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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342
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IO. BAPT. BENED.
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n
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354
"
file
="
0354
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0354
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<
p
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<
s
xml:id
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xml:space
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">Alia etiam via poſſumus idem concludere. </
s
>
<
s
xml:id
="
echoid-s4153
"
xml:space
="
preserve
">Imaginemur maiorem axem alicu-
<
lb
/>
ius ellipſis tranſire per duo puncta
<
var
>.r.</
var
>
et
<
var
>.b.</
var
>
ſupponendo ipſa puncta, ea eſle, quæ ita
<
lb
/>
axem diuidunt, vt ſingula produ-
<
lb
/>
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385
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0354-01
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</
figure
>
cta fectionum ſint, vt inquit Per-
<
lb
/>
geus. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">imaginemur, etiam
<
var
>.p.h.</
var
>
con
<
lb
/>
tiguam eſſe ipſi ellipſi in
<
reg
norm
="
puncto
"
type
="
context
">pũcto</
reg
>
<
var
>.a.</
var
>
<
lb
/>
vnde ſi protractæ fuerint duæ
<
var
>.r.a.</
var
>
<
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/>
et
<
var
>.b.a.</
var
>
habebimus ex .48. tertijip-
<
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/>
ſius Pergei angulos
<
var
>.b.a.h.</
var
>
et
<
var
>.r.a.
<
lb
/>
p.</
var
>
inuicem æquales. </
s
>
<
s
xml:id
="
echoid-s4155
"
xml:space
="
preserve
">Ducendo
<
lb
/>
poſtea ad quoduis punctum ipſius
<
lb
/>
<
var
>p.h.</
var
>
duas
<
var
>.b.o.</
var
>
et
<
var
>.r.o.</
var
>
certi erimus,
<
lb
/>
quod ſecabuntur à gyro oxygo-
<
lb
/>
nio, quarum vna ſecta ſit in pun-
<
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/>
cto
<
var
>.i.</
var
>
ducta poſtea
<
var
>.i.r.</
var
>
clarum erit ex .52. dicti, quod longitudo
<
var
>.b.i.r.</
var
>
æqualis erit lon
<
lb
/>
gitudini
<
var
>.b.a.r.</
var
>
& minor ipſa
<
var
>.b.o.r.</
var
>
ex .21. primi Euclid.</
s
>
</
p
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</
div
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<
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style
="
it
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xml:space
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">Deerrore Euclidis circa ſpeculum vstorium.</
head
>
<
head
xml:id
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xml:space
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">AD EVNDEM.</
head
>
<
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>
<
s
xml:id
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xml:space
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">VErum ſpeculum vſtorium, illud non eſt, quod ab Euclide traditum fuit, &
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quod
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type
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reg
>
<
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tu etiam putas, Nam Euclides errat, cum credat radios reflexos à ſuperficie
<
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ſphærica concaua ſeinuicem in centro ſpeculi interſecare. </
s
>
<
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xml:id
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xml:space
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preserve
">Nam cum omnes lineę
<
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/>
recte à centro, & cir cunferentia alicuius ſphæræ terminatæ, ſint eidem circunferen-
<
lb
/>
tiæ perpendiculares, ſequeretur ex neceſſitate radios incidentiæ etiam perpendicu
<
lb
/>
lares eidem ſuperficiei eſſe, cum anguli incidentiæ ſemper æquales ſint angulis re-
<
lb
/>
flexionis, vnde etiam ex neceſſitate ſequeretur punctum corporis lucidi, à quo radij
<
lb
/>
luminoſi excunt, in centro ſpeculi reperiri. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">quod quidem falſiſſimum eſt.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4159
"
xml:space
="
preserve
">Alia etiam via poſſum hanc oſtendere impoſſibilitatem, & tibi probabo, quod
<
lb
/>
in nullo aliquo puncto poſſunt inuicem conuenire ipſi radijrefle xi omnes.</
s
>
</
p
>
<
p
>
<
s
xml:id
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xml:space
="
preserve
">Sit igitur
<
var
>.l.a.c.</
var
>
<
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conis
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type
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">cõis</
reg
>
ſectio ſuperficiei reflexionis cum ſpeculo, cuius centrum ſit
<
var
>.o.</
var
>
<
lb
/>
punctum verò lucidum ſit
<
var
>.g.</
var
>
<
reg
norm
="
protrahaturque
"
type
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">protrahaturq́</
reg
>
<
var
>.g.o.a</
var
>
. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Nunc autem primum dico, quod
<
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/>
radij reflexi à punctis diuerſarum
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diſtantiarum
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type
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">diſtantiarũ</
reg
>
ab
<
var
>.a.</
var
>
non
<
reg
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coincident
"
type
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">coincidẽt</
reg
>
inuicem in aliquo
<
lb
/>
puncto lineę
<
var
>.g.o.a</
var
>
: ſint ergo duo puncta
<
var
>.u.</
var
>
et
<
var
>.r.</
var
>
diuerſarum
<
reg
norm
="
diſtantiarum
"
type
="
context
">diſtantiarũ</
reg
>
ab
<
var
>.a.</
var
>
à quibus
<
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/>
veniant duo radij incidentiæ
<
var
>.g.r.</
var
>
et
<
var
>.g.u.</
var
>
radius verò reflexus ab
<
var
>.r.</
var
>
ſit
<
var
>.r.e.</
var
>
protrahatur
<
lb
/>
<
var
>u.e.</
var
>
quam dico effe non poſſe radium reflexum ab
<
var
>.u.</
var
>
quotieſcunque eius incidens
<
lb
/>
deſcendat ab
<
var
>.g</
var
>
. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Protrahantur ergo duæ lineæ
<
var
>.o.r.</
var
>
et
<
var
>.o.u.</
var
>
vnde cum dixerit aliquis
<
lb
/>
<
var
>u.e.</
var
>
<
reg
norm
="
reflexum
"
type
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context
">reflexũ</
reg
>
eſſe ipſius
<
var
>.g.u.</
var
>
igitur anguli
<
var
>.g.u.o.</
var
>
et
<
var
>.o.u.e.</
var
>
erunt inuicem æquales, & ſic
<
lb
/>
etiam erunt duo
<
var
>.g.r.o.</
var
>
et
<
var
>.o.r.e.</
var
>
vnde ex tertia ſexti & .11. quinti Eucli. proportio
<
var
>.g.
<
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u.</
var
>
ad
<
var
>.u.e.</
var
>
æqualis eſſet ei, quæ
<
var
>.g.r.</
var
>
ad
<
var
>.r.e.</
var
>
quod quidem impoſſibile eſſe demonſtra-
<
lb
/>
bo, eo quod cum
<
var
>.g.u.</
var
>
maior ſit
<
var
>.g.r.</
var
>
ex .8. tertij, erit ex .8. quinti proportio ipſius
<
var
>.g.u.</
var
>
<
lb
/>
ad
<
var
>.r.e.</
var
>
maior proportione ipſius
<
var
>.g.r.</
var
>
ad
<
var
>.r.e.</
var
>
ſed ex .7. tertij
<
var
>.u.e.</
var
>
minor eſt
<
var
>.r.e.</
var
>
erit igi-
<
lb
/>
tur ex dicta .8. quinti maior proportio
<
reg
norm
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ipſius
"
type
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">ipſiꝰ</
reg
>
<
var
>.g.u.</
var
>
ad
<
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>.u.e.</
var
>
quam
<
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>.g.u.</
var
>
ad
<
var
>.r.e.</
var
>
vnde eo ma </
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