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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381
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EPISTOLAE.
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393
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file
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0393
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0393
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tractat de centris libræ, ſeu ſtateræ: </
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>
<
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xml:space
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preserve
">A ſpice igitur in .4. ſupradicta, quod cum appen-
<
lb
/>
ſæ fuerint omnes illæ partes ponderum, partibus longitudinis ipſius
<
var
>.l.K.</
var
>
in qua volo
<
lb
/>
vt à punctis
<
var
>.e.</
var
>
et
<
var
>.d.</
var
>
imagineris duas lineas
<
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>.e.o.</
var
>
et
<
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>.d.u.</
var
>
inuicem æquales, & ferè per-
<
lb
/>
pendiculares ipſi
<
var
>.l.K.</
var
>
hoc eſt reſpicientes mundi centrum; </
s
>
<
s
xml:id
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xml:space
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preserve
">imagineris etiam
<
var
>.o.u.</
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>
<
lb
/>
<
handwritten
xlink:label
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hd-0393-01
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xlink:href
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hd-0393-01a
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quæ ſit paralle la ipſi
<
var
>.l.k.</
var
>
quæ diuiſa ſit in puncto
<
var
>.i.</
var
>
ſupra
<
var
>.g</
var
>
. </
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>
<
s
xml:id
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echoid-s4509
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xml:space
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preserve
">Hinc nulli dubium erit,
<
lb
/>
cum
<
var
>.g.</
var
>
fuerit centrum totius ponderis appenſi ipſi
<
var
>.l.K.</
var
>
quod
<
var
>.i.</
var
>
ſimiliter erit centrum
<
lb
/>
cum directe locatum ſit ſupra
<
var
>.g.</
var
>
hoc eſt in eadem directionis linea, quod quidem
<
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non indiget aliqua demonſtratione, cum per ſe ſatis pateat. </
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<
s
xml:id
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xml:space
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preserve
">Vnde ex communi
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lb
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conceptu
<
var
>.o.</
var
>
erit centrum ponderis appenſi ipſi
<
var
>.l.h.</
var
>
et
<
var
>.u.</
var
>
erit centrum ponderis ap-
<
lb
/>
penſi. ipſi
<
var
>h.K</
var
>
. </
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<
s
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xml:space
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">Scimus
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igitur
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type
="
simple
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reg
>
<
var
>.i.</
var
>
eſſe
<
reg
norm
="
centrum
"
type
="
context
">cẽtrum</
reg
>
duorum, hoc eſt ipſius
<
var
>.l.h.</
var
>
& ipſius
<
var
>.h.k.</
var
>
con
<
lb
/>
tinuatorum per totam
<
var
>.l.k</
var
>
. </
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>
<
s
xml:id
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xml:space
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preserve
">Nunc ergo ſi conſideremus
<
var
>.l.k.</
var
>
diuiſam eſſe, hoc eſt di-
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lb
/>
ſiunctam in puncto
<
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>.h.</
var
>
inueniemus nihilominus
<
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>.i.</
var
>
centrum eſſe dictorum ponderum,
<
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/>
& quod tantum eſt, ipſam eſſe
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norm
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continuam
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type
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>
, quantum diuiſam in dicto puncto
<
var
>.h.</
var
>
neque
<
lb
/>
ex hoc, punctum
<
var
>.i.</
var
>
erit magis vel minus centrum duorum ponderum
<
var
>.l.h.</
var
>
et
<
var
>.h.k.</
var
>
quo
<
lb
/>
rum vnum pendet totum ab
<
var
>.o.</
var
>
aliud verò totum ab
<
var
>.u.</
var
>
& hoc modo in longitudine
<
var
>.
<
lb
/>
o.u.</
var
>
diuiſa vt dictum eſt, habebimus propoſitum.</
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>
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<
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<
s
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xml:space
="
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">Reliquam propoſitionem tibi relinquo.</
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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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preserve
">Illa verò propoſitio, quam tibi dixi Archimedem tacuiſſe in huiuſmodi materia
<
lb
/>
eſt, quod ſi duo pondera æquilibrant ab extremis alicuius ſtateræ, in certis præfixis
<
lb
/>
diſtantijs à centro. </
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>
<
s
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xml:space
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">Tunc dico ſi eorum vno manente alterum moueatur remotius
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lb
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ab ipſo centro quod illud deſcendet, & ſi vicinius ipſi centro appenſum fuerit aſcen-
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det. </
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<
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xml:space
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">Hæc enim propoſitio quotidie omnibus in locis videtur, ipſam verſo4; </
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<
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xml:space
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">puto Ar
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chimedem prætermiſiſſe ob facilitatem, cum ab antedicta ferè dependeat.</
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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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">Sit exempli gratia ſtatera
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>.a.u.</
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>
cuius centr um ſit
<
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>.i.</
var
>
& pondera
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var
>.u.a.</
var
>
appenſa, ſein-
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uicem habeant vt
<
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>.i.u.</
var
>
et
<
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>.i.a.</
var
>
ſe inuicem habent. </
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>
<
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xml:id
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xml:space
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preserve
">Nunc dico quod ſi pondus ipſius
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>.u.</
var
>
<
lb
/>
poſitum fuerit vicinius centro vt puta in
<
var
>.o.</
var
>
inmoto exiſtente pondere, a. quod bra-
<
lb
/>
chium
<
var
>.i.o.u.</
var
>
aſcendet, & è conuerſo, ſi remotius poſitum fuerit, deſcendet.</
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>
</
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<
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<
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<
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norm
="
Ponatur
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type
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">Ponat̃</
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>
ergo vt
<
reg
norm
="
dictum
"
type
="
context
">dictũ</
reg
>
eſt in
<
var
>.o.</
var
>
vicinius
<
reg
norm
="
centro
"
type
="
context
">cẽtro</
reg
>
, quapropter brachium
<
var
>.i.o.</
var
>
<
reg
norm
="
breuius
"
type
="
simple
">breuiꝰ</
reg
>
erit
<
lb
/>
brachio
<
var
>.i.u.</
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>
vnde minor proportio erit ipſius
<
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>.i.o.</
var
>
ad
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>.i.a.</
var
>
quàm.i.u. ad eundem
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>.a.i.</
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>
&
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/>
conſequenter quam ponderis ipſius
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>.a.</
var
>
(quod ſit
<
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>.n.e.</
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>
) ad pondus ipſius
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>.u</
var
>
. </
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<
s
xml:id
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xml:space
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">Quare ſi cx
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pondere
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>.n.e.</
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dempta fuerit
<
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>.e.</
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>
pars eius, ita quod reliqua pars
<
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>.n.</
var
>
ſe habeat ad pondus
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/>
o. vt ſe habet. i
<
unsure
/>
<
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>.o.</
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>
ad
<
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>.i.a.</
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>
tunc ſtatera non mouebitur; </
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>
<
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xml:id
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xml:space
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">addita verò parte
<
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>.e.</
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>
ex com-
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muni conceptu, a. deſcendet vnde
<
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>.o.</
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>
aſcenderet conuerſum verò ex ſimilibus ratio-
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nibus per te concludes.</
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>
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