Full text: Volumen primum. Opera mechanica (1)

CHRISTIANI HUGENII horizonti parallelum, A D vero verticale: ut inveniatur
ſumma quadratorum à diſtantiis à plano A D, noſcenda eſt
diſtantia centri gr. parabolæ O V H ab O H, quæ ſit Φ P,
eſtque {2/5} V P. Deinde, diviſâ P V bifariam in Δ, conſtat
rectangulum Δ Ρ Φ, multiplex per numerum particularum
ſphæræ A B C, æquari quadratis diſtantiarum à plano A D . Eſt autem rectangulum Δ Ρ Φ æquale {1/5} quadrati P V, vel
quadrati B E.

124.1.

TAB. XXVI.
Fig. 2.
De centro
OSCILLA
TIONIS .
Prop. 15.
@n fine.

Atqui, quadrata diſtantiarum à plano B C, æqualia eſſe
liquet quadratis diſtantiarum à plano A D, ac proinde ei-
dem rectangulo Δ Ρ Φ, multiplici per dictum particularum
numerum. Ergo ſpatium applicandum, in ſphæra A B C,
erit duplum rectanguli Δ Ρ Φ; ideoque æquale {2/5} quadrati à
radio E B.

Itaque, ſi ſphæra ſuſpenſa ſit ex puncto in ſuperficie ſua
A, erit E S, à centro ſphæræ E ad centrum agitationis S,
æqualis {2/5} ſemidiametri A E. Totaque A S æqualis {7/10} dia-
metri A D. Si vero ex puncto alio, ut L, ſphæra ſuſpenſa
ſit; erit E S æqualis {2/5} tertiæ proportionalis duabus L E, E B.

125. Centrum oſcillationis Cylindri.

In cylindro, invenimus ſpatium applicandum æquari {@/12}
quadrati altitudinis, una cum {1/4} quadrati à ſemidiametro ba-
ſis. Unde, ſi cylindrus à centro baſis ſuperioris ſuſpendatur,
fit longitudo penduli iſochroni æqualis {2/3} altitudinis, una cum
ſemiſſe ejus, quæ ſit ad ſemidiametrum baſis ut hæc ad alti-
tudinem.

126. Centrum oſcillationis Conoidis Parabolici.

In conoide parabolico, rectangulum oſcillationis eſt {@/18}
quadrati altitudinis, cum {1/6} quadrati à ſemidiametro baſis. Unde, ſi à puncto verticis fuerit ſuſpenſum, fit longitudo
penduli iſochroni {3/4} axis, cum {1/4} ejus quæ ſit ad ſemidiame-
trum baſis, ſicut hæc ad axem, id eſt, una cum {1/4} lateris re-
cti parabolæ genitricis.

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