Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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182FED. COMMANDINI nis, quouſque in unum punctum r conueniant; erit pyra-
midis a b c r, &
pyramidis d e f r grauitatis centrum in li-
nea r h.
ergo & reliquæ magnitudinis, uidelicet fruſti cen-
trum in eadem linea neceſſario comperietur.
Iungantur
d b, d c, d h, d m:
& per lineas d b, d c ducto altero plano
intelligatur fruſtum in duas pyramides diuiſum:
in pyra-
midem quidem, cuius baſis eſt triangulum a b c, uertex d:
& in eam, cuius idem uertex, & baſis trapezium b c f e. erit
igitur pyramidis a b c d axis d h, &
pyramidis b c f e d axis
d m:
atque erunt tres axes g h, d h, d m in eodem plano
d a K l.
ducatur præterea per o linea ſt ip ſi a K æquidiſtãs,
quæ lineam d h in u ſecet:
per p uero ducatur x y æquidi-
ſtans eidem, ſecansque d m in
z:
& iungatur z u, quæ ſecet
g h in φ.
tranſibit ea per q: &
erunt φ q unum, atque idem
pun ctum;
ut inferius appare-
bit.
Quoniam igitur linea u o
æ quidiſtat ipſi d g, erit d u ad
112. ſexti. u h, ut g o ad o h.
Sed g o tri-
pla eſt o h.
quare & d u ipſius
u h eſt tripla:
& ideo pyrami-
dis a b c d centrum grauitatis
erit punctum 11.
Rurſus quo-
niam z y ipſi d l æquidiſtat, d z
a d z m eſt, utly ad y m:
eſtque