Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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nem, quam ad eam, quæ uſque ad axem.</
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_ter portioms n o ad f ω proportionem eandem, quam quindeeim ad_
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_quatuor; </
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<
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">ad eam uero, quæ uſque ad axem minorem proportionem_
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_habere ponitur, quàm quindecim ad quatuor. </
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<
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">quare n o ad f ω ma_
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_iorem habebit proportionem, quàm ad eam, quæ uſque ad axem: </
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<
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_propterea quæ uſque ad axem ipſa f ω maior erit_.
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<
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<
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">Quoniam ergo in portione a p o l, quæ continetur re-
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cta linea, & </
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<
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">rectanguli coni ſectione, _k_ ω quidem æ quidi-
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ſtans eſt ipſi a l; </
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<
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">p i uero diametro æquidiſtat; </
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</
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<
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<
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xml:space
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">a c æquidiſtat contingenti in p neceſ-
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ſarium eſt ipſam p i ad p h uel eandem proportionem ha
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bere, quam habet n ω ad ω o, uel maiorem. </
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<
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">hoc enim iam
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demonſtratum eſt] _Vbi hoc demonſtratum ſit uel ab ipſo Ar-_
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_chimede, uel ab alio, numdum apparet, quocircanos demonstra-_
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_tionem afferemus, poſteaquam non nulla, quæ ad eam pertinent ex-_
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_plicauerimus_.</
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<
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<
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<
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puncto d, quod in linea a c ſumptum ſit, ducantur d e,
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d f utcunque ad ipſam a b. </
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<
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<
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">nea quotlibet punctis g l, ducantur g h, l m ipſi d e
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æquidistantes; </
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<
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xml:space
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<
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">g k, l n æquidiſtantes f d. </
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<
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punctis d, g uſque ad lineam m l ducantur, d o p qui
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dem ſecans g h in o; </
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<
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xml:space
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<
s
xml:id
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">g q, quæ æquidistent ipſi b a. </
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Dico lineas, quæ inter æquidiſtantes ipſi f d ad eas, quæ
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inter æquidiſtantes d e interiiciuntur, uidelicet k n ad g q,
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uel ad o p; </
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<
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">f n ad d p eandem inter ſe ſe
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proportionem habere: </
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<
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