Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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0100
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GEOMETRIÆ
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<
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<
s
xml:id
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echoid-s2006
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xml:space
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preserve
">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
="
echoid-s2008
"
xml:space
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preserve
">triangulum, APQ, in cono, deinde ſecentur
<
lb
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altero plano, cuius, & </
s
>
<
s
xml:id
="
echoid-s2009
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xml:space
="
preserve
">plani recti ad axem (quo productus ſit circu-
<
lb
/>
lus, PMQE,) communis ſectio ſit, EM, perpendicularis ipſi, PQ,
<
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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
xml:id
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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, & </
s
>
<
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xml:id
="
echoid-s2012
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xml:space
="
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">in cono circa axem,
<
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<
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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
="
echoid-s2013
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xml:space
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">axem, vel diametrum eſſe, BD, communem ſe-
<
lb
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ctionem productarum figurarum. </
s
>
<
s
xml:id
="
echoid-s2014
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xml:space
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">Si ergo ſecundò producta figura
<
lb
/>
per axem pariter ducta eſſet, manifeſtum eſt in ſolido rotundo fore
<
lb
/>
<
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left
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xlink:label
="
note-0100-02
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xlink:href
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note-0100-02a
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xml:space
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preserve
">33. huius.</
note
>
figuram talem circa axem, & </
s
>
<
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xml:id
="
echoid-s2015
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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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note-0100-03
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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.</
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AC, ſi ſecaret æquidiſtantes baſi talis trianguli ad angulos rectos,
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cum illas bifariam diuidat, eſſet talis triangulus figura circa axem, ſi
<
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/>
verò ad angulos non rectos, eſſet figura circa diametrum, nempè
<
lb
/>
circa, AC. </
s
>
<
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="
echoid-s2016
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xml:space
="
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">Sed non tranſeat hęc ſecunda figura per axem, ſint au-
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lb
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tem puncta, B, D, extrema communis ſectionis primæ, & </
s
>
<
s
xml:id
="
echoid-s2017
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xml:space
="
preserve
">ſecundę
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figuræ, ideſt ip-
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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
<
lb
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in ſolido rotun-
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do (& </
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<
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="
echoid-s2018
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xml:space
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">in-cono,
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dum triangulus,
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APQ, per axem
<
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ductus tranſit e-
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tiam per ductam
<
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/>
à vertice, A, per-
<
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pẽdicularem ipſi
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baſi, PEQM,
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ideſt cum trian-
<
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gulus, APQ, eſt
<
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/>
erectus baſi, PE
<
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QM,) ipſa, EM, communis ſectio ſecundi plani ſecantis, &</
s
>
<
s
xml:id
="
echoid-s2019
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xml:space
="
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">, PQ,
<
lb
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<
note
position
="
left
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xlink:label
="
note-0100-04
"
xlink:href
="
note-0100-04a
"
xml:space
="
preserve
">4. Defin.
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vndec. El.</
note
>
plani rectè axim ſecantis, cum ſit perpendicularis, PQ, communi ſe-
<
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/>
ctioni planorum, PEQM, APQ, ad inuicem erectorum, erit etiam
<
lb
/>
perpendicularis plano per axem, & </
s
>
<
s
xml:id
="
echoid-s2020
"
xml:space
="
preserve
">ideò erit perpendicularis ad om-
<
lb
/>
nes per eam in tali plano tranſeuntes, ideò, BD, rectè ſecabit ipſam,
<
lb
/>
EM, & </
s
>
<
s
xml:id
="
echoid-s2021
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xml:space
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">quæ ducuntur per extrema, BD, æquidiſtantes ipſi, EM,
<
lb
/>
tangent ipſa ſolida, vnde, B, D, erunt oppoſiti vertices figurarum,
<
lb
/>
BEDM, reſpectu ipſius, EM, ſumptarum, quare, BD, ſecabit
<
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<
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xml:space
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">1. Defin.</
note
>
omnes illi æquidiſtantes in figura, BEDM, ductas, & </
s
>
<
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xml:id
="
echoid-s2022
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xml:space
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">quia ſumpto
<
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<
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xlink:label
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note-0100-06
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note-0100-06a
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xml:space
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">Corol. 2.
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4. Huius.</
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>
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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note-0100-07a
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">Coroll. 1.
<
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4. Huius.</
note
>
ctus, O, à quo ipſi, EM, ſit ducta parallela ipſa, OR, igitur, </
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