Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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<
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xml:space
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">Sit ſruſtum a e a pyramide, quæ triangularem baſim ha-
<
lb
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beat abſciſſum: </
s
>
<
s
xml:id
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xml:space
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">cuius maior baſis triangulum a b c, minor
<
lb
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d e f; </
s
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<
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xml:space
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">& </
s
>
<
s
xml:id
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xml:space
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">axis g h. </
s
>
<
s
xml:id
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xml:space
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">ducto autem plano per axem & </
s
>
<
s
xml:id
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xml:space
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">per lineã
<
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d a, quod ſectionem faciat d a k l quadrilaterum; </
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>
<
s
xml:id
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xml:space
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">puncta
<
lb
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K l lineas b c, e f bifariam ſecabunt. </
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<
s
xml:id
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xml:space
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">nam cum g h ſit axis
<
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ſruſti: </
s
>
<
s
xml:id
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"
xml:space
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">erit h centrum grauitatis trianguli a b c: </
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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">g
<
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centrum trianguli d e f: </
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<
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xml:space
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<
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fig-0181-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0181-01
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xml:space
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">3. diffi. hu
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ius.</
note
>
trum uero cuiuslibet triangu
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li eſt in recta linea, quæ ab an-
<
lb
/>
gulo ipſius ad dimidiã baſim
<
lb
/>
ducitur ex decimatertia primi
<
lb
/>
libri Archimedis de cẽtro gra
<
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uitatis planorum. </
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<
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xml:space
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xlink:label
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xml:space
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">Vltima e-
<
lb
/>
auſdẽ libri
<
lb
/>
Archime-
<
lb
/>
dis.</
note
>
trũ grauitatis trapezii b c f e
<
lb
/>
eſt in linea _K_ l, quod ſit m: </
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>
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xml:space
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<
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xml:space
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<
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puncto m ad axem ducta m n
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ipſi a k, uel d l æquidiſtante;
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</
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<
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xml:space
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">erit axis g h diuiſus in portio-
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nes g n, n h, quas diximus: </
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<
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xml:space
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<
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dem enim proportionem ha-
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bet g n ad n h, quã l m ad m _k_. </
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<
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At l m ad m K habet eam, quã
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duplum lateris maioris baſis
<
lb
/>
b c una cum latere minoris e f
<
lb
/>
ad duplum lateris e f unà cum
<
lb
/>
later b c, ex ultima eiuſdem
<
lb
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libri Archimedis. </
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<
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xml:space
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">Itaque à li-
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nea n g abſcindatur, quarta
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pars, quæ ſit n p: </
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xml:space
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<
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xml:id
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xml:space
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">ab axe h g abſcindatur itidem
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quarta pars h o: </
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<
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xml:space
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<
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xml:id
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xml:space
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">quam proportionem habet fruſtum ad
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pyramidem, cuius maior baſis eſt triangulum a b c, & </
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<
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tudo ipſi æqualis; </
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<
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<
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xml:space
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tatis fruſti eſſe in linea p o, & </
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<
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<
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eſſe in linea g h manifeſte conſtat. </
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<
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