DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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<
chap
id
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N10019
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077/01/073.jpg
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pagenum
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69
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habebit proportionem kN ad C, quàm kM ad eandem
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lb
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C. tota verò KM ad C eſt, vt DE ad EF; ergo KN ad
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C minorem habet proportionem; quàm DE ad EF.
<
emph
type
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italics
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Quo
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niam igitur magnitudines AC,
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emph.end
type
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italics
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hoc eſt KN C,
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emph
type
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italics
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ſunt commenſurabi
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lb
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les, & minorem habet proportionem A,
<
emph.end
type
="
italics
"/>
hoc eſt kN
<
emph
type
="
italics
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ad C, quàm DE
<
lb
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ad EF; non æ〈que〉ponderabunt A C,
<
emph.end
type
="
italics
"/>
hoc eſt KN C,
<
emph
type
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italics
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ex distantiis
<
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type
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italics
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n
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<
lb
/>
<
emph
type
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DE EF, poſito quidem A,
<
emph.end
type
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italics
"/>
hoc eſt KN
<
emph
type
="
italics
"/>
ad F, C verò ad D.
<
emph.end
type
="
italics
"/>
&
<
lb
/>
vt æ〈que〉ponderent, oporter, vt in F maior ſit magnitudo,
<
lb
/>
quàm KN; ita vt ipſi C in D æ〈que〉ponderate poſſit. </
s
>
<
s
id
="
N12736
">Ac
<
lb
/>
propterea cùm ſit kH adhuc minor, quàm KN, ſi igitur
<
lb
/>
KH ponatur ad F, & C ad D, nullo modo æ〈que〉ponde
<
lb
/>
rabunt. </
s
>
<
s
id
="
N1273E
">quod tamen fieri non poteſt. </
s
>
<
s
id
="
N12740
">ſupponebatur enim eas
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lb
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æ〈que〉ponderare. </
s
>
<
s
id
="
N12744
">Non igitur magnitudo minor, quàm tota
<
lb
/>
KM in F magnitudini C in D æ〈que〉ponderat.
<
emph
type
="
italics
"/>
Eadem au
<
lb
/>
tem ratione, ne〈que〉 ſi C maior fuerit, quàm vt æ〈que〉ponderet ipſi A
<
emph.end
type
="
italics
"/>
B,
<
lb
/>
hoc eſt ipſi KM. etenim grauiore
<
expan
abbr
="
exiſtẽte
">exiſtente</
expan
>
C ad D, quàm KM
<
lb
/>
ad F. primùm auferatur ex C exceſſus, quo C grauior eſt,
<
lb
/>
quàm KM, ita vt æ〈que〉ponderet ipſi KM. Deinde rurſus
<
lb
/>
auferatur quædam magnitudo minor exceſſu, quo grauior
<
lb
/>
eſt C, quàm kM, ita vt æ〈que〉ponderent; reſiduum verò ſit
<
lb
/>
ipſi KM commenſurabile, & c. </
s
>
<
s
id
="
N12760
">ſimiliter oſtendetur
<
expan
abbr
="
nullã
">nullam</
expan
>
<
lb
/>
magnitudinem ipſa C minorem poſitam ad D vllo modo
<
lb
/>
æ〈que〉ponderare ipſi KM ad F poſitæ. </
s
>
<
s
id
="
N1276A
">Quare magnitudo
<
lb
/>
C ad D, kM verò ad F ę〈que〉ponderant. </
s
>
<
s
id
="
N1276E
">Vnde ſequitur ma
<
lb
/>
gnitudinis ex vtriſ〈que〉 magnitudinibus compoſitæ centrum
<
lb
/>
grauitatis eſſe punctum E. ac propterea incommenſurabiles
<
lb
/>
magnitudines AB C ex diſtantiijs ED EF, quæ permutatim
<
lb
/>
eandem habent proportionem, vt magnitudines, æ〈que〉pon
<
lb
/>
derare. </
s
>
<
s
id
="
N1277A
">quod demonſtrare oportebat. </
s
>
</
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<
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id
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<
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type
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ex proxi
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mo proble
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lb
/>
mate.
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type
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italics
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8.
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emph
type
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italics
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quinti.
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<
p
id
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N12791
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type
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">
<
s
id
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N12793
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<
margin.target
id
="
marg61
"/>
<
emph
type
="
italics
"/>
ex præce
<
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/>
denti.
<
lb
/>
ex prima
<
lb
/>
propoſitio
<
lb
/>
ne.
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emph.end
type
="
italics
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</
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</
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<
p
id
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type
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">
<
s
id
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N127A5
">SCHOLIVM.</
s
>
</
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>
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p
id
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">
<
s
id
="
N127A9
">In demonſtratione occurrit obſeruandum, quòd ſi exceſ
<
lb
/>
ſus HL ita diuideret magnitudinem KM, vt reſiduum KH
<
lb
/>
fuerit commenſurabile ipſi C; tunc abſ〈que〉 alia conſtructio
<
lb
/>
ne, magnitudines commenſurabiles KH C ex diſtantijs DE
<
lb
/>
EF æ〈que〉ponderarent; quod fieri non poteſt. </
s
>
<
s
id
="
N127B3
">cùm minorem </
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>
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p
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>
</
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>
</
archimedes
>