Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
centrum z: parallelogram mi a d, θ: parallelogrammi f g, φ:
parallelogrammi d h, χ: &
Figure: /permanent/library/4E7V2WGH/figures/0132-01 not scanned
[Figure 88]
parallelogrammi c g centrũ
ψ:
atque erit ω punctum me
dium uniuſcuiuſque axis, ui
delicet eius lineæ, quæ oppo
ſitorum planorũ centra con
iungit.
Dico ω centrum effe
grauitatis ipſius ſolidi.
eſt
enim, ut demonſtrauimus,
6. huiusſolidi a f centrum grauitatis
in plano K n;
quod oppoſi-
tis planis a d, g f æ quidiſtans
reliquorum planorum late-
ra biſariam diuidit:
& fimili
rationeidem centrum eſt in plano o r, æ quidiſtante planis
a e, b f oppo ſitis.
ergo in communi ipſorum fectione: ui-
delicet in linea y z.
Sed eſt etiam in plano t u, quod quidẽ
y z ſecat in ω.
Conſtat igitur centrum grauitatis ſolidi eſſe
punctum ω, medium ſcilicet axium, hoc eſt linearum, quæ
planorum oppoſitorum centra coniungunt.
Sit aliud prima a f; & in eo plana, quæ opponuntur, tri-
angula a b c, d e f:
diuiſisq; bifariam parallelogrammorum
lateribus a d, b e, c f in punctis g h κ, per diuiſiones planũ
ducatur, quod oppoſitis planis æ quidiſtans faciet ſe ctionẽ
triangulum g h k æ quale, &
ſimile ipſis a b c, d e f. Rurſus
diuidatur a b bifariam in l:
& iuncta c l per ipſam, & per
c _K_ f planum ducatur priſma ſecans, cuius, &
parallelogrã
mi a e communis ſcctio ſit l m n.
diuidet pun ctum m li-
neam g h bifariam;
& ita n diuidet lineam d e: quoniam
triangula a c l, g k m, d f n æ qualia ſunt, &
ſimilia, ut ſu pra
5. huiusdemonſtrauimus.
Iam ex iis, quæ tradita ſunt, conſtat cen
trum greuitatis priſmatis in plano g h k contineri.
Dico
ipſum eſſe in linea k m.
Si enim fieri poteſt, ſit o centrum;

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