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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98ARCHIMEDIS ſuperficiem recto, ſit portionis ſectio anzg; ſuperficiei
humidi ez:
a-
64[Figure 64] xis portionis,
&
ſectionis dia-
meter b d:
ſece-
turq, b d in pũ-
ctis _K_r, ſicuti
prius;
& duca-
tur n l quidem
ipſi e z æquidi-
ſtans, quæ con-
tingat ſectionẽ
a n z g in n;
&
n t æquidiſtans
ipſi b d;
n s ue-
ro ad b d perpẽ
dicularis.
Itaq;
quoniam portio ad humidum in grauitate eam proportio
nem habet, quam quadratum, quod fit à linea ψ ad quadra
tum b d:
erit ψ ipſi n t æqualis: quod ſimiliter demonſtrabi
tur, ut ſuperius.
quare & n t eſt æqualis ipſi u i. portiones
igitur a u q, e n z inter ſe ſunt æquales.
Et cum in æquali-
bus, &
ſimilibus portionibus a u q l, a n z g ductæ ſint a q
e z, quæ æquales portiones auferunt;
illa quidem ab extre
mitate baſis;
hæc autem non ab extremitate: minorem fa-
ciet acutum angulum cum portionis diametro, quæ ab ex-
tremitate baſis ducitur.
At triangulorum n l s, u ω c angu
lus ad l angulo ad ω maior eſt.
ergo b s minor erit, quam
b c:
& ſ r maior, quàm c r: ideoq; n χ maior, quam u h; &
χ t minor, quàm h i.
Quoniam igitur u y dupla eſt ipſius
y i;
conſtat n χ maiorem eſſe, quàm duplã χ t. Sit n m dupla
ipſius m t.
perſpicuũ eſt ex iis, quæ dicta ſunt, non manere
portionẽ;
ſed in clinari, donec eius baſis contingat ſuperfi-
ciem humidi:
contingat autem in puncto uno, ut patet in

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