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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6929DE IIS QVAE VEH. IN AQVA. interdũ quidem ita, ut baſis in humidum magis
11C demergatur:
interdum uero ita, ut ſuperficiem
22D humidi nullo modo contingat;
ſecundum pro-
33E portionem, quam habet ad humidum in grauita-
te.
Eorum quæ dicta ſunt, ſingula inferius de-
monſtrabuntur.
SIT portio qualis dicta eſt: & ſecta ipſa plano per axẽ.
recto ad ſuperficiem humidi, ſectio ſit a p o l rectanguli co
ni ſeccio:
axis portionis, & ſectionis diameter b d: ſece-
turq;
b d in puncto quidem _k_ ita, ut b k dupla ſitipſius
_k_ d:
in c uero ita, ut b d ad K C proportionẽ habeat ean-
dem, quam quindecim ad quatuor.
conſtat igitur k c ma-
44F iorem eſſe, quàm quæ uſque ad axem.
Sit ei quæ uſque ad
55G axem æqualis k r:
& ipſius k r ſeſquialtera d s. Eſt autem
66H&
s b ſeſquial-
43[Figure 43] tera ipſius b r.
Itaque iũgatur
a b, &
per c du
catur c e per-
pẽdicularis ad
b d, quæ lineã
a b in puncto
e ſecet:
& per
e ducatur e z
æquidiſtãs b d.

Rurſus ipſa a b
bifariã in t di-
uiſa, ducatur t
h eidem b d æ-
quidiſtans:
&
intelligantur rectanguli coni ſectiones deſcriptæ a e i

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