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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146
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rhead
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IO. BAPT. BENED.
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n
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158
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file
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0158
"
xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0158
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huius effectus conuerſo, ideſt, vt quemadmodum nunc ſupponuntur
<
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et
<
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>.u.</
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eſſe duo
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lb
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centra quibus
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norm
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ſuſtinetur
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type
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simple
">ſuſtinet̃</
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pondus
<
var
>.e.</
var
>
ipſius
<
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>.n.</
var
>
imaginemur
<
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>.n.</
var
>
eſſe quoddam centrum à
<
lb
/>
quo pendeant duo pondera
<
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>.o.</
var
>
et
<
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>.u.</
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>
ſic inuicem proportionata, ut ſunt
<
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>.u.i.</
var
>
et
<
var
>.i.o.</
var
>
<
lb
/>
certe horum ponderum cauſa ſtatera
<
var
>.o.s.</
var
>
quam vectem appellabamus à nulla parte
<
lb
/>
inclinabitur. </
s
>
<
s
xml:id
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echoid-s1750
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xml:space
="
preserve
">Redeuntes nunc ad propoſitum, dicemus
<
reg
norm
="
quod
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type
="
simple
">ꝙ</
reg
>
annitente pondere ipſius
<
var
>.
<
lb
/>
n.</
var
>
minus ad
<
var
>.u.</
var
>
quam ad
<
var
>.o.</
var
>
ideſt ad
<
var
>.t.</
var
>
minori vi opus erit in
<
var
>.u.</
var
>
quàm in
<
var
>.t.</
var
>
ad attollen-
<
lb
/>
dum pondus ipſius
<
var
>.n.</
var
>
& ſic per conſequens quantò longius erit punctum
<
var
>.u.</
var
>
ab
<
var
>.t.</
var
>
tan
<
lb
/>
tò minori quoque vi egebit, & conſequenter quando vis, aut reſiſtentia in
<
var
>.u.</
var
>
ita pro
<
lb
/>
portionata erit illi, quæ eſt ipſius
<
var
>.o.</
var
>
vt eſt
<
var
>.o.i.</
var
>
ad
<
var
>.i.u.</
var
>
vectis non mouebitur. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Sed quan
<
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/>
do erit proportio maior, reſiſtentiæ ipſius
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var
>.u.</
var
>
ad eam, quæ eſt ipſius
<
var
>.o.</
var
>
ea, quæ eſt
<
var
>.o.
<
lb
/>
i.</
var
>
ad
<
var
>.i.u.</
var
>
</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">tunc vectis à par-
<
lb
/>
teipſius
<
var
>.u.s.</
var
>
eleuabitur, ſi
<
lb
/>
<
figure
xlink:label
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fig-0158-01
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xlink:href
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fig-0158-01a
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number
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215
">
<
image
file
="
0158-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0158-01
"/>
</
figure
>
vero proportio minor eſſet
<
lb
/>
quàm.o.i. ad
<
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>.i.u.</
var
>
</
s
>
<
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xml:id
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xml:space
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">tunc ve-
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ctis ab eadem parte depri-
<
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metur.</
s
>
</
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</
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<
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type
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<
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style
="
it
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xml:space
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">De ratione cuiuſdam uis adauctæ.</
head
>
<
head
xml:id
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xml:space
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">CAP. VI.</
head
>
<
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<
s
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xml:space
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">QVibuſdam in locis vtuntur
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norm
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quidam
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type
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">quidã</
reg
>
<
reg
norm
="
quodam
"
type
="
context
">quodã</
reg
>
<
reg
norm
="
inſtrumento
"
type
="
context
">inſtrumẽto</
reg
>
piſtorio ad
<
reg
norm
="
ſubigendam
"
type
="
context context
">ſubigẽdã</
reg
>
pa-
<
lb
/>
ſtam, vnius tantum hominis ui adhibita, quæ quidem machina cum mihi di-
<
lb
/>
gna contemplatione eſſe videatur, eius aliquam rationem proponere volui, pro cu-
<
lb
/>
ius deſcriptione imaginemur planum, in quo ſedet ille, qui voluit paſtam, & in quo
<
lb
/>
ipſa paſta eſt repoſita
<
var
>.T.S.D.</
var
>
& triangulum
<
var
>.T.A.S.</
var
>
immobile perpendiculare-
<
lb
/>
q́ue ſuperficiei dicti plani, angulo autem
<
var
>.A.</
var
>
coniunctum lignum
<
var
>.A.E.</
var
>
vt ſemidiame
<
lb
/>
trum mobilem, & æqualem perpendiculari ipſius trianguli, </
s
>
<
s
xml:id
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xml:space
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preserve
">unde
<
var
>.A.</
var
>
loco centri erit
<
lb
/>
et
<
var
>.D.O.</
var
>
ſit ſemidiameter, qui paſtam contundit, & ab eius extremo
<
var
>.O.</
var
>
(quod
<
var
>.O.</
var
>
<
lb
/>
quando
<
var
>.D.O.</
var
>
orizontalis eſt, in baſi dicti trianguli reperitur) veniat lignum
<
var
>.O.V.</
var
>
<
lb
/>
quod cum
<
var
>.A.V.</
var
>
ſit æquale perpendiculari imaginatæ ab angulo
<
var
>.A.</
var
>
baſi
<
var
>.T.S.</
var
>
<
reg
norm
="
deno- datum
"
type
="
context
">deno-
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lb
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datũ</
reg
>
<
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norm
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tantum
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type
="
wordlist/context
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reg
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utvulgo
<
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dicitur
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type
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simple
">dicit̃</
reg
>
ſeu flexile in
<
var
>.O.</
var
>
& in
<
var
>.V.</
var
>
vt elleuare
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
deprimere ſemidiame
<
lb
/>
trum
<
var
>.D.O.</
var
>
poſſit, et
<
var
>.V.O.</
var
>
ſit æqualis
<
var
>.A.V.</
var
>
et
<
var
>.V.</
var
>
medium ſit inter
<
var
>.A.</
var
>
et
<
var
>.E.</
var
>
vnde
<
var
>.A.V.</
var
>
<
lb
/>
cum
<
var
>.O.V.</
var
>
æquales erunt
<
var
>.A.E.</
var
>
ſunt deinde duo ligna
<
reg
norm
="
perpendicularia
"
type
="
context
">perpẽdicularia</
reg
>
ab
<
var
>.A.</
var
>
ad baſim
<
lb
/>
fixa, & immobilia inter ſe adeò diſtantia, vt inter ipſa
<
reg
norm
="
pertranſeant
"
type
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context context
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>
<
var
>.O.V.</
var
>
et
<
var
>.D.O.</
var
>
ſupra
<
lb
/>
& infra, ne deuiet ſemidiametrum
<
var
>.D.O</
var
>
. </
s
>
<
s
xml:id
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xml:space
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">In extremitate deinde ipſius
<
var
>.E.</
var
>
ſit lignum
<
lb
/>
quoddam tenue, vt digitus polex, ad angulos rectos cum
<
var
>.A.E.</
var
>
quod ab aliquo, qui
<
lb
/>
antedictam machinam ſtet, manibus teneatur, qui quidem homo idipſum lignum,
<
lb
/>
ideſt ſemidiametrum
<
var
>.A.E.</
var
>
à ſuperficie trianguli dicti, ad ſe trahendo, & deinde ver
<
lb
/>
ſus eundem triangulum impellendo, vim quandam maximam mediante ſemidia
<
lb
/>
metro
<
var
>.D.O.</
var
>
ſuper paſtam excitat.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
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xml:space
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preserve
">Pro cuius rei contemplatione volo vt ſecundam hanc ſubſcriptam figuram
<
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>.b.a.
<
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/>
u.x.</
var
>
imaginemur, in qua
<
var
>.u.</
var
>
exprimat
<
var
>.A.</
var
>
primæ figuræ, &
<
var
>.a.</
var
>
denotet
<
var
>.O.</
var
>
&
<
var
>.o.V.</
var
>
&
<
var
>.x.
<
lb
/>
E.</
var
>
imaginemur etiam
<
var
>.u.a.</
var
>
baſem trianguli
<
var
>.a.u.o.</
var
>
cui
<
var
>.o.t.</
var
>
perpendicularis dictæ baſi
<
var
>.
<
lb
/>
u.a.</
var
>
addatur. </
s
>
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xml:space
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<
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Hucuſque
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>
igitur
<
var
>.u.o.</
var
>
æqualis erit
<
var
>.o.x.</
var
>
& ipſi
<
var
>.o.a.</
var
>
imaginemur etiam
<
var
>.a.o.</
var
>
<
lb
/>
vſque ad
<
var
>.b.</
var
>
ita productam vt
<
var
>.o.b.</
var
>
æqualis ſit
<
var
>.o.a.</
var
>
ponamus etiam pondus in
<
var
>.a.</
var
>
impel- </
s
>
</
p
>
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