Clavius, Christoph
,
Geometria practica
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LIBER QVINTVS.
"/>
latera aquæ in aſſeribus arcæ, vt habeatur altitudo aquæ vſque ad arcæ fundũ:
<
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</
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<
s
xml:id
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xml:space
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">Extracto deinde corpore, ita tamen, vt nihil aquæ extra arcam cadat, notentur
<
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rurſum latera aquæ, poſtquam quieuerit. </
s
>
<
s
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echoid-s10987
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xml:space
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">Quod ſi per cap. </
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<
s
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xml:space
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">1. </
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>
<
s
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">huius lib. </
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>
<
s
xml:id
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xml:space
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">metia-
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mur duo parallelepipeda, quorũ baſis communis eſt arcæ fundus, ſiue baſis, al-
<
lb
/>
titudines vero rectæ à lateribus aquæ notatis vſque ad baſem, & </
s
>
<
s
xml:id
="
echoid-s10991
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xml:space
="
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">minus à maio-
<
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re ſubtrahamus, relinquetur parallelepipedũ ſoliditati corporis propoſiti o-
<
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/>
mnino æquale. </
s
>
<
s
xml:id
="
echoid-s10992
"
xml:space
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preserve
">quod parallelepipedũ etiam conſequeris, ſi altitu dinem inter
<
lb
/>
latera aquæ bis notata duces in baſem arcæ. </
s
>
<
s
xml:id
="
echoid-s10993
"
xml:space
="
preserve
">Sunt, qui infuſa a qua in arcam,@la-
<
lb
/>
tera eius in aſſeribus primo loco notent. </
s
>
<
s
xml:id
="
echoid-s10994
"
xml:space
="
preserve
">Deinde impoſito corpore, eiuſdem a-
<
lb
/>
quæ latera ſignent. </
s
>
<
s
xml:id
="
echoid-s10995
"
xml:space
="
preserve
">Si enim altitudo inter poſteriora latera, ac priora ducatur in
<
lb
/>
baſem arcæ, pro ducetur ſoliditas corporis impoſiti.</
s
>
<
s
xml:id
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xml:space
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</
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<
s
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xml:space
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">2. </
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<
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vrnis, at que amphoris, ſiue eæ lapideæ ſint, ſiue cretaceæ, ita fa cie-
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mus. </
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>
<
s
xml:id
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xml:space
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">Impleatur vas arena, & </
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>
<
s
xml:id
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xml:space
="
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">eius orificiumita obturetur, vt a qua ingredi nul-
<
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lo modo poſsit. </
s
>
<
s
xml:id
="
echoid-s11001
"
xml:space
="
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">Impoſito deinde vaſe in aqua intra arcam contenta, ac ſi eſſet
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/>
corpus quod piam irregulare, inueſtigetur eius ſoliditas, vt Num. </
s
>
<
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xml:space
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">1. </
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>
<
s
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">diximus. </
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<
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xml:space
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">De-
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inde extra cta arena, notentur latera aquæ, antequam vas vacuum impo natur.
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/>
</
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<
s
xml:id
="
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xml:space
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">Impoſito denique vaſe vacuo, ſignentur iterum latera a quæ. </
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<
s
xml:id
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xml:space
="
preserve
">Si namque altitu-
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do inter poſteriora, ac priora latera multiplicetur per baſem arcæ: </
s
>
<
s
xml:id
="
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xml:space
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">pro creabitur
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ſoliditas ſolius vaſis: </
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>
<
s
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xml:space
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">quæ detracta ex priori ſoliditate, notamrelin quet vaſis
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/>
@apacitatem.</
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>
<
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</
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</
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<
head
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">DE SVPERFICIE CONVEXA
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coni & cylindri recti.</
head
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<
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<
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>
XII.</
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<
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">1. </
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<
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<
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>
ex Archimede demonſtrauimus, qua ratione ſuperficies
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<
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xlink:label
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note-265-01
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xlink:href
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note-265-01a
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xml:space
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">Superficies co-
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nica, dempta
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baſe, cui cir-
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culo ſit æqua-
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lis.</
note
>
conuexa, ſphæræ eiuſque portionum inueſtiganda ſit: </
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>
<
s
xml:id
="
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xml:space
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">non deerit for-
<
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taſſe, qui idem deſi deret in cono, ac cylindro recto. </
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>
<
s
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xml:space
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">quod ex ijs, quæ
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ab eo dem Archimede in lib. </
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<
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">1. </
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<
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">de ſphęra, & </
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<
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xml:space
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">cylindro demonſtrata ſunt, obtine-
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bit hoc modo. </
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<
s
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xml:space
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">Propoſito cono recto quo cunque, erit eius ſuperficies conue-
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xa conica, ſecluſa baſe, æqualis circulo, cuius ſemidiameter eſt linea media pro-
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portionalis inter latus coni, & </
s
>
<
s
xml:id
="
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xml:space
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">ſemidiametrum baſis eiuſdem coni, ex propoſ.
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</
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<
s
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position
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xlink:label
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note-265-02
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">Superficies
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fruſti coni,
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demptis baſi-
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bus, cui circu-
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lo æqualis ſit.</
note
>
14. </
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<
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<
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<
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">Archimedis de ſphęra, & </
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<
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">cylindro.</
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</
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<
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<
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<
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ſi conus rectus ſecetur plano, quod baſi æquidiſtet, erit ſuperfi-
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cies conuexa fruſti coni, demptis baſibus, æqualis circulo, cuius ſemidiameter
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eſt linea media proportionalis inter latus conicum fruſti, & </
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>
<
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">rectam ex ſemidia-
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metris duarũ baſum cõflatã, ex ꝓpoſ. </
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<
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<
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">lib. </
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<
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">Archime. </
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<
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">de ſphęra, & </
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<
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">cylindro.
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</
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<
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xml:id
="
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xml:space
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<
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xlink:label
="
note-265-03
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note-265-03a
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xml:space
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">Propo tio co-
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nicæ ſuperfi-
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ciei ad ſuam
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baſem.</
note
>
</
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</
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<
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<
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<
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style
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ſuperficies conica coni recti ad ſuam baſem, proportionẽ habet ean-
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dem, quam latus coni ad ſemidiametrum baſis coni eiuſdem, ex propoſ. </
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<
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<
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">lib.
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</
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<
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">1. </
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<
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xml:id
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xml:space
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">Archimedis de ſphæra, & </
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<
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xml:id
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">cylindro.</
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<
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</
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<
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<
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<
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<
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style
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>
ſuperficies conuexa cylindrirecti, demptis baſibus, æqualis
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<
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position
="
right
"
xlink:label
="
note-265-04
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xlink:href
="
note-265-04a
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xml:space
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">Superficies cy
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lindrica dem
<
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ptis baſibus,
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cui circulo ſit
<
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æqualis.</
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>
eſt circulo, cuius ſemidia meter eſt linea media proportio nalis inter latus cylin-
<
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dri, & </
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>
<
s
xml:id
="
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xml:space
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">diametrũ baſis cylin dri eiuſdem, ex propoſ. </
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<
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">13. </
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<
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">lib. </
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<
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">1. </
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<
s
xml:id
="
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xml:space
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">Archimedis de ſphę-
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ra & </
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>
<
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="
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">cylindro.</
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<
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</
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<
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