Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0119
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DE CENTRO GRAVIT. SOLID.
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o n ipſi a c. </
s
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<
s
xml:id
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xml:space
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">Quoniam enim triangulorum a b k, a d k, latus
<
lb
/>
b k eſt æquale lateri k d, & </
s
>
<
s
xml:id
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xml:space
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">a k utrique commune; </
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>
<
s
xml:id
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xml:space
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">anguliq́;
<
lb
/>
</
s
>
<
s
xml:id
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xml:space
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">ad k recti baſis a b baſi a d; </
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<
s
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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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">reliqui anguli reliquis an-
<
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<
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xlink:label
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note-0119-01
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xlink:href
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note-0119-01a
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xml:space
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">8. primi</
note
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gulis æquales erunt. </
s
>
<
s
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xml:space
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">eadem quoqueratione oſtendetur b c
<
lb
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æqualis c d; </
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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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">a b ipſi
<
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<
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number
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75
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<
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0119-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0119-01
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b c. </
s
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<
s
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xml:space
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">quare omnes a b,
<
lb
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b c, c d, d a ſunt æqua-
<
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les. </
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<
s
xml:id
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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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">quoniam anguli
<
lb
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ad a æquales ſunt angu
<
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lis ad c; </
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<
s
xml:id
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xml:space
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">erunt anguli b
<
lb
/>
a c, a c d coalterni inter
<
lb
/>
ſe æquales; </
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<
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xml:space
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">itemq́; </
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<
s
xml:id
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xml:space
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">d a c,
<
lb
/>
a c b. </
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>
<
s
xml:id
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xml:space
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">ergo c d ipſi b a;
<
lb
/>
</
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>
<
s
xml:id
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xml:space
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">& </
s
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<
s
xml:id
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xml:space
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">a d ipſi b c æquidi-
<
lb
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ſtat. </
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>
<
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xml:space
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">Atuero cum lineæ
<
lb
/>
a b, c d inter ſe æquidi-
<
lb
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ſtantes bifariam ſecen-
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lb
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tur in punctis e g; </
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<
s
xml:id
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xml:space
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">erit li
<
lb
/>
nea l e k g n diameter ſe
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ctionis, & </
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<
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xml:space
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">linea una, ex
<
lb
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demonſtratis in uigeſi-
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lb
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ma octaua ſecundi coni
<
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/>
corum. </
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>
<
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xml:id
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xml:space
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">Et eadem ratione linea una m f k h o. </
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>
<
s
xml:id
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xml:space
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">Sunt autẽ a d,
<
lb
/>
b c inter ſe ſe æquales, & </
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>
<
s
xml:id
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xml:space
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">æquidiſtantes. </
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<
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xml:id
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xml:space
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">quare & </
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>
<
s
xml:id
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xml:space
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">earum di-
<
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midiæ a h, b f; </
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>
<
s
xml:id
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xml:space
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">itemq́; </
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>
<
s
xml:id
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xml:space
="
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">h d, f e; </
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>
<
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xml:id
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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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">quæ ipſas coniunguntrectæ
<
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<
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position
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xlink:label
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note-0119-02
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xlink:href
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note-0119-02a
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xml:space
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">33. primit</
note
>
lineæ æquales, & </
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<
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">æquidiſtantes erunt. </
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<
s
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">æquidiſtãt igitur b a,
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c d diametro m o: </
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<
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<
s
xml:id
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xml:space
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">pariter a d, b c ipſi l n æquidiſtare o-
<
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ſtendemus. </
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<
s
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xml:space
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">Si igitur manẽte diametro a c intelligatur a b c
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portio ellipſis ad portionem a d c moueri, cum primum b
<
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/>
applicuerit ad d, cõgruet tota portio toti portioni, lineaq́;
<
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</
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<
s
xml:id
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">b a lineæ a d; </
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<
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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">b c ipſi c d congruet: </
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>
<
s
xml:id
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xml:space
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">punctum uero e ca-
<
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det in h; </
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<
s
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">f in g: </
s
>
<
s
xml:id
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xml:space
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">& </
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<
s
xml:id
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">linea k e in lineam k h: </
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<
s
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<
s
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">k f in k g. </
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<
s
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">qua
<
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re & </
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<
s
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">el in h o, et fm in g n. </
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<
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">Atipſa lz in z o; </
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<
s
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">et m φ in φ n
<
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cadet. </
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<
s
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