Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
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1236DE CENTRO GRAVIT. SOLID. habebit maiorem proportionẽ,
79[Figure 79] quam c b ad b a.
fiat o b ad b a,
ut figura rectilinea ad portio-
nes.
cum igitur à circulo, uel el-
lipſi, cuius grauitatis centrum
eſt b, auferatur figura rectilinea
e f g h k l m n, cuius centrum a;
reliquæ magnitudinis ex portio
118. Archi-
medis.
nibus compoſitæ centrum graui
tatis erit in linea a b producta,
&
in puncto o, extra figuram po
ſito.
quod quidem fieri nullo mo
do poſſe perſpicuum eſt.
ſequi-
tur ergo, ut circuli &
ellipſis cen
trum grauitatis ſit punctum a,
idem quod figuræ centrum.
ALITER.
Sit circulus, uel ellipſis a b c d,
cuius diameter d b, &
centrum e: ducaturq; per e recta li
nea a c, ſecans ipſam d b adrectos angulos.
erunt a d c,
a b c circuli, uel ellipſis dimidiæ portiones.
Itaque quo-
niam por
80[Figure 80] tiõis a d c
cétrū gra-
uitatis eſt
in diame-
tro d e:
&
portionis
a b c cen-
trum eſt ĩ
ipſa e b:
to
tius circu
li, uel ellipſis grauitatis centrum eritin diametro d b.
Sit autem portionis a d c cẽtrum grauitatis f: &

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