Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBERI.
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<
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xml:space
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tur ab eiſdem in conicos: </
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<
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xml:space
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">Etſiſecetur vtcumque planis
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coincidentibus omnibus eiuſdem lateribus, ſolida ab ijſdem
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abſciſſa verſus verticem erunt pariter conici, & </
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<
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xml:space
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">eorum baſes
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ipſæ ſiguræ abſcindentes.</
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<
s
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">Sit quilibet conicus, AMV, ſectus plano vtcum que per verticem
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ducto, quod in eo producat triangulum, ACD. </
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<
s
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xml:space
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">Dico ab hoc pla-
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no ſecante in conicos, ACVD, ACMD, fuiſſe diuiſum. </
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">Sin. </
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telligamus latus trianguli, ACD, quod ſit, AC, vel, AD, inni-
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xum puncto, A, indefinitè productum ferri per rectam, CD, ipſa
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deſcribet ſuperriciem trianguli, ACD, ad modum ſuperficiei coni-
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cularis, eſt autem reliqua, quę inſiſtit ambitui, CVD, ſic deſcripta,
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ergo tota ſuperficies, ACDV, eſt co-
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">AD, ef.4.</
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nicularis deſcripta latere, AC, vel, AD,
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properante per circuitum figuræ planæ,
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CVD, ergo erit, ACVD, conicus,
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cuius baſis ipſa figura, CVD, & </
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tex, A. </
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">Eodem modo oſtendemus, A
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CMD, eſſe conicum, cuius baſis, CM
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D, vertex, A. </
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<
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xml:space
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">Secetur nunc plano vt-
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cumque omnibus conici, AMV, late-
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ribus concidente, quod in eo producat
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figuram, BNEO. </
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<
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">Dico, ANO, eſſe
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conicum, cuius baſis figura, BNEO,
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vertex, A, nam dum latus conici, AM
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V, properat per circuitum baſis, CMD
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V, vt deſcribat eius conicularem ſuperficiem, properat etiam per
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circuitum figurę, BNEO, & </
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<
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">deſcribit ſupra ipiam ſuperficiem co-
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nicularem, igitur ſuperficies ab eadem figura, BE, ablciſia verſus,
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A, eſt conicularis, & </
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<
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">ſolidum comprehenſum ab ipſa, & </
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<
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xml:space
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">figura pla-
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na, BNEO, erit conicus, & </
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<
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xml:space
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">eiuſdem baſis ipſa figura, BNEO,
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vertex autem, A, quod oſtendere opus erat.</
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xml:space
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">_H_Inc habetur, ſi planum tranſeat per verticem conici, & </
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bet rectam lineam intra baſim conici exiſtentem, qui quidem ſe-
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cetur alio plano coincidente cum omnibus eiuſdem conici </
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