Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
"/>
horizonti parallelum, A D vero verticale: </
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<
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<
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<
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.</
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ſumma quadratorum à diſtantiis à plano A D, noſcenda eſt
<
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diſtantia centri gr. </
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<
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xml:space
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">parabolæ O V H ab O H, quæ ſit Φ P,
<
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eſtque {2/5} V P. </
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>
<
s
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xml:space
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">Deinde, diviſâ P V bifariam in Δ, conſtat
<
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/>
rectangulum Δ Ρ Φ, multiplex per numerum particularum
<
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/>
ſphæræ A B C, æquari quadratis diſtantiarum à plano A D .</
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>
<
s
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<
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xlink:label
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xml:space
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">Prop. 15.
<
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@n fine.</
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>
Eſt autem rectangulum Δ Ρ Φ æquale {1/5} quadrati P V, vel
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quadrati B E.</
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>
<
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</
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<
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<
s
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xml:space
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">Atqui, quadrata diſtantiarum à plano B C, æqualia eſſe
<
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liquet quadratis diſtantiarum à plano A D, ac proinde ei-
<
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/>
dem rectangulo Δ Ρ Φ, multiplici per dictum particularum
<
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/>
numerum. </
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>
<
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xml:space
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">Ergo ſpatium applicandum, in ſphæra A B C,
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erit duplum rectanguli Δ Ρ Φ; </
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>
<
s
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xml:space
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">ideoque æquale {2/5} quadrati à
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radio E B.</
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<
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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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">Itaque, ſi ſphæra ſuſpenſa ſit ex puncto in ſuperficie ſua
<
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/>
A, erit E S, à centro ſphæræ E ad centrum agitationis S,
<
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/>
æqualis {2/5} ſemidiametri A E. </
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>
<
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xml:space
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">Totaque A S æqualis {7/10} dia-
<
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metri A D. </
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>
<
s
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xml:space
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">Si vero ex puncto alio, ut L, ſphæra ſuſpenſa
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ſit; </
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>
<
s
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xml:space
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">erit E S æqualis {2/5} tertiæ proportionalis duabus L E, E B.</
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</
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<
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style
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">Centrum oſcillationis Cylindri.</
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>
<
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<
s
xml:id
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xml:space
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">In cylindro, invenimus ſpatium applicandum æquari {@/12}
<
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/>
quadrati altitudinis, una cum {1/4} quadrati à ſemidiametro ba-
<
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/>
ſis. </
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<
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xml:space
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">Unde, ſi cylindrus à centro baſis ſuperioris ſuſpendatur,
<
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/>
fit longitudo penduli iſochroni æqualis {2/3} altitudinis, una cum
<
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/>
ſemiſſe ejus, quæ ſit ad ſemidiametrum baſis ut hæc ad alti-
<
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/>
tudinem.</
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</
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</
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<
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style
="
it
"
xml:space
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">Centrum oſcillationis Conoidis Parabolici.</
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>
<
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>
<
s
xml:id
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xml:space
="
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">In conoide parabolico, rectangulum oſcillationis eſt {@/18}
<
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/>
quadrati altitudinis, cum {1/6} quadrati à ſemidiametro baſis.
<
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/>
</
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>
<
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xml:space
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">Unde, ſi à puncto verticis fuerit ſuſpenſum, fit longitudo
<
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/>
penduli iſochroni {3/4} axis, cum {1/4} ejus quæ ſit ad ſemidiame-
<
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/>
trum baſis, ſicut hæc ad axem, id eſt, una cum {1/4} lateris re-
<
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cti parabolæ genitricis.</
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