Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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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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134FED. COMMANDINI t u, x y ipſi g h æquidiſtare. Et quoniam triangula, quæ
fiunt à lineis K y, y u, u s, s h æqualia ſuntinter ſe, &
ſimilia
triangulo K m h:
habebit triangulum K m h ad triangulũ
1119. ſexti K δ y duplam proportionem eius, quæ eſt lineæ k h ad K y.
ſed _K_ h poſita eſt quadrupla ipſius k y. ergo triangulum
κ m h ad triangulum _K_ δ y eãdem proportionem habebit,
quam ſexdecim ad unũ &
ad quatuor triangula k δ y, y u,
u s, s α h habebit eandem, quam fexdecim ad quatuor, hoc
eſt quam h K ad κ y:
& ſimiliter eandem habere demonſtra
bitur trian-
90[Figure 90] gulum κ m g
ad quatuor
triãgula K δ
x, x γ t, t β r,
r z g.
quare
222. uel 121
quinti.
totum trian
gulum K g h
ad omnia tri
angula g z r,
r β t, t γ x, x δ
_K_, K δ y, y u,
u s, s α h ita
erit, ut h κ a d
k y, hoc eſt
ut h m ad m
q.
Si igitur in
triangulis a b c, d e f deſcribantur figuræ ſimiles ei, quæ de-
ſcripta eſt in g h K triangulo:
& per lineas ſibi reſp onden-
tes plana ducantur:
totum priſma a f diuiſum eritin tria
ſolida parallelepipeda y γ, u β, s z, quorum baſes ſunt æ qua
les &
ſimiles ipſis parallelogrammis y γ, u β, s z: & in octo
priſmata g z r, r β t, t γ x, x δ K, κ δ y, y u, u s, s α h:
quorum
item baſes æquales, &
ſimiles ſunt dictis triangulis; altitu-
do autem in omnibus, totius priſmatis altitudini æ qualis.

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