Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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<
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xml:space
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">DE AREA SPHÆROIDIS, EIVSDEM-
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que portionum.</
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<
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VII.</
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<
s
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<
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Ellipſis ABCD, cuius maior axis AC, minor B D, priorem ad angulos
<
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rectos ſecans. </
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>
<
s
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">Soliditatem ergo Sphæroidis, id eſt, ſolidi ex circumuolu-
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tione Ellipſis circa axem effecti, ita nanciſcemur. </
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<
s
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xml:space
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">Quoniam planum per
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BD, ductum, & </
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<
s
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xml:space
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">rectum ad axem AC, circulum facit, vt à Federico Commandi-
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no ad propoſ. </
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<
s
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echoid-s10823
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">12. </
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<
s
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">lib. </
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<
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">Archimedis de Conoidibus, & </
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<
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">Sphæroidib. </
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<
s
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echoid-s10827
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">demonſtratur.
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</
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<
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">cuius diameter BD, & </
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<
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">centrum E; </
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<
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">erit per propoſ. </
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<
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<
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">lib. </
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<
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xml:space
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">Archimedis de Cono-
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id. </
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>
<
s
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="
echoid-s10834
"
xml:space
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">& </
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<
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">Sphæroid. </
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>
<
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="
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xml:space
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">ſemiſsis Sphæroidis A B D, dupla coni ean dem baſem cum illa
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ſemiſſe, circulum videlicet diametri B D, habentis, & </
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>
<
s
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="
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">altitudinem eandem E A. </
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<
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Igitur ſi huius coni ſoliditas per capit. </
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<
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">2. </
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<
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">huius lib. </
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<
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">inueſtigetur, & </
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">duplicetur,
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note-262-01
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note-262-01a
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">Soliditas Sphæ
<
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roidis.</
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>
exurget ſoliditas ſemiſsis Sphæroidis: </
s
>
<
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xml:space
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">quæ duplicata ſoliditatem totius Sphę-
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roidis exhibebit.</
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>
<
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="
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</
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<
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<
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">2. </
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<
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<
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>
minori axi B D, parallela F G, ſecans maiorem axemin H,
<
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ad rectos angulos. </
s
>
<
s
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echoid-s10847
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xml:space
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">Si igitur per F G, ducatur planum rectum ad axem, fiet cir-
<
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culus in Sphæroide diametrum habens F G, & </
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>
<
s
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="
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xml:space
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">centrum H, vt Federicus Com-
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mandinus ad propoſ. </
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<
s
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">12. </
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<
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">lib. </
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<
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">Archim. </
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<
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">de Conoid. </
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<
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xml:space
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">& </
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<
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">Sphæroid. </
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<
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">demonſtrauit; </
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262-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/262-01
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ſcindentur que portiones Sphæroidis F A G, minor & </
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FCG, maior. </
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<
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">Vtriuſq; </
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<
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">ſoliditas ita fiet cognita. </
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<
s
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niam per propoſ. </
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<
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<
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">libri Archimedis de Conoid. </
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<
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xml:space
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">& </
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<
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<
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<
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xlink:label
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note-262-02a
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">Solidit{as} por-
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tionum Sphæ-
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roidis.</
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>
Sphęroid. </
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>
<
s
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="
echoid-s10865
"
xml:space
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">Conus, cuius baſis circulus diametri F G, & </
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<
s
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="
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<
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axis H A, ad minorem portionem ſphęroidis F A G,
<
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/>
proportionẽ habet, quam maioris portionis axis HC,
<
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/>
ad ſummam rectarum EC, HC: </
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>
<
s
xml:id
="
echoid-s10867
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xml:space
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">Si fiat, vt HC, maioris
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portionis axis ad ſummam rectarum E C, H C, ita co-
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nus prædictus ad aliud, (qui quidem conus ex cap. </
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<
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</
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<
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">huius libri cognitus erit.) </
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<
s
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">prodibit ſoliditas minoris
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portionis ſphęroidis F A G.</
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<
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</
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<
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<
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<
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quia per propoſ. </
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<
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">33. </
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<
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">libri Archim. </
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<
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">de Conoid. </
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>
<
s
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xml:space
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">& </
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<
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">Sphæroid. </
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>
<
s
xml:id
="
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"
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">conus,
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cuius baſis circulus diametri F G, & </
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>
<
s
xml:id
="
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xml:space
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">axis H C, ad maiorem portionem Sphęro-
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idis FCG, proportionem habet, quam minoris portionis axis HA, ad ſummam
<
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rectarum E A, H A: </
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>
<
s
xml:id
="
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xml:space
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">ſi fiat, vt H A, minoris portionis axis ad ſummam rectarum
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EA, HA, ita prædictus conus (quem per cap. </
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>
<
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">2. </
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<
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">huius lib. </
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<
s
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"
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">metieris) ad aliud, pro-
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creabitur ſoliditas maioris portionis ſphęroidis FCG.</
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<
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</
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<
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">DE AREA CONOIDIS
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parabolici.</
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<
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VIII.</
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<
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<
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<
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<
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>
Parabola A B C, cuius axis B D, ad baſem A C, rectus. </
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>
<
s
xml:id
="
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"
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">Solidita-
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<
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position
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xlink:label
="
note-262-03
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xlink:href
="
note-262-03a
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xml:space
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">Soliditas Co-
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noidis Para-
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bolici.</
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>
tem igitur Conoidis parabolici, quod parabola circa axem circumducta
<
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effi cit, ita metiemur. </
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>
<
s
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">Quo niam per ea, quæ ad prop oſ. </
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<
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">12. </
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<
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">libri Archim.</
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