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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171
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DISPVTATIONES.
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183
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file
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0183
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0183
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ad velocitatem per aquam vt
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ad
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non erit ergo vt
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ad
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. </
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<
s
xml:id
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xml:space
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">Ob hanc igitur
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cauſam nimis diſſentaneum eſt rationi, opi-
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nari proportionem velocitatis omnium cor
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porum grauium per aerem vnam
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fig-0183-01
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245
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0183-01
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xlink:href
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eſſe cum velocitate eorundem per aquam,
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quemadmodum Ariſtoteles ſenſit.</
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<
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style
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">Exempla dictorum.</
head
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<
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xml:space
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<
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xml:space
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">POnamus, exempli gratia, aquam eſſe in denſitate dupla ad aerem, & aliquod
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graue corpus in aqua duplum ad denſitatem ipſius aquæ, vnde dictum corpus in
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denſitate ad aerem quadruplum erit; </
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<
s
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xml:space
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preserve
">quam ob cauſam, mediam ſui ponderis tota-
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lis partem in aqua, & in aere quartam partem, ex .7. lib. de inſidentibus aquæ ab Ar-
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chimede conſcripto, amitteret. </
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>
<
s
xml:id
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xml:space
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preserve
">Moueretur igitur in aqua virtute illius mediæ partis
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ponderis
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type
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context
">põderis</
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ſui, in aere
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autem
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type
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wordlist
">aũt</
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uirtute
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norm
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trium
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type
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">triũ</
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<
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quartarum
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type
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">quartarũ</
reg
>
; </
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>
<
s
xml:id
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xml:space
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preserve
">vnde proportio facultatis
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norm
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mouentis
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type
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">mouẽtis</
reg
>
dicti
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corporis in aere ad facultatem mouentem eiuſde m in aqua ſeſquialtera erit. </
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>
<
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xml:space
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<
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norm
="
hocque
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type
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">hocq́;</
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>
<
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corpus appelletur
<
var
>.A</
var
>
. </
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>
<
s
xml:id
="
echoid-s2043
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xml:space
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">Sit aliud quoque corpus, quod
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>.B.</
var
>
nominetur, ſimile figura, &
<
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magnitudine corporea corpori
<
var
>.A.</
var
>
ſed
<
reg
norm
="
denſitate
"
type
="
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">dẽſitate</
reg
>
, in proportione ſeſquialtera ad
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norm
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aquam
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type
="
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">aquã</
reg
>
,
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& denſius erit aere in proportione tripla. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">quamobrem corpus
<
var
>.A.</
var
>
grauius erit cor-
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lb
/>
pore
<
var
>.B.</
var
>
in aere in proportione ſeſquialtera, vnde etiam velocius erit ipſo
<
var
>.B.</
var
>
in aere
<
lb
/>
in eadem proportione, ſed corpus
<
var
>.B.</
var
>
in aere, duplo maius pondus habebit,
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reg
norm
="
quam
"
type
="
context
">quã</
reg
>
in
<
lb
/>
aqua, cum in aere remaneant ei duæ ponderis tertiæ partes, & in aqua vna tantum,
<
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/>
ita vt Ariſtoteli concedam corpus
<
var
>.B.</
var
>
in aere, quam in aqua velocius futurum in ea-
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dem proportione, in qua, aqua eſt
<
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norm
="
denſior
"
type
="
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">dẽſior</
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>
aere, ex Euclidis vndecima propoſitione
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lib. quinti. </
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>
<
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xml:space
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">Sed præter hæc omnia, ſi corpus
<
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>.A.</
var
>
eſſet etiam velocius in aere,
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
in
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aqua, in eadem proportione, ſequeretur ex .16. dicti lib. quinti proportionem velo-
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citatis
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>.A.</
var
>
in aqua ad
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ipſius
<
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>
in aqua etiam ſeſquialteram eſſe. </
s
>
<
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xml:id
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xml:space
="
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">Sed cum
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corpus
<
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>.A.</
var
>
in denſitate ad aquam
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duplum
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type
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">duplũ</
reg
>
ſit, & corpus
<
var
>.B.</
var
>
<
reg
norm
="
ſeſquialterum
"
type
="
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">ſeſquialterũ</
reg
>
ad ipſam
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reg
norm
="
aquam
"
type
="
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">aquã</
reg
>
,
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ſequetur
<
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type
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">proportionẽ</
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ponderis ipſius
<
var
>.A.</
var
>
ad
<
reg
norm
="
pondus
"
type
="
context
">põdus</
reg
>
ipſius
<
var
>.B.</
var
>
in aqua eſſe in propor-
<
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tione dupla; </
s
>
<
s
xml:id
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echoid-s2047
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xml:space
="
preserve
">Vnde ex primo ſuppoſito capitis ſecundi proportio velocitatis
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var
>.A.</
var
>
ad
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velocitatem
<
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>.B.</
var
>
in aqua dupla erit, non ſeſquialtera. </
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>
<
s
xml:id
="
echoid-s2048
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xml:space
="
preserve
">Si ergo proportio velocitatis
<
var
>.
<
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A.</
var
>
ad eam quæ eſt
<
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>.B.</
var
>
in aqua dupla eſt, & ea, quæeſt
<
var
>.B.</
var
>
in aere, ad eam, quæ eſt ipſius
<
lb
/>
per aquam eſt etiam dupla (vnde ea quę eſt
<
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>.A.</
var
>
per aquam ęqualis erit ei, quæ eſt
<
var
>.B.</
var
>
<
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peraerem, ex .9. lib. quinti) & cum ea, quæ eſt
<
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>.A.</
var
>
ſit ei, quæ eſt
<
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>.B.</
var
>
per aerem ſeſqui-
<
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altera, erit ergo ea, quæ eſt
<
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>.A.</
var
>
per aerem, ei, quæ eſt ſuimet ipſius per aquam ſeſqui
<
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altera, non autem dupla, ex .7. eiuſdem libr. quinti. </
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>
<
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xml:space
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">Hiſce rationibus accedimus ad
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confirmandam veritatem vltimi ſuppoſiti cap .2. proportionem videlicet velocita
<
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tis
<
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motus
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type
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>
naturalis in diuerſis medijs
<
reg
norm
="
alicuius
"
type
="
simple
">alicuiꝰ</
reg
>
corporis
<
reg
norm
="
ponderoſi
"
type
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">põderoſi</
reg
>
in ipſis medijs eſſe ean
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dem cum ea, quæeſt inter pondera
<
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<
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xlink:label
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fig-0183-02
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fig-0183-02a
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number
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246
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<
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file
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0183-02
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0183-02
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</
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>
dicti corporis in dictis medijs. de ijs
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tamen medijs intelligendo, quæ un-
<
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ctuoſa, aut pinguia non ſunt, ut ſunt
<
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oleum, lac, aut huiuſmodialia, quæà
<
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qualibet minima qualitate frigoris
<
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aut caloris alterantur, & impermea-
<
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biles fiunt.</
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