Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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ARCHIMEDIS
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@e centro grauitatis ſolidorum demonstrauimus: </
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<
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xml:space
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">erit magnitudi-
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nis ex utriſque portionibus b n c, b g c conſtantis; </
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<
s
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xml:space
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">hoc eſt portionis
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in humido demerſa grauitatis centrum in linea n g, quæ ipſarum
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ſphæræ portionum centra graui-
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0026-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0026-01
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tatis coniungit. </
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teſt, ſit extra lineam n g, ut in
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q: </
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<
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<
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xml:space
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">portionis b n c centrum
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grauitatis u; </
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>
<
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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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">ducatur u q.</
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<
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<
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">Quoniam igitur à portione in bu-
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lb
/>
mido demerſa aufertur ſphæræ
<
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/>
portio b n c, non habens idem cen
<
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trum grauitatis: </
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>
<
s
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">erit ex octaua
<
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primi libri Archimcdis de centro
<
lb
/>
grauitatis planorum, reliquæ por
<
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tionis b g c centrum in linea u q
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producta. </
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<
s
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">quod fieri non potest; </
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<
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">eſt enim in axe ipſius mg. </
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<
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tur ergo ut portionis in humido demerſæ centrum grauitatis ſit in li
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nean k. </
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<
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xml:space
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">quod oſtendendum propoſuimus.</
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<
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xml:space
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</
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<
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xml:space
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">_Sed totius portionis grauitatis centrum eſt in linea ft, in-_
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_ter_ k, _& </
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<
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>
<
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">]_ Compleatur ſphæra, ut ſit portionis additæ
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axis t y; </
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<
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xml:space
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<
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">centrú grauitatis z. </
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">Itaque quoniá à tota ſphæra, cuius
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grauitatis cétrum eſt k, ut etiam in eodem libro demóſtrauimus, au
<
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">8. primi
<
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Archime
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dis.</
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>
fertur portio e y h centrú grauitatis habens z: </
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<
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e f h cétrú in linea z k producta. </
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<
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">quare inter k. </
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<
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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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">f neceſſario cadet.</
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<
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<
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">Reliquæ ergo figuræ, quæ eſt extra humidum, centrum erit
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in linea r x producta.</
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>
<
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">] _Ex eadem octaua primi libri Archime-_
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_dis de centro grauitatis planorum._</
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<
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_dum per rectam s l deorſum; </
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<
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_humido ſurſum per rectam r l.</
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">]_ Ex antecedenti poſitio-
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ne. </
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<
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">magnitudo @enim, quæ in humido demerſa est, tanta ui per li-
<
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neam r l ſurſum@fertur, quanta quæ extra humidum per li-
<
lb
/>
neam s l, deorſum: </
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>
<
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">id quod ex propoſitione ſexta huius li-
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briconſtare poteſt. </
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>
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">& </
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<
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">quoniam feruntur per alias, atque alias </
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