Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VII.
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<
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">THEOREMA XIII. PROPOS. XIII.</
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">SI, expoſitis duabus quibuſcumq; </
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<
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xml:space
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">ſolidorum rectangu-
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lorum deſcriptibilium regulis, ad vnum punctum cõ-
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poſitis, iuxta eaſdem ſolidum rectangulum contineatur
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ſub parallelogrammo, & </
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<
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xml:space
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">alia quacumq; </
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<
s
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xml:space
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">figura plana in
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ambitu contenti ſolidi exiſtente, ipſum ſolidum rectangu-
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lum erit cylindricus, & </
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<
s
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xml:space
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">figura plana ſuperius dicta erit il-
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lius baſis. </
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<
s
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echoid-s13424
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xml:space
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preserve
">Quod ſi etiam prædicta figura fuerit parallelo-
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grammum, & </
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<
s
xml:id
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echoid-s13425
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xml:space
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">ambo in illius ambitu, contentum ijſdem
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ſolidum rectangulum erit parallelepipedum.</
s
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<
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"/>
</
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<
s
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xml:space
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">Exponantur duæ inuicem perpendiculares regulæ, BC, CD, ſo-
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lidorũ deſcriptib liũ ſub parallelogrammo, AC, & </
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<
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xml:id
="
echoid-s13428
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xml:space
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">figura plana qua
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cumque, HDC, ſit autem deſcriptum ſolidum rectangulum ſub eiſ-
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<
figure
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fig-0539-01
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fig-0539-01a
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number
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355
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0539-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0539-01
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</
figure
>
dem contentum, AG
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CH, iuxta regulas, B
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C, CD, ita tamen vt
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figura plana, HDC,
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ſit in ambitu ipſius
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contenti ſolidi. </
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<
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xml:space
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">Di-
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co, AGCH, eſſe cy-
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lindricum. </
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<
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">Quod. </
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<
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</
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<
s
xml:id
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xml:space
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">AC, CG, GH, ſint
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ſuperficies cylindra-
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ceæ, quarum regula,
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BC, manifeſtum eſt,
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quod verò latera per
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ſecantia para lela plana in ipſis deſignata ſint æqualia ipſi, BC, la-
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teri parallelogrammi, AC, ex dictis etiam cõſtare poteſt, ſed maio-
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ris dilucidationis gratia ſit ab aliquo dictorum ſecantium planorũ,
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in ſolido, AGHC, productum rectangulum, IMON, eſt ergo, IN,
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æqualis, MO, hoc eſt ipſi, BC, quo pacto idem de cæteris oſten-
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demus, in parallelogrammo autem, GC, eadem verificantur, & </
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<
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">in
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illi oppoſito, ſi contactus plani ipſi, GC, oppoſiti eſſent in plano,
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vt manifeſtum eſt, ergo perinde eſt ac ſi latus æquale, BC, ambitũ
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note-0539-01a
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xml:space
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preserve
">Def. 3. l. 1.</
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figuræ, HDC, extremo ſui puncto ſemper ipſi, BC, æquidiſtanter
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percuriſſet ipſam ſuperficiem, ADBH, deſcribendo, erit ergo, A
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GCH, cylindricus, cuius baſis eſt, HDC, figurá. </
s
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<
s
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="
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xml:space
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">Præfatum qui-
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dem ſolidum habet in ambitu figuras ipſum continentes, ſed ſi </
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