Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRI Æ
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neo, TGEOX, eſſe ve, RF, adportion
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em, SET, ergo ex æquali
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o nnia quadrata portionis, SMT, cum rectangulis bis ſub eadem,
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& </
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">ſub quadrilineo, MTXC, ad omnia quadrata portionis, SET,
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cum rectangulis bis ſub eadem, & </
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">ſub quadrilineo, TGEOX,
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erunt vt portio, SMT, ad portionem, SET, quod oſtendere o-
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portebat.</
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">_H_INC patet omnia quadrata parallelogrammorum in eadem al-
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titudine cum portionibus, vel portionum fruſtibus exiſtentium,
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vna cum rectangulis bis ſub ijſdem parallelogrammis, & </
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<
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">reliquis pa-
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rallelogram nis illis in directum exiſtentibus, ad omnia quadrata por.
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</
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<
s
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">tionum, vel fruſtorum eorundem, ſimul cumrectangulis bis ſub ijſdem,
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& </
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<
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">ſub quadrilineis illis in directum iacentibus, veluti fuerunt quadri-
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lineun, MTXC, TGEOX, eſſe, vt dicta parallelogramma ad di-
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ctas portiones, vel portionum fruſta; </
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<
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">quodex prædictis clarè patet; </
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Vnde ex. </
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<
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">omnia quadrata, RG, ſimul cum rectangulis bis ſub paral-
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lelogrammis, RG, GX, ad omnia quadrata fruſti, SBGT, cum re-
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ctangulis bis ſub, SGBT, & </
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<
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">quadrilineo, TG, PX, erunt vt paral-
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lelogrammum, RG, ad fruſtum, SBGT, hoc .</
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<
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">pariter oſtendetur,
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veluti probatum eſt omnia quadrata, HV, ſimul cum rectangulis bis
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ſub, HV, VC, ad omnia quadrata portionis, SMT, ſimul cum re-
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ctingulis bis ſub eadem, & </
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">ſub quadrilineo, MTXC, eſſe vt, HV,
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ad portionem, SMT, vnde manifeſtum eſt, quod in hoc Corollaris
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colligitur.</
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">SIin circulo, vel ellipſi apteturrecta linea, per cuius ex-
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trema puncta ducantur duæ rectæ lineæ, quæ ſint (exi-
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ſtente apta parallela vniaxium, vel diametrorum) paralle-
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læ ſecundo axi, vel diametro, quæ ſumatur pro regula: </
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<
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">Re-
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ctangula ſub portione minori abſciſſa per aptatam, & </
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<
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">ſub
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quadrilineo, quodaptata, & </
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">duabus dictis parallelis vſque
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ad curuam circuli, vel ellipſis productis, & </
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">ab ijſdem inclu-
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ſa curua comprehenditur, in circulo, erunt æqualia rectan-
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gulis ſub duobus triangulis per diametrum quadrati, vel
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rhombi (& </
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">hoc in ellipſicum diametri coniugatę ſe obliquę
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ſecabunt, quibus latera dictirhombi ſint æquidiſtantia) </
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