Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0045
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rhead
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DE IIS QVAE VEH. IN AQVA.
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<
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<
s
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">SIT portio, qualis dicta eſt, & </
s
>
<
s
xml:id
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xml:space
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">in humidum demittatur,
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ſicuti diximus, adeo ut baſis eius in uno puncto contingat
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/>
humidum. </
s
>
<
s
xml:id
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xml:space
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">demonſtrandum eſtnon manere ipſam portio-
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/>
nem, ſed reuoluiita, ut baſis nullo modo humidi ſuperſicie
<
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xlink:label
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note-0045-01
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contingat. </
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>
<
s
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xml:space
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">Secta enim ipſa per axem, plano ad ſuper ſiciem
<
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humidi recto, ſit ſectio ſuperſiciei portionis a p o l re-
<
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ctãguli coni ſe
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0045-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0045-01
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ctio: </
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ciei humidi ſe-
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ctio ſit a s: </
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<
s
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xml:space
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">axis
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lb
/>
autem portio-
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nis, ac ſectio-
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lb
/>
nis diameter n
<
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/>
o: </
s
>
<
s
xml:id
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xml:space
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">& </
s
>
<
s
xml:id
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xml:space
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">ſccetur in
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f quidẽ ita, ut
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o f ſit dupla ip
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ſius ſn; </
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<
s
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xml:space
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">in ω ue
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lb
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ro, ut n o ad
<
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/>
f ω eandem ha
<
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beat proportionem, quam quindecim ad quatuor: </
s
>
<
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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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">ipſi
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n o ad rectos angulos ducatur ω k. </
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>
<
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xml:space
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">Itaque quoniam n o
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ad f ω maiorem habet proportionem, quàm ad eam, quæ
<
lb
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uſque ad axem; </
s
>
<
s
xml:id
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xml:space
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">ſit ei, quæ uſque ad axem æqualis f b: </
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>
<
s
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xml:space
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">& </
s
>
<
s
xml:id
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xml:space
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catur p c quidem ipſi a s æquidiſtans, cõtingensq; </
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<
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xml:space
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nem a p o l in p; </
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<
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xml:space
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<
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xml:space
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ſecet pi ipſam κ ω in h. </
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>
<
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xml:space
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">Quoniã ergo in portione a p o l,
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xlink:label
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xlink:href
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note-0045-03a
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note
>
quæ continetur recta linea, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">rectanguli coni ſectione, κ ω
<
lb
/>
quidem æ quidiſtans eſtipſi a l; </
s
>
<
s
xml:id
="
echoid-s980
"
xml:space
="
preserve
">p i uero diametro æquidi-
<
lb
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ſtat: </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">ſecaturq; </
s
>
<
s
xml:id
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"
xml:space
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">ab ipſa κ ω in h: </
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>
<
s
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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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">a s æquidiſtat contingen-
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ti in p: </
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>
<
s
xml:id
="
echoid-s985
"
xml:space
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preserve
">neceſſarium eſtipſam p i ad p h uel ean dem pro-
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lb
/>
portionem habere, quam habet n ω ad ω o, uel maiorem:
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lb
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</
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>
<
s
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">hocenim iam demonſtratum eſt. </
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<
s
xml:id
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xml:space
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">At uero n ω ſeſquialtera
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eſt ipſius ω o. </
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>
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xml:space
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>
<
s
xml:id
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xml:space
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">pi igitur uel ſeſquialtera eſt ipſius h p; </
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<
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uel maior, quàm ſeſquialtera. </
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>
<
s
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xml:space
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">Quare ph ipſius h i aut du
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