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

FED. COMMANDINI ctiones circuli ex prima propofitione ſphæricorum Theo
doſii: unus quidem circa triangulum a b c deſcriptus: al-
ter uero circa d e f: & quoniam triangula a b c, d e f æqua-
lia ſunt, & ſimilia; erunt ex prima, & ſecunda propoſitione
duodecimi libri elementorum, circuli quoque inter ſe ſe
æquales. poſtremo a centro g ad circulum a b c perpendi
cularis ducatur g h; & alia perpendicularis ducatur ad cir
culum d e f, quæ ſit g _k_; & iungantur a h, d k. perſpicuum
eſt ex corollario primæ ſphæricorum Theodoſii, punctum
h centrum eſſe circuli a b c, & k centrum circuli d e f. Quo
niam igitur triangulorum g a h, g d K latus a g eſt æquale la
teri g d; ſunt enim à centro ſphæræ ad ſuperficiem: atque
eſt a h æquale d k: & ex ſexta propoſitione libri primi ſphæ
ricorum Theodoſii g h ipſi g K: triangulum g a h æquale
erit, & ſimile g d k triangulo: & angulus a g h æqualis an-
gulo d g _K_. ſed anguli a g h, h g d ſunt æquales duobus re-
ctis. ergo & ipſi h g d, d g k duobus rectis æquales erunt. & idcirco h g, g _K_ una, atque eadem erit linea. cum autem
h ſit centrũ circuli, & tri-
anguli a b c grauitatis cen
trũ probabitur ex iis, quæ
in prima propoſitione hu
ius tradita funt. quare g h
erit pyramidis a b c g axis. & ob eandem cauſſam g k
axis pyramidis d e f g. Ita-
que centrum grauitatis py
ramidis a b c g ſit púctum
l, & pyramidis d e f g ſit m. Similiter ut ſupra demon-
ſtrabimus m g, g linter ſe æquales eſſe, & punctum g graui
tatis centrum magnitudinis, quæ ex utriſque pyramidibus
conſtat. eodem modo demonſtrabitur, quarumcunque
duarum pyramidum, quæ opponuntur, grauitatis centrũ

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