Full text: Archimedes: Archimedis De iis qvae vehvntvr in aqva libri dvo

DE CENTRO GRAVIT. SOLID. æquidiſtant autem c g o, m n p. ergo parallelogrãma ſunt
o n, g m, & linea m n æqualis c g; & n p ipſi g o. aptatis igi-
tur K l m, a b c triãgulis, quæ æqualia & ſimilia sũt; linea m p
in c o, & punctum n in g cadet. Quòd cũ g ſit centrum gra-
uitatis trianguli a b c, & n trianguli K l m grauitatis cen-
trum erit id, quod demonſtrandum relinquebatur. Simili
ratione idem contingere demonſtrabimus in aliis priſma-
tibus, ſiue quadrilatera, ſiue plurilatera habeant plana,
quæ opponuntur.

69.1.

10. unde
cimi
10. unde-
cimi
4. ſexti
0126-01
per 5. pe-
titionem
Archime
dis.

70. COROLLARIVM.

Exiam demonſtratis perſpicue apparet, cuius
Iibet priſmatis axem, parallelogrammorum lat eri
bus, quæ ab oppoſitis planis ducũtur æquidiſtare.

71. THEOREMA VI. PROPOSITIO VI.

Cuiuslibet priſmatis centrum grauitatis eſt in
plano, quod oppoſitis planis æquidiſtans, reli-
quorum planorum latera bifariam diuidit.

Sit priſma, in quo plana, quæ opponuntur ſint trian-
gula a c e, b d f: & parallelogrammorum latera a b, c d,
e f bifariam diuidãtur in punctis g h _K_: per diuiſiones au-
tem planum ducatur; cuius ſectio figura g h _K_. eritlinea
g h æquidiſtans lineis a c, b d & h k ipſis c e, d f. quare ex
decimaquinta undecimi elementorum, planum illud pla
nis a c e, b d f æquidiſtabit, & ſaciet ſectionem figu-
ram ipſis æqualem, & ſimilem, ut proxime demonſtra-
uimus. Dico centrum grauitatis priſmatis eſſe in plano
g h K . Si enim fieri poteſt, ſit eius centrum l: & ducatur
l m uſque ad planum g h K , quæ ipſi a b æquidiſtet.

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