746346

Liber

6~7

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R O

O S I T I O

1I l.

Theorema.

Reft11aio

jit

reciproco per

rofdem r..diot,

Fiar rcfraél:io A,B

ab acre, in aquam, nempa

lit

radius incidcns dué\:us in aé!re,

u -

ª.qu~

effe

·ad ,+ fiippon.arur angulus inclina–

uom

ABI

effe ferc rcll:us,

Ita

ur vix phylicc de-

tlius refraél:us in aqua; dico quod li tadius luml–

nis ex punl'l:o

ferarur pee lineam CB, ulreriuf–

que prop•gerur in aere, ralem radium ecfringcn–

dum in BA.

Demonfl:rario. Efl: eadem differentia ihrer

aé·

eem,& aquam,quz imcrccdir inrer aqaam

acrE:

ergo cxceffus velociraris lurrtinis in acre íupra ve–

locitatem quam in aqua obrinet , ídem efl: ac de–

feél:us velocitatis radii in aqua,

velocirate quam

haber in aecc : ergo quanrum linus inclinarionis

fupcrar limun anguli rcfraél:i, dum radius incidir

ex medio rariori in denlius, ramum linus inclina-

rionis minuS'cfl: linu anguli refraél:i,dum lit rran

firus

medio

~cnliore

in rarius. Sed boc efl: vicif–

lim

fcu

reciproce rcfraélionem fieri per cofdem

radios, ergo refralHo íua relcgit vefl:igia. ldern–

que radius qui in prima refraé\:ione erar refra"él:us

tranlir in angulurn ind inationis.

ficiar

reél:o, ejus linus cric 10000000. cujus li

fumanrur quatuor quinrz, babcbimt1S'8000000.

peo linu anguli refraél:i

!BE,

graduum

4¡.

rnip.8.

cum rcfraél:io

tic

reciproca, li lucidurn agac

pcr lineam

B, ejus angulus cefrall:us fere relh1s

crir.

~me

ponarur lucidum in

F ,

agarqué pee

lineam FB,ica

lit

angulus inclinationis

FBE.,

lit

6ei

graduum,cujus finus lit

8660254.Si

fiac

lit

ica hic nurnerus ad quanum,invenies t08

17.

numemrn

rn~

jorern

rell:o,

quarc radius non egre•

diernr, fcd mancbir in corpore denfo.

Hxc fpecies rcfraétionis ctiam veccribus in–

cognira non fuir, nam Virello& Alhazcn, non–

nnnquam ponunc

~ngulum

refr:ill:um majorern

reéto. Urrum :imem hzc refralbo dtbear vocari

, F.1vet expcritncia. Si enirn diligenter neitemr

progreffi1s radii

facc prodeuntis

punéh1rn in

q11od incidir, li fax in eo collocemr, viciillm lo–

cus prior facis il1L1rninabirur.

lilOO!lll'lll'.!ri:¡¡<llJ•®llilllil~:¡)'l¡~1l"l!Nl®!l11!ll!¡i:¡jlltlil!

P R O P O S l T

Tbeorema.

N11ll1u rj! ang11IUJ inclínationú in raro

ctti ali-

9"''

non

re[pondeat Mgulm rrfraflsu in denfo;

eJI tamm ali9uu

a11g11l.u

inclinationu in.

den–

c11i

nullUI

competit

a¡1g.,lm

refraF11u irt

raro.

Prima pars propofttionis ira onendirur.

~10-

ties procedirur

raro in denfurn , cories lit re–

fralHo ad perpendicularern, angulufque refra61:us

minor evadir angulo inclinationis,qui fernper cfl:

minar rcél:o , ergo angulus refra61:us multo rninor

crir reél:o.

Ar vero curn procedirur

denfo in rarum, quia

une refraél:io lir

perpendicubci , radius re–

fraél:us rnajor efl: angulo inclinationis; ergo

an–

gulns inclinationis

!ir

rcll:us am fer

reél:us, an–

gulus refrall:us

rnajor reél:o. Sed li

!ir

major

rell:o, no,n egredietur

corpore dcnío, ergo alicui

angulo inclinarionis in medio denío, nullus ref–

ponder angulus refra61:us in raro.

Ur autem melius hanc propolicionem ocnlis

íubjiciarnus, fupponfllus racionero linus anguli

in6linationis in aere,

linum anguli eefraé\i

Üi

T~m.

//,

refr;él:io, eft qua:[\io de voce.

C O R O L L AR 1

Ra~ius

perpendicularis noh refringirnr ,

qui~

hulla efl: ratio cur pocius in unam parrcm deflell:at

<rnm.in

ali<im. Uc aucem perpcndicul.ris

cenfe~rnr ad lineam cnrvam

CBD,

deber effc perpendi–

cularis ad rangemern EF,

confequenrer li linea

cutva foerír circularis, linea

e1m perpendicu•

laris,

anlic pcr ejus cenrrum.

COROLLARIUM

II.

Majori angulo inclinationis majar refpondet

angulus refrall:us, cmn cnim eadem ícmper

lit

rotio /1nus angl•li

indinacionis ad lim1m angnli

refrall:i, nbi primus majar eric

confequencer

majoremJinum habebic: alrer ctiam majorem

fi–

num h"b:ns major erir.

·~ffoi!;M&fi~ei&-•Wi;f&€<!EtHJe~NIJi

P R O P O S I T I O

t heorerna.

R'fr.1tiio nec .¡,;vida eft, nec ordinata niji11tri1i.t

que diaphaui fuperftcitt fi1erit poli111.

Pni:rer cxperientiarn quz omnibus obvia

e~,

aliquid addendum cenfeo,

illius rationem ah-

9uarn ex refraétionis namra petitam affi¡(.nemus.

Cenurn efl: ccy{hllllln eciam

pe.rfeébaima~

ornnique ca.rentem na:vo, vix pelluc1dom,aut

dta~

phanarn

e{fe,

nec rnagis lumen ad'."mere, quam

charra , am etiam quam c:eten lapi.des li P?lmwt

carear.

quo

licet

conc!uderc,

d'.aphane1rate1~

non in qualicate fuperadd1ta ,. fed

111

lignrz

um–

formiratc qnam poliru'.a mduc11, íahem

parre;

poÍl'rarn erfe. Ratio .v1derur

e~~

qn.od

~r-yfl:allus

impolica fociccu\is

d•vedim~de

nclm3,

t1S

exafpeJ

rcrur, quz licue inord1nate

quali in ornnén'I

ero

pat~e~