Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
partes
d
.
in
pyramide
igitur
inſcripta
erit
quædam
figura
,
ex priſinatibus
æqualem
altitudinem
habentibus
cóſtans,
ad
partes
e
:
&
altera
circumſcripta
ad
partes
d
.
Sed
unum-
quodque
eorum
priſmatum
,
quæ
in
figura
inſcripta
conti-
nentur
,
æquale
eſt
priſmati
,
quod
ab
eodem
fit
triangulo
in
figura
circumſcripta
:
nam
priſma
p
q
priſmati
p
o
eſt
æ-
quale
;
priſma
s
t
æquale
priſmati
s
r
;
priſma
x
y
priſmati
x
u
;
priſma
η θ priſinati η
z
;
priſina μ ν
priſmati
μ λ;
priſ-
ma
ρ σ
priſmati
ρ π;
&
priſma
φ χ priſinati φ τ
æquale
.
re-
linquitur
ergo
,
ut
circumſcripta
figura
exuperet
inſcriptã
priſmate
,
quod
baſim
habet
a
b
c
triangulum
, &
axem
e
f
.
Illud
uero
minus
eſt
ſolida
magnitudine
propoſita
.
Eadȩ
ratione
inſcribetur
, &
circumſcribetur
ſolida
figura
in
py-
ramide
,
quæ
quadrilateram
,
uel
plurilaterã
baſim
habeat
.
PROBLEMA
II
.
PROPOSITIO
XI.
Dato
cono
,
fieri
poteſt
,
ut
figura
ſolida
in-
ſcribatur
, &
altera
circumſcribatur
ex cylindris
æqualem
habentibus
altitudinem
,
ita
ut
circum-
ſcripta
ſuperet
inſcriptam
,
magnitudine
,
quæ
ſo-
lida
magnitudine
propoſita
ſit
minor
.
SIT
conus,
cuius
axis
b
d
:
&
ſecetur
plano
per
axem
ducto
,
ut
ſectio
ſit
triangulum
a
b
c
:
intelligaturq;
cylin-
drus
,
qui
baſim
eandem
, &
eundem
axem
habeat
.
Hoc
igi-
tur
cylindro
continenter
bifariam
ſecto
,
relinquetur
cylin
drus
minor
ſolida
magnitudine
propoſita
.
Sit
autem
is
cy
lindrus,
qui
baſim
habet
circulum
circa
diametrum
a
c
, &
axem
d
e
.
Itaque
diuidatur
b
d
in
partes
æquales
ipſi
d
e
in
punctis
f
g
h
_K_lm:
&
per
ea
ducantur
plana
conum
ſe-
cantia
;
quæ
baſi
æquidiſtent.
erunt
ſectiones
circuli
,
cen-
tra
in
axi
habentes
,
ut
in
primo
libro
conicorum, propoſi-
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