Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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337
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rhead
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EPISTOLAE.
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n
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349
"
file
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0349
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0349
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oculorum clauderetur, nihilominus cum reliquo obiectum vidiſſemus in
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type
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ipſo
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loco
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>.d.</
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& non in alio ex ſuperius dictis rationibus.</
s
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</
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<
p
>
<
s
xml:id
="
echoid-s4092
"
xml:space
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preserve
">Et ſi ſtantibus ijs terminis volueremus pupillam oculi
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var
>.u.</
var
>
verſus aliam
<
var
>.a.</
var
>
ad aſpi-
<
lb
/>
ciendum punctum
<
var
>.n.</
var
>
in ſuperficie
<
var
>.g.h.</
var
>
ipſius ſpeculi, hoc eſt ſi fecerimus quod axes
<
lb
/>
viſuales ſeinuicem ſecarent in ipſo puncto
<
var
>.n</
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>
. </
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>
<
s
xml:id
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echoid-s4093
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xml:space
="
preserve
">tunc videremur nobis videre duas
<
lb
/>
imagines ipſius obiecti
<
var
>.b.</
var
>
intra ſpeculum, eo quod obiectum, propter hoc non
<
lb
/>
ceſſaret reflectere ad oculos ab ipſis punctis
<
var
>.n.</
var
>
et
<
var
>.t.</
var
>
quapropter recipiendo ra-
<
lb
/>
dium
<
var
>.t.u.</
var
>
in ſitu axis oculi
<
var
>.u.</
var
>
& radium
<
var
>.n.a.</
var
>
in ſitu axis oculi
<
var
>.a.</
var
>
hi axes ex neceſſitate
<
lb
/>
(vt probauimus ) ſeinuicem ſecant in puncto
<
var
>.d.</
var
>
vnde vnam tantummodo imaginem
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ipſius obiecti nobis apparebit.</
s
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</
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<
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<
s
xml:id
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xml:space
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">Ex his igitur omnibus potes facilè videre omnem imaginem, cuiuſuis obiecti, re-
<
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/>
flexam à ſpeculo, reperiri in ipſo catheto incidentiæ, cum ipſe ſemper ſit communis
<
lb
/>
ſectio duarum ſuperficierum reflexionis, in quo catheto concurrunt ipſæ axes vi-
<
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/>
ſuales.</
s
>
</
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<
p
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<
s
xml:id
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xml:space
="
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">Exijſdem etiam dictis rationibus facile compræhendere poteris, vnde fiat, vt vi-
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/>
deamus imaginem reflexam à ſpeculis ſphęricis concauis citra
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type
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ſuperficiem, &
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non vltra. </
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<
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xml:id
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xml:space
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">Quod
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euenit, niſi quando
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type
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>
<
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>.d.</
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>
interſectionis
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type
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>
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/>
viſualium (quod alio in loco non fit, niſi in catheto incidentiæ hoc eſt in communi
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ſectione duarum ſuperficierum reflexionis. </
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<
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xml:space
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">Dato quod obiectum non ſit in vna ea-
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demq́ue ſuperficie, in qua reperti fuerint axes viſuales, hoc eſt dato,
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type
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ambo axes
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viſuales non ſint in vna
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norm
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eademque
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type
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">eademq́;</
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>
ſuperficie reflexionis) reperitur citra & non vltra ſu
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perficiem ipſius ſpeculi.</
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>
</
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<
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>
<
s
xml:id
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xml:space
="
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">Ad cuius rei euidentiam non
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dicere, quod cum debeant ſemper ſu-
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perficies reflexionum perpendiculares eſſe, velad rectos ſecare ſuperficiem ipſius
<
lb
/>
ſpeculi, ipſarum communes ſectiones cum ſuperficie ſpeculi ſphęrici, ſemper erunt
<
lb
/>
circunferentiæ magnorum circulorum illius ſphæræ, cuius portio eſt ſpeculum
<
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propoſitum, vt etiam Vitellio affirmat in prima ſexti libri. </
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<
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xml:space
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">Vnde vnuſquiſque ca-
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thetus incidentiæ tranſibit per centrum ſpeculi, cum ipſe ſit communis ſectio dua-
<
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/>
rum ſuperficierum reflexionis, </
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>
<
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xml:space
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preserve
">quare in ipſo catheto erit punctum interſectionis ip
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ſorum axium viſualium ex neceſſitate, vt videbimus, ſi vnam tantummodo
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obiecti nobis videremur videre.</
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<
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<
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xml:space
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">Exempli gratia, ſint duæ ſuperficies reflexionis ſpeculi ſphærici concaui
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>
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et
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>
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ſit
<
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>
oculi autem ſint
<
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>.a.u.</
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>
punctum verò ſuperficiei ſpeculi, à
<
lb
/>
quo obiectum emittit reflexionem ſuę
<
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/>
imaginis ad oculum
<
var
>.a.</
var
>
ſit
<
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>.n.</
var
>
<
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norm
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punctum
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type
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au-
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<
figure
xlink:label
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fig-0349-01
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xlink:href
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fig-0349-01a
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number
="
376
">
<
image
file
="
0349-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0349-01
"/>
</
figure
>
<
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="
fig-0349-02
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xlink:href
="
fig-0349-02a
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number
="
377
">
<
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file
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0349-02
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0349-02
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tem à quo eandem reflectit oculo
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>.u.</
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>
ſit
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/>
t. communis autem ſectio harum dua-
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rum ſuperficierum ſit
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>
ſed
<
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>
<
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ſit ſpeculi, radius verò incidentię ſuper
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/>
ficiei
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>.b.n.c.</
var
>
erit
<
var
>.b.n.</
var
>
cuius reflexus ſit
<
var
>.n.
<
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/>
a.</
var
>
radij autem alterius ſuperficiei erunt
<
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/>
<
var
>b.t.</
var
>
et
<
var
>.t.u</
var
>
. </
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>
<
s
xml:id
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xml:space
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">Imaginemur nunc duos ſemi
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diametros
<
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>.x.n.</
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>
et
<
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>.x.t.</
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>
quæ angulos
<
var
>.b.n.
<
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/>
a.</
var
>
et
<
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>.b.t.u.</
var
>
per æqualia diuidant ex ſup-
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poſito.</
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>
</
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<
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>
<
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xml:id
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xml:space
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">Nunc ijs ſuppoſitis, ſi vnam tantum-
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modo obiecti imaginem videbimus, </
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