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Optic~
!l!!'ílf!ílf!:~!l!11l!l1ll:!lll:!ll!llll!l@l!illl!l!lfi!l'll!J:¡jll!lll111lWllloo
Ehzng11la in E, erit ergo
(
per
47.
1.)
quadra111m
PRO.POSITIO XXV.
Theorema.
.AC
~q11ale
quadratu EA , EC, jicut q1111dratum
Af,
~qua/e
q1rndra1u AE, Ef,
&
q11i11
(
per
7.;.)
EC m11¡or eft, q11/11" EF, ern111q1Mdr,,ta AE,EC
major11 9111draru
AE,
EF,
&
confeqrm11er linea
Si magnitudo in cemro circuli ercllajit perpend'.-
AC major,qwim AF.Eodem modo oftendam linearn
citlariter,
&
oculU6
maveatur
in
circumfannt•a
AD mfl.jorem e/fe
linea
AC;
ideoque
mm
in tr;an-
cirfuli, magni111do[cmper apparebit
4<f""J;1.
gulif ABE, ABC latera duo
fim
~qualia
mrttmque
utriqt«, nempe AB comm1me, BF , irem
&
BC
Sir magnitudo AB , crcél:a
perpendicularir~r
( per def. circ. )
jint
~q11alia
,
&
bajis AC
Jit
ma-
in centro circuli
B.
Oculus aurem, movearur 1n
jor bafi
1
AF,
erit (
per
15.
1.)
ang11IUJ ABC ma–
jar a11g11/o ABF.
I ta
ojf~ndam
,mg1ilum ABD,
majorcm ej]e ang¡¡/o ABC.
A
. circumferentia circuli. Sirque íucccffivc in C,
&
D . Oico rnagnitudinem AB videri íub eodem an–
gulo in C
&
O,
fe"
angulas ACB, ADB a:qua–
les effe.
Demonílratio. In triangulis ACB, ADB, cum
latus AB
Ílt
commune,& latera BC, BD (
per def
circuli)
fine a:qualia ,
&
anguli ABC, ABO finr
a:quales , urpote rell:i , erunr (
per
4.
1. )
angnli
ACB,ADB 'a:quales; quod erar demonílrandum.
L
E M M A.
Si linea ad plamnn inclin11ta jit,
&
ex
e
jiu
pun–
Efo in fi1blirni dimittar11r perpendirnlarú, ang11-
lm q11i
fiet
a
linea duE!-a
a
p11nEfo
in
quod cadit
perpendic11laru ad lineam obliquttm
'
&
a
linea
obliquA; niinimiu efl,
ttl1i
pro,1.t ab to recedent
fimt majorts, maxim™
qui
rninimo contigm-u eft.
Linea AB cadat obliq1ú
in
plan11rn CD
,
&
ex
e
pw1ffo
A
demittamr
perp~ndicularú
AE
ad pla–
n11m; dico .wg11l111n
EB
A effe mininl11m
,
qHi
fiet
a
lineú in plano CD duéfo
,.d
ptmEfom
B,
&
pro–
d11Eft. line!i
E
B
in
D.
Dicó angulum A B D ejfo
maximum. Fiat
enh-11
ex
p11nf10
B
, m
umro
fo..
tervallo majori quam BE c1rc11I.u CD fi1mant11r–
q11e prmEla CD. Ducamrque linea BC. Debeopro–
bare angulum
ABE
minort7n ejfo, q11am ABC,
&
ABC 11y11ore•
q11am
AIJD. D11ca!11m· line.t
.AD,
AC.
Demo11f/r11tio, Triangula AEF
,
AEC fimt re-
illlll!lllll~00·001m!ll1.!1i
¡¡¡¡,¡¡¡¡g¡¡¡¡:¡¡llMimll!l!lli:!!llll
PROPOSITI O
XXVI.
Thcorema.
Si linea ad plan11m circ11li fuerit obliq11a, 71ravea–
wrq1<e in ejt<J cirmmferenr
ia
femper fibi ipji
paral/ela,
OGll/O
in Centro conjifte11tc, eo appa–
rentiam mirlorem habebit
h.tclinea
'l"º
remove–
b11,.r magis
a
diarnctro cu
m q1111 minorem ang"–
liim facit•
Sir linea AB obliquc incidens, in.planum cit–
culi BDF, Íupra cujus circumferentiam moV'ea–
tur in lirn íemper parallelo. Sirque oculus in C
immotus. Er
fir
ira AB uc
Ílt
A~C
minimus an–
gulus quem facir ha=c linea cum lineis duébs in
plano circuli , hoc eíl: perpendicularis ex punél:o
A dull;a cadat in BC. Dico AB eo minorem ap–
.parent1am habere, quo magts removerur
a
diame–
rro BC, hoc eíl:
(j
AB transferarnr in DE., angu–
lum OCE. minorem effe angulo llCA,item anau–
lum DGE majorem effe angulo FCG.
Ducan~ur
enim linea: AC , EC, GC, irem linea OH paral–
lela diamerro BC.
E
. Demon!hado
linb
D E fupponitur parallda
!mere AB, linea OH dlléh etiam eíl: parallela
li–
nea: DC; ergo (
per
10. 1
t.)
anguli ABC, DHE
Ítmr requales ; cíl: aucem
(per Lemmafl•peri1<1)an–
g11lus EDC: majar quam EDH,ergo angulus EOC
majar eíl: angulo ABC , ergo reliqui duo íimul
DCE, DEIS minores funr duobus fimul BAC ,
BC A. Sinus amem anguli DCE, ad finum anguli
DEC re haber, (
per primam tertii Trigon.)ut
DE
ad OC, Íeu ur AB ad BC, Ílcut (
per eandem
)
fe
lubet finus angu\i ACB ad finum anguli B A C,
~rgo
ut linus anguli DCE ad finun¡ anguli DEC,
Ita finus anguli BCA ad finum anguli BAC : íed
aggregatum duornm priorum angnlornm,
mi~us
eíl •ggregato poíleriorum lit jam oíl:endimus,1g1-
tur angu.\us OCE, minar cíl angulo ACB quoci
erar oílendendllm.
p
R oP ·O