Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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43
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file
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0197
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197
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rhead
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DE CENTRO GRAVIT. SOLID.
"/>
b m. </
s
>
<
s
xml:id
="
echoid-s4927
"
xml:space
="
preserve
">ergo circulus a c circuli _k_ g: </
s
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<
s
xml:id
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echoid-s4928
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
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echoid-s4929
"
xml:space
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">idcirco cylindrus
<
lb
/>
a h cylindri _k_ l duplus erit. </
s
>
<
s
xml:id
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echoid-s4930
"
xml:space
="
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">quare & </
s
>
<
s
xml:id
="
echoid-s4931
"
xml:space
="
preserve
">linea o p dupla
<
lb
/>
ipſius p n. </
s
>
<
s
xml:id
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echoid-s4932
"
xml:space
="
preserve
">Deinde inſcripta & </
s
>
<
s
xml:id
="
echoid-s4933
"
xml:space
="
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">circumſcripta portioni
<
lb
/>
alia figura, ita ut inſcripta conſtituatur ex tribus cylin-
<
lb
/>
dris q r, s g, tu: </
s
>
<
s
xml:id
="
echoid-s4934
"
xml:space
="
preserve
">circumſcripta uero ex quatuor a x, y z,
<
lb
/>
_K_ ν, θ λ: </
s
>
<
s
xml:id
="
echoid-s4935
"
xml:space
="
preserve
">diuidantur b o, o m, m n, n d bifariam in punctis
<
lb
/>
μ ν π ρ. </
s
>
<
s
xml:id
="
echoid-s4936
"
xml:space
="
preserve
">Itaque cylindri θ λ centrum grauitætis eſt punctum
<
lb
/>
μ: </
s
>
<
s
xml:id
="
echoid-s4937
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4938
"
xml:space
="
preserve
">cylindri
<
emph
style
="
sc
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emph
>
ν centrum ν. </
s
>
<
s
xml:id
="
echoid-s4939
"
xml:space
="
preserve
">ergo ſi linea μ ν diuidatur in σ,
<
lb
/>
ita ut μ σ ad σ ν proportionẽ eã habeat, quam cylindrus K ν
<
lb
/>
ad cylindrum θ λ, uidelicet quam quadratum
<
emph
style
="
sc
">K</
emph
>
m ad qua-
<
lb
/>
dratum θ o, hoc eſt, quam linea m b ad b o: </
s
>
<
s
xml:id
="
echoid-s4940
"
xml:space
="
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">erit σ centrum
<
lb
/>
<
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="
right
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xlink:label
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xlink:href
="
note-0197-01a
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xml:space
="
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">20. primi
<
lb
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conicorũ</
note
>
magnitudinis compoſitæ ex cylindris
<
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="
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>
ν, θ λ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4942
"
xml:space
="
preserve
">cum linea
<
lb
/>
m b ſit dupla b o, erit & </
s
>
<
s
xml:id
="
echoid-s4943
"
xml:space
="
preserve
">μ σ ipſius σ ν dupla. </
s
>
<
s
xml:id
="
echoid-s4944
"
xml:space
="
preserve
">præterea quo-
<
lb
/>
niam cylindri y z centrum grauitatis eſt π, linea σ π ita diui
<
lb
/>
ſa in τ, ut σ τ ad τ π eam habeat proportionem, quam cylin
<
lb
/>
drus y z ad duos cylindros K ν, θ λ: </
s
>
<
s
xml:id
="
echoid-s4945
"
xml:space
="
preserve
">erit τ centrum magnitu
<
lb
/>
dinis, quæ ex dictis tribus cylindris conſtat. </
s
>
<
s
xml:id
="
echoid-s4946
"
xml:space
="
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">cylindrus au-
<
lb
/>
tẽ y z ad cylindrum θ λ eſt, ut linea n b ad b o, hoc eſt ut 3
<
lb
/>
ad 1: </
s
>
<
s
xml:id
="
echoid-s4947
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4948
"
xml:space
="
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">ad cylindrum k ν, ut n b ad b m, uidelicet ut 3 ad 2.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4949
"
xml:space
="
preserve
">quare y z cylĩdrus duobus cylindris k ν, θ λ æqualis erit. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">
<
lb
/>
propterea linea σ τ æqualis ipſi τ π. </
s
>
<
s
xml:id
="
echoid-s4952
"
xml:space
="
preserve
">denique cylindri a x
<
lb
/>
centrum grauitatis eſt punctum ρ. </
s
>
<
s
xml:id
="
echoid-s4953
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4954
"
xml:space
="
preserve
">cum τ ζ diuiſa fuerit
<
lb
/>
in eã proportionem, quam habet cylindrus a x ad tres cy-
<
lb
/>
lindros y z, _k_ ν, θ λ: </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">erit in eo puncto centrum grauitatis
<
lb
/>
totius figuræ circũſcriptæ. </
s
>
<
s
xml:id
="
echoid-s4956
"
xml:space
="
preserve
">Sed cylindrus a x ad ipſum y z
<
lb
/>
eſt ut linea d b ad b n: </
s
>
<
s
xml:id
="
echoid-s4957
"
xml:space
="
preserve
">hoc eſt ut 4 ad 3: </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4959
"
xml:space
="
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">duo cylindri _k_ ν
<
lb
/>
θ λ cylindro y z ſunt æquales. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">cylindrns igitur a x ad tres
<
lb
/>
iam dictos cylindros eſt ut 2 ad 3. </
s
>
<
s
xml:id
="
echoid-s4961
"
xml:space
="
preserve
">Sed quoniã μ σ eſt dua-
<
lb
/>
rum partium, & </
s
>
<
s
xml:id
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"
xml:space
="
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">σ ν unius, qualium μ π eſt ſex; </
s
>
<
s
xml:id
="
echoid-s4963
"
xml:space
="
preserve
">erit σ π par-
<
lb
/>
tium quatuor: </
s
>
<
s
xml:id
="
echoid-s4964
"
xml:space
="
preserve
">proptereaq; </
s
>
<
s
xml:id
="
echoid-s4965
"
xml:space
="
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">τ π duarum, & </
s
>
<
s
xml:id
="
echoid-s4966
"
xml:space
="
preserve
">ν π, hoc eſt π ρ
<
lb
/>
trium. </
s
>
<
s
xml:id
="
echoid-s4967
"
xml:space
="
preserve
">quare ſequitur ut punctum π totius figuræ circum
<
lb
/>
ſcriptæ ſit centrum. </
s
>
<
s
xml:id
="
echoid-s4968
"
xml:space
="
preserve
">Itaque fiat ν υ ad υ π, ut μ σ ad σ ν. </
s
>
<
s
xml:id
="
echoid-s4969
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4970
"
xml:space
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">υ ρ
<
lb
/>
bifariam diuidatur in φ. </
s
>
<
s
xml:id
="
echoid-s4971
"
xml:space
="
preserve
">Similiter ut in circumſcripta figu
<
lb
/>
ra oſtendetur centrum magnitudinis compoſitæ ex </
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