DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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pagenum
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54
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ſint æquales, erit G centrum grauitatis magnitudinis ex AF
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lb
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compoſitæ. </
s
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<
s
id
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N11E35
">quia verò AB eſt ipſi EF æqualis, reliqua BG
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lb
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ipſi GE æqualis exiſtet. </
s
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<
s
id
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N11E39
">& ſunt magnitudines BE ę〈que〉gra
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lb
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ues, erit idem G centrum grauitatis
<
expan
abbr
="
magnitudinũ
">magnitudinum</
expan
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BE. ſimili
<
lb
/>
ter cùm ſit BC æqualis DE, relin〈que〉tur CG ipſi GD ęqua
<
lb
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lis; magnitudinesquè CD ſunt ę〈que〉graues. </
s
>
<
s
id
="
N11E45
">ergo
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expan
abbr
="
pũctum
">punctum</
expan
>
G
<
expan
abbr
="
cẽ
">cem</
expan
>
<
lb
/>
trum eſt quo〈que〉 magnitudinum CD. Vnde ſequitur,
<
expan
abbr
="
punctũ
">punctum</
expan
>
<
lb
/>
G magnitudinis ex omnibus magnitudinibus ABCDEF
<
expan
abbr
="
cõ-poſitæ
">con
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lb
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poſitæ</
expan
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centrum grauitatis exiſtere. </
s
>
</
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type
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4
<
emph
type
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italics
"/>
huius.
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type
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</
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id
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type
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id
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Hoc quo〈que〉 loco verba illa
<
emph
type
="
italics
"/>
magnitudineſquè æqualem habuerint
<
lb
/>
grauitatem.
<
emph.end
type
="
italics
"/>
Græcus codex ita mendosè legit.
<
foreign
lang
="
grc
">καὶ τὰ μέσα αὔτης ἴσον
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lb
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βάρος ἔχωντι</
foreign
>
, quæ quidem verba hoc modo reſtitui poſſunt.
<
lb
/>
<
foreign
lang
="
grc
">καὶ τὰ μεγέθεα ἴσον βάρος ἔχωντι. </
foreign
>
</
s
>
</
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p
id
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type
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">
<
s
id
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*</
s
>
</
p
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<
p
id
="
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type
="
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">
<
s
id
="
N11E8A
">In præcedenti propoſitione oſtendit Archimedes, quomo
<
lb
/>
do ſe habet centrum grauitatis magnitudinis ex duabus ma
<
lb
/>
gnitudinibus ęqualibus compoſitæ. </
s
>
<
s
id
="
N11E90
">In hac autem
<
expan
abbr
="
demõſtrat
">demonſtrat</
expan
>
,
<
lb
/>
vbi ſimiliter grauitatis centrum reperitur inter plures magni
<
lb
/>
tudines æ〈que〉graues, & inter ſe ęqualiter diſtantes. </
s
>
<
s
id
="
N11E9A
">ex quibus
<
lb
/>
tandem colliget fundamentum ſæpiùs dictum. </
s
>
<
s
id
="
N11E9E
">nempè ſi ma
<
lb
/>
gnitudines ę〈que〉ponderare debent; ita ſe habebit magnitudi
<
lb
/>
num grauitas ad grauitatem, ut ſe habent diſtantiæ permuta
<
lb
/>
tim, ex quibus ſuſpenduntur. </
s
>
<
s
id
="
N11EA6
">& hoc demonſtrat Archimedes
<
lb
/>
in duabus ſe〈que〉ntibus propoſitionibus. </
s
>
<
s
id
="
N11EAA
">nam magnitudines,
<
lb
/>
vel ſunt commenſurabiles interſeſe, vel incommenſurabiles.
<
lb
/>
de commenſurabilibus aget in ſe〈que〉nti: de incommenſurabi
<
lb
/>
libus verò in ſeptima propoſitione. </
s
>
<
s
id
="
N11EB2
">& Archimedes duas
<
expan
abbr
="
ſe〈quẽ〉-tes
">ſe〈que〉n
<
lb
/>
tes</
expan
>
propoſitiones ueluti coniunctas proponit. </
s
>
<
s
id
="
N11EBA
">Nam in ſexta
<
lb
/>
inquit
<
emph
type
="
italics
"/>
Magnitudines commenſurabiles,
<
emph.end
type
="
italics
"/>
&c. </
s
>
<
s
id
="
N11EC4
">in ſeptima uerò in
<
lb
/>
quit,
<
emph
type
="
italics
"/>
Si autem magnitudines ſuerint incommenſurabiles,
<
emph.end
type
="
italics
"/>
quaſi vna
<
expan
abbr
="
tã
">tam</
expan
>
<
lb
/>
tùm ſit propoſitio in duas partes diuiſa. </
s
>
<
s
id
="
N11ED6
">ita ut ne〈que〉 numeris
<
lb
/>
eſſent diſtinguende, ſed pro vna tantùm propoſitione
<
expan
abbr
="
ſummẽ-dæ
">ſummen
<
lb
/>
dæ</
expan
>
, obſe〈que〉ntis autem demonſtrationis faciliorem
<
expan
abbr
="
intelligẽ-tiam
">intelligen
<
lb
/>
tiam</
expan
>
hęc priùs præmittimus. </
s
>
</
p
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<
p
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type
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head
">
<
s
id
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N11EE9
">LEMMA.</
s
>
</
p
>
<
p
id
="
N11EEB
"
type
="
main
">
<
s
id
="
N11EED
">Si duę fuerint magnitudines in æquales, quarum maior ſit
<
lb
/>
alterius dupla, tertia verò quędam magnitudo minorem </
s
>
</
p
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</
chap
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</
body
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