Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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132
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FED. COMMANDINI
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centrum z: </
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xml:id
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echoid-s3348
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xml:space
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">parallelogram mi a d, θ: </
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<
s
xml:id
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echoid-s3349
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xml:space
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">parallelogrammi f g, φ:
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</
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<
s
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echoid-s3350
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xml:space
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<
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<
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fig-0132-01
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88
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0132-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0132-01
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parallelogrammi c g centrũ
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ψ: </
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<
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">atque erit ω punctum me
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dium uniuſcuiuſque axis, ui
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delicet eius lineæ, quæ oppo
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ſitorum planorũ centra con
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iungit. </
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<
s
xml:id
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echoid-s3354
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xml:space
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">Dico ω centrum effe
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grauitatis ipſius ſolidi. </
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<
s
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enim, ut demonſtrauimus,
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xlink:label
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note-0132-01
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note-0132-01a
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">6. huius</
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ſolidi a f centrum grauitatis
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in plano K n; </
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<
s
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xml:space
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">quod oppoſi-
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tis planis a d, g f æ quidiſtans
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reliquorum planorum late-
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ra biſariam diuidit: </
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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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">fimili
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rationeidem centrum eſt in plano o r, æ quidiſtante planis
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a e, b f oppo ſitis. </
s
>
<
s
xml:id
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xml:space
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">ergo in communi ipſorum fectione: </
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<
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xml:id
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xml:space
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">ui-
<
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delicet in linea y z. </
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>
<
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xml:id
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"
xml:space
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">Sed eſt etiam in plano t u, quod quidẽ
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y z ſecat in ω. </
s
>
<
s
xml:id
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echoid-s3362
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xml:space
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preserve
">Conſtat igitur centrum grauitatis ſolidi eſſe
<
lb
/>
punctum ω, medium ſcilicet axium, hoc eſt linearum, quæ
<
lb
/>
planorum oppoſitorum centra coniungunt.</
s
>
<
s
xml:id
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xml:space
="
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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 aliud prima a f; </
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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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">in eo plana, quæ opponuntur, tri-
<
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angula a b c, d e f: </
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<
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xml:id
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xml:space
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">diuiſisq; </
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>
<
s
xml:id
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xml:space
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">bifariam parallelogrammorum
<
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/>
lateribus a d, b e, c f in punctis g h κ, per diuiſiones planũ
<
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/>
ducatur, quod oppoſitis planis æ quidiſtans faciet ſe ctionẽ
<
lb
/>
triangulum g h k æ quale, & </
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>
<
s
xml:id
="
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xml:space
="
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">ſimile ipſis a b c, d e f. </
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<
s
xml:id
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xml:space
="
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">Rurſus
<
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diuidatur a b bifariam in l: </
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<
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xml:id
="
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xml:space
="
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">& </
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<
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xml:id
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xml:space
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">iuncta c l per ipſam, & </
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>
<
s
xml:id
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xml:space
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">per
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c _K_ f planum ducatur priſma ſecans, cuius, & </
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<
s
xml:id
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xml:space
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">parallelogrã
<
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mi a e communis ſcctio ſit l m n. </
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<
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xml:id
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xml:space
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">diuidet pun ctum m li-
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neam g h bifariam; </
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<
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xml:space
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<
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xml:id
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">ita n diuidet lineam d e: </
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>
<
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xml:id
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xml:space
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">quoniam
<
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triangula a c l, g k m, d f n æ qualia ſunt, & </
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<
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xml:space
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">ſimilia, ut ſu pra
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<
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xlink:label
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note-0132-02
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note-0132-02a
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xml:space
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">5. huius</
note
>
demonſtrauimus. </
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<
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">Iam ex iis, quæ tradita ſunt, conſtat cen
<
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trum greuitatis priſmatis in plano g h k contineri. </
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<
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xml:space
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">Dico
<
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ipſum eſſe in linea k m. </
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>
<
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xml:space
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">Si enim fieri poteſt, ſit o centrum;</
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>
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