Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0173
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DE CENTRO GRAVIT. SOLID.
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<
s
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xml:space
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">SIT fruſtum pyramidis a e, cuius maior baſis triangu-
<
lb
/>
lum a b c, minor d e f: </
s
>
<
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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">oporteat ipſum plano, quod baſi
<
lb
/>
æquidiſtet, ita ſecare, ut ſectio ſit proportionalis inter triã
<
lb
/>
gula a b c, d e f. </
s
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<
s
xml:id
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echoid-s4327
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xml:space
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preserve
">Inueniatur inter lineas a b, d e media pro-
<
lb
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portionalis, quæ ſit b g: </
s
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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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">à puncto g erigatur g h æquidi-
<
lb
/>
ſtans b e, ſecansq; </
s
>
<
s
xml:id
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xml:space
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">a d in h: </
s
>
<
s
xml:id
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"
xml:space
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">deinde per h ducatur planum
<
lb
/>
baſibus æ quidiſtans, cuius ſectio ſit triangulum h _k_ 1. </
s
>
<
s
xml:id
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echoid-s4332
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xml:space
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preserve
">Dico
<
lb
/>
triangulum h K l proportionale eſſe inter triangula a b c,
<
lb
/>
d e f, hoc eſt triangulum a b c ad
<
lb
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0173-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0173-01
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triangulum h K l eandem habere
<
lb
/>
proportionem, quam triãgulum
<
lb
/>
h K l ad ipſum d e f. </
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>
<
s
xml:id
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xml:space
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">Quoniã enim
<
lb
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lineæ a b, h K æquidiſtantium pla
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xlink:label
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note-0173-01a
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xml:space
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">16. unde
<
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cimi</
note
>
norum ſectiones inter ſe æquidi-
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ſtant: </
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<
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xml:id
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xml:space
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">atque æquidiſtant b _k_, g h:
<
lb
/>
</
s
>
<
s
xml:id
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xml:space
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">linea h _k_ ipſi g b eſt æqualis: </
s
>
<
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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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">pro
<
lb
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<
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xlink:label
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note-0173-02
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xlink:href
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note-0173-02a
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xml:space
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">34. primi</
note
>
pterea proportionalis inter a b,
<
lb
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d e. </
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>
<
s
xml:id
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xml:space
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">quare ut a b ad h K, ita eſt h
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style
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emph
>
<
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ad d e. </
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>
<
s
xml:id
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xml:space
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">fiat ut h k ad d e, ita d e
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lb
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ad aliam lineam, in qua ſit m. </
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<
s
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xml:space
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">erit
<
lb
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ex æquali ut a b ad d e, ita h k ad
<
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m. </
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<
s
xml:id
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xml:space
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">Et quoniam triangula a b c,
<
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<
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note-0173-03
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xlink:href
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note-0173-03a
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xml:space
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">9. huius
<
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/>
corol.</
note
>
h K l, d e f ſimilia ſunt; </
s
>
<
s
xml:id
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xml:space
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">triangulū
<
lb
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a b c ad triangulum h k l eſt, ut li-
<
lb
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<
note
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right
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xlink:label
="
note-0173-04
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xlink:href
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note-0173-04a
"
xml:space
="
preserve
">20. ſexti</
note
>
nea a b ad lineam d e: </
s
>
<
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xml:space
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">triangulũ
<
lb
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autem h k l ad ipſum d e f eſt, ut h _k_ ad m. </
s
>
<
s
xml:id
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xml:space
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">ergo tríangulum
<
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<
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xlink:label
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note-0173-05
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note-0173-05a
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xml:space
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">11. quinti</
note
>
a b c ad triangulum h k l eandem proportionem habet,
<
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quam triangulum h K l ad ipſum d e f. </
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>
<
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xml:space
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">Eodem modo in a-
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liis fruſtis pyramidis idem demonſtrabitur.</
s
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</
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<
p
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<
s
xml:id
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xml:space
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">Sit fruſtum coni, uel coni portionis a d: </
s
>
<
s
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xml:space
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preserve
">& </
s
>
<
s
xml:id
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xml:space
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">ſecetur plano
<
lb
/>
per axem, cuius ſectio ſit a b c d, ita ut maior ipſius baſis ſit
<
lb
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circulus, uel ellipſis circa diametrum a b; </
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>
<
s
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">minor circa c d.
<
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</
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>
<
s
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xml:space
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">Rurſus inter lineas a b, c d inueniatur proportionalis b e: </
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>
<
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xml:space
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<
lb
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& </
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>
<
s
xml:id
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"
xml:space
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">ab e ducta e ſ æquid_i_ſtante b d, quæ lineam c a in f </
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>
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