Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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18135DE CENTRO GRAVIT. SOLID.
Sit ſruſtum a e a pyramide, quæ triangularem baſim ha-
beat abſciſſum:
cuius maior baſis triangulum a b c, minor
d e f;
& axis g h. ducto autem plano per axem & per lineã
d a, quod ſectionem faciat d a k l quadrilaterum;
puncta
K l lineas b c, e f bifariam ſecabunt.
nam cum g h ſit axis
ſruſti:
erit h centrum grauitatis trianguli a b c: & g
centrum trianguli d e f:
cen-
134[Figure 134]113. diffi. hu
ius.
trum uero cuiuslibet triangu
li eſt in recta linea, quæ ab an-
gulo ipſius ad dimidiã baſim
ducitur ex decimatertia primi
libri Archimedis de cẽtro gra
uitatis planorum.
quare cen-
22Vltima e-
auſdẽ libri
Archime-
dis.
trũ grauitatis trapezii b c f e
eſt in linea _K_ l, quod ſit m:
& à
puncto m ad axem ducta m n
ipſi a k, uel d l æquidiſtante;
erit axis g h diuiſus in portio-
nes g n, n h, quas diximus:
ean
dem enim proportionem ha-
bet g n ad n h, quã l m ad m _k_.

At l m ad m K habet eam, quã
duplum lateris maioris baſis
b c una cum latere minoris e f
ad duplum lateris e f unà cum
later b c, ex ultima eiuſdem
libri Archimedis.
Itaque à li-
nea n g abſcindatur, quarta
pars, quæ ſit n p:
& ab axe h g abſcindatur itidem
quarta pars h o:
& quam proportionem habet fruſtum ad
pyramidem, cuius maior baſis eſt triangulum a b c, &
alti-
tudo ipſi æqualis;
habeat o p ad p q. Dico centrum graui-
tatis fruſti eſſe in linea p o, &
in puncto q. namque ipſum
eſſe in linea g h manifeſte conſtat.
protractis enim fruſti

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