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