DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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habeat proportionem KH ad C, quàm ED ad EF.
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ſiquidẽ
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ſupponitur KM ad C ita eſſe, vt ED ad EF. Archimed es ve
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iò, vt demonſtratio abſ〈que〉 diſtinctione ſit vniuerſalis, prę
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cipit (exiſtente KH ipſi C commenſurabili, ſiue incommen
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ſurabili) vt auferatur pars aliqua minor exceſſu HL, ut AL,
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ita tamen, vt reliqua KN ſit commenſurabilis ipſi C. quod qui
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dem fieri poſſe oſtenſum eſt in proximo problemate. </
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<
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enim magnitudine KM partem abſcindere poſſumus, vt KN
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minorem quidem tota KM, maiorem verò KH, quæ ipſi
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C commenſurabilis exiſtat. </
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<
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">Cognita Archimedis demonſtratione de incommenſura
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bilibus magnitudinibus, idem alio quo〈que〉 modo oſtendere
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poſſumus, applicando nempè diuiſibilitatem, & commenſura
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bilitatem non magnitudinibus, verùm diſtantijs. </
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<
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priùs demonſtrata propoſitione. </
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<
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<
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">Si commenſurabiles diſtantię maiorem habuerint pro
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portionem, quàm magnitudines permutatim habent; vt
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ę〈que〉ponderent, maiori opus erit longitudine, quàm ſit
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ea, ad quam altera longitudo maiorem habet proportio
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nem. </
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number
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<
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">Sint diſtantiæ DE EH commenſurabiles, magnitudines
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verò ſint A C. habeatquè ED ad EH maiorem proportio
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nem, quàm A ad C. Dico vt AC ę〈que〉ponderent, maiori opus </
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