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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IO. BAPT. BENED.
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376
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0376
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<
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xml:space
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">DE AVGMENTO PONDERIS CORPORIS
<
lb
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ad ſtateram appenſi, & quadam alia demonſtratione,
<
lb
/>
& quibuſdam erroribus Tartaleæ.</
head
>
<
head
xml:id
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style
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xml:space
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">Mutio Groto.</
head
>
<
p
>
<
s
xml:id
="
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xml:space
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preserve
">SI ea quæ à me audiuiſti non credis, conſidera quæſo libram ſeu ſtateram
<
lb
/>
<
var
>o.a.</
var
>
cuius centrum non longitudinis ſed ponderum ſit
<
var
>.i.</
var
>
quę ſtatera, vt ori
<
lb
/>
zontaliter conſiſtat, oportebit pondus extremitatis
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var
>.o.</
var
>
ita ſe habere
<
lb
/>
ad pondus extremitatis
<
var
>.a.</
var
>
ut
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var
>.a.i.</
var
>
ſe habet ad
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var
>.o.i.</
var
>
quod te ſcire puto, ima
<
lb
/>
ginemur nunc d uas lineas
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var
>.a.e.</
var
>
et
<
var
>.o.n.</
var
>
paralle las
<
reg
norm
="
infinitasque
"
type
="
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">infinitasq́;</
reg
>
& à puncto
<
var
>.n.</
var
>
immobili,
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lb
/>
& fixo extra ſtateram, tranſeat per
<
var
>.i.</
var
>
linea
<
var
>.n.i.e</
var
>
. </
s
>
<
s
xml:id
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xml:space
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preserve
">Cogitemus etiam punctum
<
var
>.e.</
var
>
inter
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/>
ſectionis ipſius
<
var
>.n.i.e.</
var
>
cum
<
var
>.a.e.</
var
>
progredi vniformiter
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reg
norm
="
continuòque
"
type
="
simple
">continuòq́;</
reg
>
ab
<
var
>.a.</
var
>
per lineam
<
var
>.a.e.</
var
>
<
lb
/>
vnde punctum
<
var
>.i.</
var
>
interſectionis ipſius
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var
>.n.i.e.</
var
>
cum
<
var
>.a.i.o.</
var
>
ſemper vicinius fiet puncto
<
var
>.o.</
var
>
<
lb
/>
nec unquam cum illo vnum erit, quamuis moueatur tempore infinito. </
s
>
<
s
xml:id
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xml:space
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preserve
">Nunc autem
<
lb
/>
dico, quod cum ſtateram
<
var
>.o.i.a.</
var
>
oporteat ſemper orizontalem eſſe virtute ponderis,
<
lb
/>
o. oportebit pundus
<
var
>.o.</
var
>
in infinitum etiam augeri,
<
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norm
="
quotieſcunque
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type
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">quotieſcunq;</
reg
>
pondus
<
var
>.a.</
var
>
nunquam
<
lb
/>
diminui voluerimus vel econtra hoc in infinitum diminui, ſi illud nunquam augeri
<
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/>
voluerimus.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Sedre vera non putabam te indigere aliqua demonſtratione, quod linea
<
var
>.b.h.</
var
>
di-
<
lb
/>
uiſa ſit per æqualia à
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unsure
/>
linea
<
var
>.c.a.</
var
>
cum hæc perpendicularis ſit ab
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var
>.a.</
var
>
ad baſim
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var
>.g.d.</
var
>
in
<
reg
norm
="
triam
"
type
="
context
">triã</
reg
>
<
lb
/>
gulo orthogonio
<
var
>.g.a.d.</
var
>
& cum ſit
<
var
>.b.h.</
var
>
perpendicularis ad
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var
>.a.o.</
var
>
ex ſuppoſito quæ
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var
>.a.
<
lb
/>
o.</
var
>
in ſe habet punctum medium baſis
<
var
>.g.d.</
var
>
nec
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reg
norm
="
non
"
type
="
context
">nõ</
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>
illud anguli recti
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var
>.a.</
var
>
quod per ſe cla
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lb
/>
riſſimum eſt, cum iam ſcis
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var
>.o.</
var
>
eſſe centrum circuli circundantis triangulum
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var
>.g.a.d.</
var
>
or-
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lb
/>
thogonium, et
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var
>.g.d.</
var
>
eius diameter, vnde
<
var
>.o.a.</
var
>
æquabitur ipſi
<
var
>.o.g.</
var
>
quapropter angulus
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lb
/>
o.
<
reg
norm
="
am
"
type
="
context
">ã</
reg
>
. g. æquabitur angulo
<
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>.g.</
var
>
ex quinta primi, </
s
>
<
s
xml:id
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xml:space
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preserve
">deinde ex .32. eiuſdem, angulus
<
var
>.h.</
var
>
æqua
<
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/>
bitur angulo
<
var
>.d.</
var
>
eo quod an gulus
<
var
>.e.</
var
>
rectus eſt, quemadmodum et
<
var
>.a.</
var
>
ſed angulus
<
var
>.d.</
var
>
<
lb
/>
æqualis eſt angulo
<
var
>.g.a.c</
var
>
. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">& propterea angulus
<
var
>.h.</
var
>
erit etiam æqualis angulo
<
var
>.h.a.u.</
var
>
<
lb
/>
vnde
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var
>.h.u.</
var
>
æqualis erit ipſi
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var
>.u.
<
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/>
a.</
var
>
ex .6. primi, cum poſtea angulus
<
var
>.
<
lb
/>
<
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fig-0376-01a
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number
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417
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<
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file
="
0376-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0376-01
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</
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>
o.a.d.</
var
>
æqualis ſitangulo
<
var
>.d.</
var
>
ex quin
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/>
ta primi erit angulus
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>.a.b.e.</
var
>
æqua-
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/>
lis angulo
<
var
>.g.</
var
>
ex .32. dicta, eo quod
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/>
e. rectus eſt, & ex eadem æqualis
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/>
erit angulo
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>.d.a.c.</
var
>
vnde
<
var
>.u.b.</
var
>
erit
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/>
æqualis ipſi
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>.u.a.</
var
>
ex .6. dicti, & ideo
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/>
æqualis eric ipſi
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var
>.u.h</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">Reliqua ve-
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rò illius propoſitionis credo ex te
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/>
omnia poſſe
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, excepto,
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<
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vt tibi ſignificaui ſi à
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puncto
"
type
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">pũcto</
reg
>
<
var
>.i.</
var
>
com-
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/>
muni ipſi
<
var
>.a.c.u.</
var
>
& circunferentiæ,
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lb
/>
ducta fuerit
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var
>.i.x.</
var
>
ad
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reg
norm
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punctum
"
type
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">pũctum</
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>
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var
>.x.</
var
>
com
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/>
mune vni parallelæ à
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type
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">pũcto</
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>
<
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>.g.</
var
>
ipſi
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/>
<
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>h.b.</
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>
& circunferentiæ, quod di-
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/>
cta
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var
>.i.x.</
var
>
ad rectos erit ipſi
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var
>.a.b.d.</
var
>
eo
<
lb
/>
quod cum angulus
<
var
>.a.g.x.</
var
>
æqualis </
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>
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