Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
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page |< < (28) of 213 > >|
16728DE CENTRO GRAVIT. SOLID. uel coni portionis axis à centro grauitatis ita diui
ditur, ut pars, quæ terminatur ad uerticem reli-
quæ partis, quæ ad baſim, ſit tripla.
Sit pyramis, cuius baſis triangulum a b c; axis d e; & gra
uitatis centrum _K_.
Dico lineam d k ipſius _K_ e triplam eſſe.
trianguli enim b d c centrum grauitatis ſit punctum f; triã
guli a d c centrũ g;
& trianguli a d b ſit h: & iungantur a f,
b g, c h.
Quoniam igitur centrũ grauitatis pyramidis in axe
cõſiſtit:
ſuntq; d e, a f, b g, c h eiuſdẽ pyramidis axes: conue
1117. huíus nient omnes in idẽ punctũ _k_, quod eſt grauitatis centrum.
Itaque animo concipiamus hanc pyramidem diuiſam in
quatuor pyramides, quarum baſes ſint ipſa pyramidis
triangula;
& axis pun-
88[Handwritten note 8]123[Figure 123] ctum k quæ quidem py-
ramides inter ſe æquales
ſunt, ut demõſtrabitur.
Ducatur enĩ per lineas
d c, d e planum ſecãs, ut
ſit ipſius, &
baſis a b c cõ
munis ſectio recta linea
c e l:
eiuſdẽ uero & triã-
guli a d b ſitlinea d h l.

erit linea a l æqualis ipſi
l b:
nam centrum graui-
tatis trianguli conſiſtit
in linea, quæ ab angulo
ad dimidiam baſim per-
ducitur, ex tertia deci-
ma Archimedis.
quare
221. ſexti. triangulum a c l æquale
eſt triangulo b c l:
& propterea pyramis, cuius baſis trian-
gulum a c l, uertex d, eſt æqualis pyramidi, cuius baſis b c l
triangulum, &
idem uertex. pyramides enim, quæ ab eodẽ
335. duode-
cimi.

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