Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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b m. </
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<
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xml:space
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xml:space
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">& </
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<
s
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xml:space
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">idcirco cylindrus
<
lb
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a h cylindri _k_ l duplus erit. </
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<
s
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xml:space
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">quare & </
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<
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xml:space
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ipſius p n. </
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<
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xml:space
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<
s
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xml:space
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<
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alia figura, ita ut inſcripta conſtituatur ex tribus cylin-
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dris q r, s g, tu: </
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<
s
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xml:space
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">circumſcripta uero ex quatuor a x, y z,
<
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_K_ ν, θ λ: </
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<
s
xml:id
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xml:space
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">diuidantur b o, o m, m n, n d bifariam in punctis
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μ ν π ρ. </
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<
s
xml:id
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xml:space
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μ: </
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<
s
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xml:space
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<
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xml:space
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ν centrum ν. </
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<
s
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xml:space
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">ergo ſi linea μ ν diuidatur in σ,
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ita ut μ σ ad σ ν proportionẽ eã habeat, quam cylindrus K ν
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ad cylindrum θ λ, uidelicet quam quadratum
<
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style
="
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m ad qua-
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dratum θ o, hoc eſt, quam linea m b ad b o: </
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<
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xml:space
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<
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xml:space
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conicorũ</
note
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magnitudinis compoſitæ ex cylindris
<
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ν, θ λ. </
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<
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xml:space
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s
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<
s
xml:id
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xml:space
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">cum linea
<
lb
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m b ſit dupla b o, erit & </
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<
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xml:id
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xml:space
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">μ σ ipſius σ ν dupla. </
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<
s
xml:id
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xml:space
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">præterea quo-
<
lb
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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
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drus y z ad duos cylindros K ν, θ λ: </
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<
s
xml:id
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xml:space
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">erit τ centrum magnitu
<
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dinis, quæ ex dictis tribus cylindris conſtat. </
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<
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xml:space
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<
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tẽ y z ad cylindrum θ λ eſt, ut linea n b ad b o, hoc eſt ut 3
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ad 1: </
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<
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xml:space
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">& </
s
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<
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xml:id
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xml:space
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">ad cylindrum k ν, ut n b ad b m, uidelicet ut 3 ad 2.
<
lb
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</
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<
s
xml:id
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xml:space
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">quare y z cylĩdrus duobus cylindris k ν, θ λ æqualis erit. </
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<
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xml:space
="
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">& </
s
>
<
s
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xml:space
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<
lb
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propterea linea σ τ æqualis ipſi τ π. </
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<
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xml:id
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xml:space
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<
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centrum grauitatis eſt punctum ρ. </
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<
s
xml:id
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xml:space
="
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">& </
s
>
<
s
xml:id
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xml:space
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">cum τ ζ diuiſa fuerit
<
lb
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in eã proportionem, quam habet cylindrus a x ad tres cy-
<
lb
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lindros y z, _k_ ν, θ λ: </
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<
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xml:space
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">erit in eo puncto centrum grauitatis
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totius figuræ circũſcriptæ. </
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<
s
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xml:space
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">Sed cylindrus a x ad ipſum y z
<
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eſt ut linea d b ad b n: </
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<
s
xml:id
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xml:space
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">hoc eſt ut 4 ad 3: </
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<
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xml:space
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<
s
xml:id
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xml:space
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<
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θ λ cylindro y z ſunt æquales. </
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<
s
xml:id
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xml:space
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">cylindrns igitur a x ad tres
<
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iam dictos cylindros eſt ut 2 ad 3. </
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<
s
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xml:space
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">Sed quoniã μ σ eſt dua-
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rum partium, & </
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<
s
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xml:space
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">σ ν unius, qualium μ π eſt ſex; </
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<
s
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xml:space
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">erit σ π par-
<
lb
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tium quatuor: </
s
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<
s
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xml:space
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<
s
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xml:space
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">τ π duarum, & </
s
>
<
s
xml:id
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xml:space
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">ν π, hoc eſt π ρ
<
lb
/>
trium. </
s
>
<
s
xml:id
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xml:space
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">quare ſequitur ut punctum π totius figuræ circum
<
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ſcriptæ ſit centrum. </
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<
s
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xml:space
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">Itaque fiat ν υ ad υ π, ut μ σ ad σ ν. </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">υ ρ
<
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bifariam diuidatur in φ. </
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<
s
xml:id
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xml:space
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">Similiter ut in circumſcripta figu
<
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ra oſtendetur centrum magnitudinis compoſitæ ex </
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