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. BABPT. BENED.
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<
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style
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xml:space
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">De quibuſdam erroribus Nicolai Tartaleæ circa pondera
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corporum & eorum motus, quorum aliqui deſumpti
<
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fuerunt à fordano ſcriptore quodam antiquo.</
head
>
<
head
xml:id
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xml:space
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head
>
<
p
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<
s
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xml:space
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">CVm magis amici veritatis eſſe debeamus quàm cuiuſquam hominis, quemad-
<
lb
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modum Ariſto. ſcribit, detegam hoc loco quoſdam errores Nicolai Tartaleę
<
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de ponderibus corporum, & velocitatibus motuum localium. </
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>
<
s
xml:id
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xml:space
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preserve
">Et primum decipitur
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is in .8. lib. ſuarum diuerſarum inuentionum in ſecunda propoſitione, cum non ani-
<
lb
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maduerterit quanti momenti ſint extrinſecæ reſiſtentiæ.</
s
>
</
p
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<
p
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<
s
xml:id
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xml:space
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">Subiectum quoque tertiæ propoſitionis eſt malè demonſtratum, quia idem pla-
<
lb
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nè ex eius demonſtratione iam dicta corporibus hætereogeneis, aut figura diuerſis
<
lb
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contingeret, quod ad velocitates attinet.</
s
>
</
p
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<
p
>
<
s
xml:id
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xml:space
="
preserve
">In quarta propoſitione, quod ad
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type
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context context
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reg
>
proponit
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type
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concludit melius. </
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<
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<
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norm
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type
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id
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ab eo
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type
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, quod Archimedes in .6. propoſitione lib. primi de
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type
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reg
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<
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type
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reg
>
.</
s
>
</
p
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<
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number
="
8
"/>
<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Sed in ſecunda parte quintę propoſitionis non uidet
<
reg
norm
="
quod
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type
="
simple
">ꝙ</
reg
>
uigore ſitus eo modo, quo
<
lb
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ipſe diſputat, nulla elicitur ponderis differentia. </
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>
<
s
xml:id
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xml:space
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">quia ſi corpus
<
var
>.B.</
var
>
deſcendere debet
<
lb
/>
per arcum
<
var
>.i.l.</
var
>
corpus
<
var
>.A.</
var
>
aſcendere debet per arcum
<
var
>.u.s.</
var
>
æqualem, & ſimilem. eadem
<
lb
/>
quoque ratione ſituatum, vt eſt arcus
<
var
>.i.l.</
var
>
vnde vt eſt facilè corpori
<
var
>.B.</
var
>
deſcendere
<
lb
/>
per arcum
<
var
>.i.l.</
var
>
difficile ita erit corpori
<
var
>.A.</
var
>
aſcendere per arcum
<
var
>.u.s</
var
>
. </
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>
<
s
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xml:space
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">Hęc autem qnin
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lb
/>
ta propoſitio Tartaleæ eſt ſecuuda quæſtio à Iordano propoſita.</
s
>
</
p
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<
p
>
<
s
xml:id
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xml:space
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">Quòd autem ad primum corollarium dictæ propoſitionis attinet, verum ille qui
<
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dem ſcribit, eius tamen effectus cauſa & à Iordano prius, & ab ipſo poſtea citata, na-
<
lb
/>
tura ſua vera non eſt. </
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>
<
s
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xml:space
="
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">quia vera cauſa per ſe ab eo oritur,
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norm
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quod
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type
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>
à centro libræ dependeat
<
lb
/>
vt primo cap. huius tractatus oſtendi. </
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>
<
s
xml:id
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xml:space
="
preserve
">Secundum verò corollarium falſum eſſe, ijs ra
<
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tionibus quas nunc ſubiungam, patebit. </
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>
<
s
xml:id
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xml:space
="
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">Imaginemur
<
var
>.u.</
var
>
pro centro regionis ele-
<
lb
/>
mentaris, & libram
<
var
>.b.o.a.</
var
>
obliquam reſpectu ad
<
var
>.u.</
var
>
& brachijs æqualibus
<
reg
norm
="
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"
type
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">conſtãtem</
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>
,
<
lb
/>
& pondera in
<
var
>.a.</
var
>
et in
<
var
>.b.</
var
>
etiam æqualia. </
s
>
<
s
xml:id
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xml:space
="
preserve
">lineæ autem inclinationum ſint
<
var
>.a.u.</
var
>
et
<
var
>.b.u.</
var
>
<
lb
/>
imaginemur etiam lineam
<
var
>.o.u.</
var
>
& à centro
<
var
>.o.</
var
>
libræ duas
<
var
>.o.t.</
var
>
et
<
var
>.o.e.</
var
>
perpendiculares
<
lb
/>
inclinationum lineis; </
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>
<
s
xml:id
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xml:space
="
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">vnde pondus ipſius
<
var
>.a.</
var
>
in huiuſmodi ſitu tam erit proportiona
<
lb
/>
tum ponderi
<
var
>.b.</
var
>
quam proportionata erit linea
<
var
>.o.t.</
var
>
lineæ
<
var
>.o.e.</
var
>
ex eo
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type
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>
tertio cap. hu-
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/>
iustractatus probaui, ſed linea
<
var
>.o.t.</
var
>
maior eſt linea
<
var
>.o.e.</
var
>
quod ſic probo. </
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>
<
s
xml:id
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xml:space
="
preserve
">Imaginemur
<
lb
/>
triangulum
<
var
>.u.a.b.</
var
>
circunſcriptum eſſe à circulo
<
var
>.u.a.n.b.</
var
>
cuius
<
var
>.c.</
var
>
ſit centrum,
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norm
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type
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reg
>
erit
<
lb
/>
extra lineam
<
var
>.u.o.</
var
>
cum ſupponatur
<
var
>.a.o.b.</
var
>
obliquam eſſe reſpectu ad
<
var
>.u.o</
var
>
. </
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>
<
s
xml:id
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xml:space
="
preserve
">Imagine-
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lb
/>
mur deinde à centro
<
var
>.c.</
var
>
lineam
<
var
>.c.o.s.</
var
>
vſque ad circunferentiam, quæ perpendicula-
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lb
/>
ris erit ipſi
<
var
>.a.b.</
var
>
ex tertia lib. 3. Eucli. </
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>
<
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xml:space
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">ſi poſteà imaginemur duas lineas
<
var
>.c.a.</
var
>
et
<
var
>.c.b.</
var
>
ha
<
lb
/>
bebimus ex .8. lib. primi, angulum
<
var
>.a.c.o.</
var
>
æqualem angulo
<
var
>.b.c.o</
var
>
. </
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>
<
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xml:id
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xml:space
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">Vnde ex .25. lib. 3.
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arcus
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var
>.a.s.</
var
>
æqualis erit arcui
<
var
>.b.s.</
var
>
ſed ſi imaginabimur
<
var
>.u.o.</
var
>
ad circunferentiam vſque
<
lb
/>
productam, clarum erit
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arcum
<
var
>.s.b.</
var
>
ſecaret in puncto
<
var
>.n.</
var
>
vnde arcus
<
var
>.n.b.</
var
>
minor erit
<
lb
/>
arcu
<
var
>.n.a.</
var
>
& ſic etiam angulus
<
var
>.n.u.b.</
var
>
minor erit angulo
<
var
>.n.u.a.</
var
>
ex
<
ref
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">ultima lib. 6.</
ref
>
</
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>
<
s
xml:id
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xml:space
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">Imagi-
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/>
nemur nunc alium quendam circulum, cuius
<
var
>.o.u.</
var
>
ſit diameter, cuius circunferentia
<
lb
/>
per duo puncta
<
var
>.e.</
var
>
et
<
var
>.t.</
var
>
<
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, cum in ipſis ſint angulirecti, quod quilibet ex
<
lb
/>
ſeratio cinando colligere poteſt, ſi .30. lib. 3. in mentem reuocauerit. </
s
>
<
s
xml:id
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xml:space
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">Sed cum angu-
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lb
/>
lus
<
var
>.o.u.t.</
var
>
ſit maior angulo
<
var
>.o.u.e.</
var
>
arcus
<
var
>.o.t.</
var
>
maior erit arcu
<
var
>.o.e.</
var
>
ex vltima .6. vnde cor
<
lb
/>
da
<
var
>.o.t.</
var
>
maior erit corda ipſius
<
var
>.o.e.</
var
>
ex conuerſo .27. lib. 3. quod eſt propoſitum. </
s
>
<
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xml:space
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">Pon-
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dusigitur ipſius
<
var
>.a.</
var
>
in huiuſmodi ſitu, pondere ipſius
<
var
>.b.</
var
>
grauius erit. </
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>
<
s
xml:id
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"
xml:space
="
preserve
">Quod è directo ijs
<
lb
/>
repugnat quæ Tartalea in 2. parte quinræ propoſitionis ediſerit, & per conſequens
<
lb
/>
2. corollarij falſitatem oſtendit, vt eam quoque, quæ in 6. propoſitione latet. </
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>
<
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xml:space
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