Cavalieri, Buonaventura
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Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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<
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<
s
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echoid-s2006
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xml:space
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">Sit ſolidum rotundum, APCQ, & </
s
>
<
s
xml:id
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echoid-s2007
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xml:space
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preserve
">conusicalenus, APEQM,
<
lb
/>
vtraque autem ſecentur plano per axem, quod producat figuram, A
<
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PCQ, in ſolido, & </
s
>
<
s
xml:id
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echoid-s2008
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xml:space
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preserve
">triangulum, APQ, in cono, deinde ſecentur
<
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altero plano, cuius, & </
s
>
<
s
xml:id
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echoid-s2009
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xml:space
="
preserve
">plani recti ad axem (quo productus ſit circu-
<
lb
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lus, PMQE,) communis ſectio ſit, EM, perpendicularis ipſi, PQ,
<
lb
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communi ſectioni eiuſdem, & </
s
>
<
s
xml:id
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echoid-s2010
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xml:space
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">plani per axem ducti. </
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<
s
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echoid-s2011
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xml:space
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">Dico figuram,
<
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BEDM, in ſolido rotundo eſſe circa axem, & </
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>
<
s
xml:id
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echoid-s2012
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xml:space
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">in cono circa axem,
<
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<
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position
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left
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xlink:label
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note-0100-01
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xlink:href
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note-0100-01a
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xml:space
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">6. Defin.</
note
>
vel diametrum, & </
s
>
<
s
xml:id
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echoid-s2013
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xml:space
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preserve
">axem, vel diametrum eſſe, BD, communem ſe-
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lb
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ctionem productarum figurarum. </
s
>
<
s
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echoid-s2014
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xml:space
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preserve
">Si ergo ſecundò producta figura
<
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per axem pariter ducta eſſet, manifeſtum eſt in ſolido rotundo fore
<
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<
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left
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xlink:label
="
note-0100-02
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xlink:href
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xml:space
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">33. huius.</
note
>
figuram talem circa axem, & </
s
>
<
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xml:space
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">in cono fore triangulum, in quo axis,
<
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<
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left
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xlink:label
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xlink:href
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note-0100-03a
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xml:space
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">16. huius.</
note
>
AC, ſi ſecaret æquidiſtantes baſi talis trianguli ad angulos rectos,
<
lb
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cum illas bifariam diuidat, eſſet talis triangulus figura circa axem, ſi
<
lb
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verò ad angulos non rectos, eſſet figura circa diametrum, nempè
<
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circa, AC. </
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xml:space
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">Sed non tranſeat hęc ſecunda figura per axem, ſint au-
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tem puncta, B, D, extrema communis ſectionis primæ, & </
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>
<
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echoid-s2017
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xml:space
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">ſecundę
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figuræ, ideſt ip-
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55
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0100-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0100-01
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ſius, BD, ergo
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in ſolido rotun-
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do (& </
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<
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xml:space
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">in-cono,
<
lb
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dum triangulus,
<
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APQ, per axem
<
lb
/>
ductus tranſit e-
<
lb
/>
tiam per ductam
<
lb
/>
à vertice, A, per-
<
lb
/>
pẽdicularem ipſi
<
lb
/>
baſi, PEQM,
<
lb
/>
ideſt cum trian-
<
lb
/>
gulus, APQ, eſt
<
lb
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erectus baſi, PE
<
lb
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QM,) ipſa, EM, communis ſectio ſecundi plani ſecantis, &</
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<
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">, PQ,
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<
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xlink:href
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xml:space
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">4. Defin.
<
lb
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vndec. El.</
note
>
plani rectè axim ſecantis, cum ſit perpendicularis, PQ, communi ſe-
<
lb
/>
ctioni planorum, PEQM, APQ, ad inuicem erectorum, erit etiam
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perpendicularis plano per axem, & </
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>
<
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="
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xml:space
="
preserve
">ideò erit perpendicularis ad om-
<
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nes per eam in tali plano tranſeuntes, ideò, BD, rectè ſecabit ipſam,
<
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EM, & </
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<
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xml:space
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">quæ ducuntur per extrema, BD, æquidiſtantes ipſi, EM,
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tangent ipſa ſolida, vnde, B, D, erunt oppoſiti vertices figurarum,
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BEDM, reſpectu ipſius, EM, ſumptarum, quare, BD, ſecabit
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xml:space
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">1. Defin.</
note
>
omnes illi æquidiſtantes in figura, BEDM, ductas, & </
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>
<
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<
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<
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">Corol. 2.
<
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4. Huius.</
note
>
in figura, BEDM, puncto, qui non ſit vertex reſpectu ipſius, EM,
<
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& </
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<
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">ab eo ducta eidem, EM, parallela intra figuram cadit, ſit is pun-
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<
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4. Huius.</
note
>
ctus, O, à quo ipſi, EM, ſit ducta parallela ipſa, OR, igitur, </
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