Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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_ propoſitionis demonſtratio iniuria temporum deſidera-
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tur, quam nos ita reſtituimus, ut ex figuris, quæ remanſerunt Archi
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medem ſcripſiſſe colligi potuit: </
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<
s
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">neque enim eas immutare uiſum est,
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quæ uero ad declarationem, explicationémque addenda fuerant, in
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commentarijs ſuppleuimus, id quod etiam præstitimus in ſecunda
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propoſitione ſecundi libri.</
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<
s
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">_SI aliqua magnitudo ſolida leuior humido.</
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<
s
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">]_ Ea uerba,
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leuior bumido, nos addidimus, quæ in translatione non erant; </
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<
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niam de eiuſmodi magnitudinibus in bac propoſitione agitur.</
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<
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<
s
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">In humidũ demittatur, ita ut baſis portionis nõ tangat hu
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midum.</
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<
s
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">] _Hoc est in humidum ita demitt atur, ut baſis ſurſum ſpe_
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_ctet; </
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<
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">uertex autem deorſum. </
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<
s
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">quod quidem opponitur ei, quod in ſe-_
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_quenti dixit._ </
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<
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">In humidum demittatur, ita ut baſis tota ſit in
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humido. </
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<
s
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">_His enim uerbis ſignificat portionem oppoſito modo in_
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_humidum demitti, ut ſcilicet uertex ſurſum; </
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<
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">baſis autem deorſum_
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_uergat. </
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<
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">eodem dicendi modo frequenter uſus est in ſecundo libro; </
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_quo de portionibus conoidis rectangulitractatur._</
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<
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">ſphæræ portio axẽ habet in linea,_
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_quæ à cẽtro ſphæræ ad eius baſim perpẽdicularis ducitur.</
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Iungatur enim b c, & </
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<
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</
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<
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<
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">quoniam duo circuli a b c d, e f b
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ſecant ſe ſe in punctis b c; </
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">recta linea, quæ ipſorum centra coniun-
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git, uidelicet k l lineam b c bifariam, & </
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ut in commentarij s in Ptolemæi planiſpbærium oſtendimus. </
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<
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">quare
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portionis circuli b n c diameter eſt m n; </
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<
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">portionis b g c diame-
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ter m g: </
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<
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">nam rectæ lineæ, quæ ipſi b c æquidistantes ex utraque
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parte ducuntur, cum linea n g rectos angulos faciunt; </
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<
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ipſa bifariam ſecantur. </
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<
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">portionis igitur ſpbæræ b n c axis eſt n m;
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</
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<
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<
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">portionis b g c axis m g. </
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<
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">ex quo ſequitur, portionis in bumido
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demerſæ axem eſſe in linea k l; </
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<
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tis centrum cuius libet ſpbæræ portionis ſit in axe; </
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<
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