Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0045
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45
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rhead
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DE IIS QVAE VEH. IN AQVA.
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<
s
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xml:space
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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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echoid-s961
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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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note-0045-01a
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contingat. </
s
>
<
s
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echoid-s962
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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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26
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0045-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0045-01
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ctio: </
s
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<
s
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">ſuperſi-
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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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/>
autem portio-
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nis, ac ſectio-
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/>
nis diameter n
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o: </
s
>
<
s
xml:id
="
echoid-s965
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s966
"
xml:space
="
preserve
">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
xml:id
="
echoid-s967
"
xml:space
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">in ω ue
<
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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
>
<
s
xml:id
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echoid-s968
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s969
"
xml:space
="
preserve
">ipſi
<
lb
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n o ad rectos angulos ducatur ω k. </
s
>
<
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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
<
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uſque ad axem; </
s
>
<
s
xml:id
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echoid-s971
"
xml:space
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">ſit ei, quæ uſque ad axem æqualis f b: </
s
>
<
s
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xml:space
="
preserve
">& </
s
>
<
s
xml:id
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echoid-s973
"
xml:space
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">du
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catur p c quidem ipſi a s æquidiſtans, cõtingensq; </
s
>
<
s
xml:id
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xml:space
="
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">ſectio-
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nem a p o l in p; </
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>
<
s
xml:id
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xml:space
="
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">pi uero æquidiſtans ipſi n o: </
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<
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xml:space
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>
<
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xml:space
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">primum
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ſecet pi ipſam κ ω in h. </
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>
<
s
xml:id
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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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xml:space
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">C</
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-
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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: </
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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">a s æquidiſtat contingen-
<
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/>
ti in p: </
s
>
<
s
xml:id
="
echoid-s985
"
xml:space
="
preserve
">neceſſarium eſtipſam p i ad p h uel ean dem pro-
<
lb
/>
portionem habere, quam habet n ω ad ω o, uel maiorem:
<
lb
/>
</
s
>
<
s
xml:id
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xml:space
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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. </
s
>
<
s
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="
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s989
"
xml:space
="
preserve
">pi igitur uel ſeſquialtera eſt ipſius h p; </
s
>
<
s
xml:id
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xml:space
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<
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uel maior, quàm ſeſquialtera. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Quare ph ipſius h i aut du
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<
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