DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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<
archimedes
>
<
text
>
<
body
>
<
chap
id
="
N10019
">
<
p
id
="
N118A1
"
type
="
main
">
<
s
id
="
N11913
">
<
pb
xlink:href
="
077/01/048.jpg
"
pagenum
="
44
"/>
gnitudine ex
<
expan
abbr
="
plurib^{9}
">pluribus</
expan
>
magnitudinibus compoſita accipere po
<
lb
/>
terimus, veluti Archimedes in ſe〈que〉ntibus accipiet. </
s
>
</
p
>
<
p
id
="
N1191D
"
type
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main
">
<
s
id
="
N1191F
">Argumentandi modus in eſt in hac demonſtratione maxi
<
lb
/>
ma conſideratione dignus, & huius ſcientiæ maximè pro
<
lb
/>
prius. </
s
>
<
s
id
="
N11925
">cùm enim dixiſſet Archimedes poſito centro grauitatis
<
lb
/>
magnitudinis ex AB compoſitæ in puncto D, ſtatim infert.
<
lb
/>
<
emph
type
="
italics
"/>
Quoniam igitur punctum D centrum eſt grauitatis magnitudinis ex
<
lb
/>
AB compoſita, ſuſpenſo puncto D, magnitudines AB æ〈que〉pondera
<
lb
/>
bunt.
<
emph.end
type
="
italics
"/>
hoc eſt ſi magnitudo ex AB compoſita ſuſpendatur ex
<
lb
/>
D, manebit, vt reperitur; nec amplius in alteram partem in cli
<
lb
/>
nabit. </
s
>
<
s
id
="
N11938
">quod euenit ob naturam centri grauitatis, quod talis
<
lb
/>
eſt naturæ (ſicuti initio explicauimus) ut ſi graue in eius cen
<
lb
/>
tro grauitatis ſuſtineatur, eo modo manet, quo reperitur,
<
expan
abbr
="
dũ
">dum</
expan
>
<
lb
/>
ſuſpenditur; parteſquè undiquè æ〈que〉ponderant. </
s
>
<
s
id
="
N11944
">& ob id ſi
<
lb
/>
magnitudo ex AB compoſita ſuſpendatur in eius centro gra
<
lb
/>
uitatis, manet; parteſquè AB æ〈que〉ponderant. </
s
>
<
s
id
="
N1194A
">ac propterea
<
lb
/>
quando in ſe〈que〉ntibus quærit Archimedes, quoniam grauia
<
lb
/>
æ〈que〉ponderare debent, tunc tantùm quærit ipſorum
<
expan
abbr
="
cẽtrum
">centrum</
expan
>
<
lb
/>
grauitatis, ut in ſexta, ſeptimaquè propoſitione in quit Archi
<
lb
/>
medes magnitudines ę〈que〉ponderare ex diſtantijs, quę permu
<
lb
/>
tatim proportionem habent, ut ipſarum grauitates, in
<
expan
abbr
="
demõ
">demom</
expan
>
<
lb
/>
ſtratione tamen quærit, vbi nam eſt
<
expan
abbr
="
cẽtrum
">centrum</
expan
>
grauitatis magni
<
lb
/>
tudinis ex vtrisquè compoſitę. </
s
>
<
s
id
="
N11966
">quo inuento, ſtatim neceſſariò
<
lb
/>
ſequitur, magnitudines, ſi ex ipſo centro ſuſpendantur, æ〈que〉
<
lb
/>
ponderare. </
s
>
</
p
>
<
p
id
="
N1196C
"
type
="
main
">
<
s
id
="
N1196E
">Hinc colligere poſſumus alterum argumentandi modum,
<
lb
/>
conuerſo nempè modo, veluti in eadem figura, ſi dicamus
<
lb
/>
grauia AB ſuſpenſa ex C æ〈que〉ponderant, ſtatim inferre
<
lb
/>
poſſumus, punctum C ipſorum ſimul grauium, hoc eſt ma
<
lb
/>
gnitudinis ex ipſis AB compoſitę centrum eſſe grauitatis.
<
lb
/>
Quare ad ſe inuicem conuertuntur, hoc punctum eſt horum
<
lb
/>
grauium centrum grauitatis; ergo hęc grauia ex hoc puncto
<
lb
/>
æqùeponderant; & è conuerſo, nempè hæc grauia ex hoc pun
<
lb
/>
cto æ〈que〉ponderant, ergo idem punctum eſt ipſorum
<
expan
abbr
="
cẽtrum
">centrum</
expan
>
<
lb
/>
grauitatis. </
s
>
<
s
id
="
N11986
">ſed ad uertendum hanc ſequi
<
expan
abbr
="
conuertibilitatẽ
">conuertibilitatem</
expan
>
,
<
expan
abbr
="
quã-do
">quan
<
lb
/>
do</
expan
>
præfatum punctum eſt in recta linea, quæ centra grauita
<
lb
/>
tum ponderum coniungit; deinde quando hęc linea non eſt </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>