Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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118FED. COMMANDINI do in reliquis figuris æquilateris, & æquiangulis, quæ in cir-
culo deſcribuntur, probabimus cẽtrum grauitatis earum,
&
centrum circuli idem eſſe. quod quidem demonſtrare
oportebat.
Ex quibus apparet cuiuslibet figuræ rectilineæ
in circulo plane deſcriptæ centrum grauitatis idẽ
eſſe, quod &
circuli centrum.
Figuram in circulo plane deſcriptam appella-
11γνωρ@ μω@ mus, cuiuſmodi eſt ea, quæ in duodecimo elemen
torum libro, propoſitione ſecunda deſcribitur.
ex æqualibus enim lateribus, & angulis conſtare
perſpicuum eſt.
THEOREMA II. PROPOSITIO II.
Omnis figuræ rectilineæ in ellipſi plane deſcri-
ptæ centrum grauitatis eſt idem, quod ellipſis
centrum.
Quo modo figura rectilinea in ellipſi plane deſcribatur,
docuimus in commentarijs in quintam propoſitionem li-
bri Archimedis de conoidibus, &
ſphæroidibus.
Sit ellipſis a b c d, cuius maior axis a c, minor b d: iun-
ganturq́;
a b, b c, c d, d a: & bifariam diuidantur in pun-
ctis e f g h.
à centro autem, quod ſit k ductæ lineæ k e, k f,
k g, k h uſque ad ſectionem in puncta l m n o protrahan-
tur:
& iungantur l m, m n, n o, o l, ita ut a c ſecet li-
neas l o, m n, in z φ punctis, &
b d ſecet l m, o n in χ ψ.
erunt l k, k n linea una, itemq́ue linea unaipſæ m k, k o:
&
lineæ b a, c d æquidiſtabunt lineæ m o: & b c, a d ipſi
l n.
rurſus l o, m n axi b d æquidiſtabunt: & l