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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page |< < (7) of 213 > >|
1257DE CENTRO GRAVIT. SOLID. metrum habens e d. Quoniam igitur circuli uel ellipſis
a e c b grauitatis centrum eſt in diametro b e, &
portio-
nis a e c centrum in linea e d:
reliquæ portionis, uidelicet
a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
octaua propoſitione eiuſdem.
THEOREMA V. PROPOSITIO V.
SI priſma ſecetur plano oppoſitis planis æqui
diſtante, ſectio erit figura æqualis &
ſimilis ei,
quæ eſt oppoſitorum planorum, centrum graui
tatis in axe habens.
Sit priſma, in quo plana oppoſita ſint triangula a b c,
d e f;
axis g h: & ſecetur plano iam dictis planis æquidiſtã
te;
quod faciat ſectionem K l m; & axi in pũcto n occurrat.
Dico _k_ l m triangulum æquale eſſe, & ſimile triangulis a b c
d e f;
atque eius grauitatis centrum eſſe punctum n. Quo-
niam enim plana a b c
82[Figure 82] K l m æquidiſtantia ſecã
1116. unde-
cimi.
tur a plano a e;
rectæ li-
neæ a b, K l, quæ ſunt ip
ſorum cõmunes ſectio-
nes inter ſe ſe æquidi-
ſtant.
Sed æquidiſtant
a d, b e;
cum a e ſit para
lelogrammum, ex priſ-
matis diffinitione.
ergo
&
al parallelogrammũ
erit;
& propterea linea
2234. prim@ _k_l, ipſi a b æqualis.
Si-
militer demonſtrabitur
l m æquidiſtans, &
æqua
lis b c;
& m K ipſi c a.

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