746346

Liber

lll

.noris fphzrz,

cum

fü

patallela linez AD, an–

gulus BE C zqualis erit angulo interno A D C

(

per

19.1.)

igicur

(per

14.

¡.)linea BE cangir ,

circulum in E.

Demonfl:raciq¡ln criangulis CBE , cum angu–

lus E icél:us

fir,

angulus CBE minor efl: reéto,

tonfequenrcr EBG major reél:o; igicpr arcus GE

major eíl: quadrancc ;

1E minor efl: quadrance.

Oíl:cndam paricer arcum K D minorcm cífe qua–

drance. Si ergo immoca linea CA incelligawr

volvi,cocum triangulum CAD punél:um D defi–

nier in fphzra lucida fegme'!cum LKIJl minus he–

mifphzrio,& íegmencum MGE ma¡us hemifphz–

rio, fed fegm·enrum DKL efl: illuminans compre–

henfum nempc cangemibus ,

MGE illumina–

nfm:; igicur illuminatum m•jus efi hemifphzrio,

illuminans cfl:

minus.~od

era¡ demonfl:randum.

CORO~LARIUM

hac paree convcrfa ,

nempe fph:era illu–

minan~

íl:acuacur mihor,

opaca major, pars .ma- .

joris illumirtata minor erit hcmifphzrio,

1llu–

minans major.

C O R O L L A R I

lJ'M

11.

minor erit qüamNC; ex punélo

ducacut can•

gens circulmn SI' in

ofieodam ur prius eandem

cangere circulum 1E.

RurÍus obfcindatur

lin~a

AV, a:qualis

lin~a:

RN,ducamr ex pnnélo

cangens circulum KD,

qn"' neque cadecin punétum D ne dcncur duo

anguli reéti ina:quales, neque ultra punélum D'

ergo citra ; ponawr caderc in punétom X,critquo

arcus K

minorarcu

KD.

In irfongulis

VAX,

RKI', reél:angulis in

P, (

per

16.3.) cum re–

liqua

RN, VA,

ítem

NP,

AX fine p:qualia, reli–

qua :rqualia ernm, (

per lemma

ante

17,

1.E11cl.)

ergo angnli RKI',

V AX

zqualcs

font

conCc–

quenter arcus SI',

NX :

fed

minor cfi qnam

ND, ergo

P eodem minoc crir. Sed

arcus

limilis efl: arcui

S P ,

igirur in hoc fecundo cafu

arcus

T non illuminatus , minor erir:

confe–

quenccr arcl!S

reliquus ad fcmicirculum ma–

jor¡ faél:a igitur circmnvoludonc arcus G T dc–

fcribet fegmencum illuminacum majus, quod era

dcmonfirandum,

C O R O L L

R 1 U M

hoc fecundo caíu pars fph:rrz majoris illu–

minans minor cric., ofiendimus cnim arcum

mioorem effe.

Linca conncél:ens cenera fphzrarnm eran lir per

polos fegmenronnn illuminantis

illuminati.

O R O L L AR I

i.J

. COR O LLAR

I U

I I

conrra fl:aruatur íphzra minor eífe illuml-

Sol majus fegtncntum

hemi~phzrio,t'am

in luna

nans , dum magis accedet ad majorem , minorem

ei~1s

partero illuminabit \ ofl:endimus enim arcum

quam in cerra illuminar.

mi1loremeífe arcu KD. Pars vero fpha:rz mi-

ORO LLAR

I U

IV.

noris propioris illumiuans maior efl:·; nam ofl:en-

l>ai"s hon illuminata fph<trz minoris opac:1:

dimus arcum GT majorcm cífe.

fimilis efl: pmi illuminanr1fphuz ma joris luci-

O R O L L

I U

I I

d:1:: cum emm linez AD BE finr parallcla:,anguli

Luna in plenilunio minus extcnfivc illumina·

IBE,

KAD zquaks ewnt,

arcus

KD, IE

fim1-

rnr, quia magis difl:at a folc, in novilunio aurem

les,

coníequenter fegmema quz per mcumvo-

major illius pars illuminamr, fed cum avería fic

luc1onem gencrancur fim1ha.

nobis non,videmr.

C4tera

<Jll&

il/11mi11a1iomm

!lllll1i

~-,.,

pertintni diaa

fiwt

citm de ill11minationt

reme,

~@'¡j¡¡llil!i1l'l!!!li1l!ll!!!!i

'1l"1J(j¡j.,.,i¡¡~!1fl~!ll!W

111114, .ieneriJ, C4teromrilqtte ;jlrornm.

RO P O S 1T1

X X V.

Theoren1a.

Sph4Ya

luminofa major,

qpac~

minori propior,

majoreTlf ei111 partem ill11min..

quam

remotior ejfot.

Supponamr fph:era lumino!'a major,cujus cen–

trum erar A,acceffilfe ad minorem, ica uc illius fic

cemrúm N , dico ejufmodi Íphzram majorern in

N politam, majorem partero fphzrz minoris illu–

minare,quam

díec in A.Falla enim eadem con–

firuétione , fir N P illius diamecer ; Citque N O

zqualis ipli AF auc BE; fiar m OP ad ON, feu

FD ad AF; ita NB ad BR, Íed uc FD ad AF, ita

erar AB ad BC; igitur erir lit AB ad BC, ica NB

ad BR. Sed N B minor eíl:

qua~

AB, igicur N R

P R O P O S

T 1O

X X V l.

Theorema;

'Íot flmt 11mbr4 ejufdem torporü

optt~i

q11dt

lucida.

Hlc Íttpponenda cífcnr aliqua qt1aíl

axi~mata

fed ita Cune clara m fufliciat i11dic

arc,11cm

pc1fh

umbraril in direél:um projici,&: i.n

dirc.ll~

1m jac~re

cum·radio qui

corpore opaco intcrc1p1rnr, cum

cnim lux per line21Tl

reél:a~

pr?fundart"., tonnn

illud fpacium quod exorb1rab1c

cxtr~ lin_~om

.ª

luminofo per corpus opacum d?él:am 1Uum1112bi.–

cur, atquc adeo umbra non em..

cu~ er~o

um•

bra uc ica dicam lhi11gacur 111m1ne In direétum

proten(Q