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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1215DE CENTRO GRAVIT. SOLID. quo ſcilicet ln, om conueniunt. Poſtremo in figura
a p l q b r m s c t n u d x o y centrum grauitatis trian
guli pay, &
trapezii ploy eſtin linea a z: trapeziorum
uero lqxo, q b d x centrum eſtin linea z k:
& trapeziorũ
b r u d, r m n u in k φ:
& denique trapezii m s t n; & triangu
li s c t in φ c.
quare magnitudinis ex his compoſitæ centrū
in linea a c conſiſtit.
Rurſus trianguli q b r, & trapezii q l
m r centrum eſt in linea b χ:
trapeziorum l p s m, p a c s,
a y t c, y o n t in linea χ φ:
trapeziiq; o x u n, & trianguli
x d u centrum in ψ d.
totius ergo magnitudinis centrum
eſtin linea b d.
ex quo ſequitur, centrum grauitatis figuræ
a p l q b r m s c t n u d x o y eſſe punctū _K_, lineis ſcilicet a c,
b d commune, quæ omnia demonſtrare oportebat.
THE OREMA III. PROPOSITIO III.
Cuiuslibet portio-
77[Figure 77] nis circuli, &
ellipſis,
quæ dimidia non ſit
maior, centrum graui
tatis in portionis dia-
metro conſiſtit.
HOC eodem prorſus
modo demonſtrabitur,
quo in libro de centro gra
uitatis planorum ab Ar-
chimede demonſtratũ eſt,
in portione cõtenta recta
linea, &
rectanguli coni ſe
ctione grauitatis cẽtrum
eſſe in diametro portio-
nis.
Etita demonſtrari po
77[Handwritten note 7]

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