Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11.] PROPOSITIO IIII.
[12.] PROPOSITIO V.
[13.] PROPOSITIO VI.
[14.] PROPOSITIO VII.
[15.] POSITIO II.
[16.] COMMENTARIVS.
[17.] PROPOSITIO VIII.
[18.] COMMENTARIVS.
[19.] PROPOSITIO IX.
[20.] COMMENTARIVS.
[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.
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190FED. 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-
1113. primi 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
2214. primi h ſit centrũ circuli, &
tri-
141[Figure 141] 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

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