Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0014
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ARCHIMEDIS
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<
s
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xml:space
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">SECETVR ſuperficies aliqua plano per k punctum
<
lb
/>
ducto: </
s
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<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">ſicſectio ſemper circuli circunferentia, centrum
<
lb
/>
habens punctum k. </
s
>
<
s
xml:id
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xml:space
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">Dico eam ſphæræ ſuperficiem eſſe. </
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<
s
xml:id
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xml:space
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<
lb
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enim non eſt ſphæræ ſuperfi-
<
lb
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0014-01
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cies; </
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<
s
xml:id
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xml:space
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">rectæ lineæ, quæ à pun-
<
lb
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cto k ad circunferentiam du-
<
lb
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cuntur non omnes æquales e-
<
lb
/>
runt. </
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>
<
s
xml:id
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xml:space
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">Itaque ſint a b puncta
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lb
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in ſuperficie; </
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xml:space
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<
s
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xml:space
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">inæquales li-
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lb
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neæ a k k b: </
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<
s
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xml:space
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">per ipſas autem
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lb
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a k k b planum ducatur, quod
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lb
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ſectionem faciat in ſuperficie
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lb
/>
lineam d a b c. </
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>
<
s
xml:id
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xml:space
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">ergo d a b c cir
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lb
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culi circunferentia eſt, cuius
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lb
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centrum k; </
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<
s
xml:id
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xml:space
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">quoniam ſuperficies eiuſmodi ponebatur: </
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xml:space
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">& </
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<
s
xml:id
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xml:space
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<
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idcirco æquales inter ſe ſunt a k k b, ſed & </
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xml:id
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">inæquales; </
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<
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xml:space
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<
lb
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fieri non poteſt. </
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>
<
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xml:id
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xml:space
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">conſtat igitur ſuperficiem eam eſſe ſphæ-
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lb
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ræ ſuperficiem.</
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xml:id
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xml:space
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</
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<
head
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head
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<
emph
style
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emph
>
humidi conſiſtentis, atque manen-
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tis ſuperficies ſphærica eſt; </
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<
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xml:id
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eſtidem, quod centrum terræ.</
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</
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<
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<
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xml:space
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">:
<
lb
/>
& </
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>
<
s
xml:id
="
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xml:space
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">ſecetur ipſius ſuperficies plano per centrum terræ du-
<
lb
/>
cto. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">ſit autem terræ centrum k: </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
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"
xml:space
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">ſuperficieiſectio, linea
<
lb
/>
a b c d. </
s
>
<
s
xml:id
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"
xml:space
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preserve
">Dico lineam a b c d circuli circunferentiam eſſe, cu
<
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/>
ius centrum k. </
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>
<
s
xml:id
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xml:space
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">Si enim non eſt, rectæ lineæ à puncto k ad
<
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lineam a b c d ductæ non erunt æquales. </
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>
<
s
xml:id
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xml:space
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">Sumatur recta li
<
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nea quibuſdam quidem à puncto k ad ipſam a b c d ductis
<
lb
/>
maior; </
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>
<
s
xml:id
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xml:space
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">quibuſdam uero minor; </
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>
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xml:space
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>
<
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">ex centro k, </
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