Imur;

[ hi~

,IIHle,

tUII\ dIe.!

nl"oe uOlil Ihc illdes rOlOlS 10 Ih.: upl

'er AI

ami Ihen

alllhe pl,lees d,,1I

un,kr Ihe br,de1

mw.lI,

ln I",'e noon

al that lime.

1J.

The urrer

XI I

~: \\'.tys

fI,ln.!s for noon; and

when the bringirg 01' .!IIy rl

,ce

10 Ihe "ra!en OIrridi In is

menllOned, Ihe li,1e pf tlloll OI\,ri.!..o on "hich the

(le·

trccs are reekone.! flollllhe t

u~11II'

" Oledrol, cniLf. the

cOl1ll'ary fiJe be meOliol1e,1.

PROD,

IX .

'Tf.thQ/l1'

'{I

hol

1)' 01

n':;

/,.',c,· h,i"g ~i,',n,

filld"¡j"h,11D'c/IJI-l ;11/1(1:

il JI

In)

'iI"o'/I"c ..·.-BI':nri

tIH:gi~

ven rlaee 10 the brafcn meli,li,ln, aud f, I the iorlex 10

the siren hour; Ihen turo Ihe bloo:, untillhe place ",here

lhe hour is reqllired comes

the meridian, and the inJex

will poin! OUt the haur

that place.

P ROB o

r ofill./

ti,,·

fi"¡'J

I"oa

ill Ih,' teliPlic, o'.d

~it

d<tlil.Jlioll,/"

o'~r

vOl

d,'l o[

Ih, ),or.-Look

the horizon for the sire't d.ty, and right "S"ion it you

have tile desree of the figo in which Ihe fuo is (or his

place) on Ihal day at 0000. Fiod the fame degree of that

tigo in Ihe ecliptic line opuo theslobe, aod h,wing brousht

il tO the brofen Oleridiao, obferve wh.t desrec of the

meridian naods over it; for that is the fuo 's declinatioo,

reckooed from the equator.

PRO Bo

Xl.

Th,ddl

lA, IIIDl/lh brill! giv" II, lofilld

, /l lho/< /,lnClJ o[ Ih, ,arlh Dt':r ,uhh'h Ih, jun 'Will pnJi

1I,,'ical&'

DII

Ihul

do)'.-Find Ihe fuo's place in the eelip.

tic for the given ddy, and haviog brousht it ro the bra·

feo meridian, obfene what point of rhe meridian is orer

it ; then, turniog rhe glooe roune! ils axis, all rhofe pla.

ces \Vhieh pafs uoder lhal poinr of the meridian, are rhe

places required; for as Iheir Jatitude is equal, in

d~grees

and pans of a degree, tOthe fuo's declioation, the fun

mull be direaly over hcad

¡¡eh of theOl at irs refpec.

tive noon.

ROB o

XII. A

plou ¿f;ng givrn in

Ih~

ID"rid

ZMt,

'nd

Ib.ft

I,uo tlo)'J

lb,

) ~ar

on 'Which In'

[1111/"011

1I,,' ;coIIOl1al

plna,-BrioS Ihe given place tO the bra·

feomeridian, and ma' k dIe desree of Ialitude that is ex·

aaly over it on the meddian; theo rurn Ihe slobe round

irs axis, and obferve the til'O desrees of rhe ecliptic

whieh pafs exaaly under that desrec of Iaritude: laUly,

lind on the \Voodeo horizon, the 111'0 da)'s of the year in

which the fun is in Ihofe degrees of the eeliprie, aod rhey

are lhe day' required: for 00 them, and nooe elfe, Ihe

fun's declination is equal 10 rhe lalirude of rhe sivcn

place; and

e~of<queotly,

he \ViII theo be ve,rical tOir

at ooon,

PROB .

XllI.

r ofil/d nll lhoft

pl~C(J'[ Ih~

II1rlhIr;.

gid

ZOII',

'WhfT( Ih, fun b:ginJ lo/him cOl/jlo/lII)'

'Wilh~ul

ft"i~l'

on O"Ygiv," d"l , [rOIll III<

rjl

o! /l'lprch IDIh,

23d

S,p"lIIb"

-00 thefe tWO da)'s, the fuo is in the

cq uiooaial, aod enlighrcos rhe slobe cxaaly from pole

tOpole: thcrdore, a, the C3 rth turns rouod ils axir.,

",hieh terOllOdles 'o rhe

p~les,

cvery pbce upoo it \ViII go

equally Ihrou

gh rhe l

ighl aorl the d>rk, aod fo make c·

qJ.1 day aod

nir.ht

all places of Il,e earth. But as

the fuo declines írom Ihe equator, tnv'ards eilher pole,

he \ViII Olioc jull as maoy degrees 10llOII Ihal role, a! are

t r!ual to his

d~c1iD¡lion

(rom lhe \,';lJalOr; fo lhal no

I'I.ICC wilh;o Ihat

di(J.loc~

of the pok

l~:li

tl.eogo

:1'1'00[,'5

:col' l!.Irr of Ihe lLllk,

arod

eon~cqueotly

the fuo will Out

!':t

11.

Juw,

liS tlh!

fun':;

lkclm:,tlOn is

northwJrd,

frolll Ihl'

di uf

~1.1I·ch

10 tite :;d oí

~:pr

elllb

er,

llIuU

Ce"

lI,orly fi,io: roun.! the oor·:h

Ide all

d1.lt

lime ;

aod 00 rhe d.,y d" tt he '5 io Ihe noulltrn Iropic, heOlines

~'r"n

rhe 1¡J1U," o\llth f,igid , oOt' ;

1!lar 00 p!ace wirh.

'o the oorth r"lar ci rele g/Je5 thruugh aoy pon of the

da,k 00 Ihat ,I.y.

h ~l cfvre,

I[,"'ing b"'''blt t rhe fun 's rll.Cc for Ihe gil'eoday

the

br.lco n,aid'do, and f"uod IlIs decl,o"tiun \by I'lOb. !X )

eoulIt as OMOy

d' we~s

00 r!,c meridi,lo, f, (1m rhe north

rol: , as ue 'qu.,)

Ihe tuo's dedll,",iuo f,om the equa.

to~,

aod n""k th,u <legrec froll1 the polI' IVhere the reck.

oo,r.g ends: Iheo , luroins Ihe glohc round ils axis, oo.

teno

\\I'Jt pla:cs i" the oorth frigid zone paf! dlretlly

uoJer Ih.1I onrk; for Ihey are Ihe plJees required.

'fhe

may be done for Ihe {oulh trigid zone, from

the

jd ef

Septc

m~er

to rhe

di of lIlarch, duriog

which ¡ime rhe fuo

Olir.es

eoon antly on rhe foulh pole.

. Poo a.

XI V.

'T?fi".1Ih,/r/OCf

DVfT'W

hi,·h lh'jull iJv".

Ilcal (IInll)'

h~l/r

ogivm

do)'.

-H.II'

iog fouod d,e fuo 's

ecliwi

on for the givenday

(~y

Probo

IX.)

mark it wirh

ch.lk

on rhe brac' o mtndian:

th~o

bring t oe place

whcre you arc (fu ppofc Edioburgh) tothe orafen

m~ridiao,

anJ fel Ihc index tO the giveo hour; which done, turn

the slobe 00 irs axis, IImil rhe iodex poiors tO

XII

0000; anJ Ihe place 00 the glooe, which is rheo direaly

under rhe poiol of the fuo'sdeclinalioo marked upoo rhe

meridian, has rhe fun that mOllleot iD the zenith, or di–

reél ly over head.

P RO ~ .

XV .

n t da)' ond hOllr

o lunor ,dipft

h,·

illg givfIJ; ID filld all lhoft placu

Ih, t.1rlh lO''Which

'U'ill

vijib!e

The moon is never eelipfed bllt when!he

is full, and lo dire,qly oppofire ro tbefun, that the earth's

Olado\V falls upoo her. Therefore, wharever place of

the

e~rth

the fun is vertical tO at thar time, the moon

mu!! be I'm ieal to the anlÍpodes of thal place: fo that

rhe fun \ViII be Iheovifible

one half of Ihe w th, and

the moon tOthe orher.

f iod rhe pldce 10 Il'hich rhe fun is vertical at rhe given

hour (by Probo

XIV.)

elerate the pole

rhe lalirude of

that place, aod brios the place to Ihe upper part of Ihe

brafeo meridi"o, as io tIte former problem: theo, as the

fuo \ViII bevir.ble to all thofe pam of dte globe \Vhichare

aboye Ihe horizon, Ihe 1II00n will be vitible tO all lhofe

pans whieh are belolV it, at the lime of her grealc!! ob·

fcuratioo.

PRO

XVI.

r o rtf/ir)' Ih, flOR, for Ih, 101illld"

Iht unilh, nll.1 lh, jun'!

pl~Cf.-F,od

the l.uilude of rhe

place (by I'roh,

l.)

and ir rhe place be in the oorthero

hemifphere, r,life Ihe oorth pole aboye Ihe oorth puiot of

the horizon, as Olany dl'grces (couoled from the pole "p'

00 the braftn meridiao) as are equal

Ihe1. lilUde of rhe

place,

lf the plaee be in rhe foulhern hemifrhere, raife

dte foulh poie abol'e Ihe fouth poior of the horizoo, as

maoy (Iegrees as are equal 10 the I.uirn.!e. T hen. turo

rhe globe till rhe pl.lce comes uod" ils latirll,le 00

t;,c or;&o meriJi

lit,

"ne! fafleo the qnadr;mt of ahi,

tilde f", thal thc chamf

ell'u

edge of

il~

ou: (which is e–

len llilh IheCr"du,ucd

l.Jg'

·)

lIIay be joiOlJ IOthe7.milh,