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# Title: [Christiani Hugenii Zulichemii, Const. F. Horologium Oscillatorium. Sive De Motu Pendulorum Ad Horologia Aptato Demonstrationes Geometricae] Christiani Hvgenii Zvlichemii, Const. F. Horologivm Oscillatorivm. Sive De Motv Pendvlorvm Ad Horologia Aptato Demonstrationes Geometricæ (shelfmarks Leibn. Marg. 70; ZEN Leibn. Marg. 70)
# Folio 57, page id 799199311:0073
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HOROLOG. OSCILLATOR.
57
mus abinicio ad idem rempus per B T se habere ur arcus L H ad D voxu in
rectam e C. Froo tempus per n m, mulcoque magis tempus per
Elo1on
Sv, minus erit tempore per tansentes cxcloidis. Ouod est ablur-. 
dum, cum hoc cempus, illo per arcum s v, ancea minus olten - (un 1
Tum fuerit. Paret isitur rempus per arcum crcloidis B E ad tem-
pus per ransentem BI cum celeritare aquabili dimidia ex B ∞,
non minorem rationem habere quam arcus F e ad rectam F C.
Sed nec majorem habere ostenlum fuic. Frgo candem habeatne-
cesse est. quod erar demonstrandum.
PROPOSITTO XXV
NCycloide cujus axis ad perpendiculum erectus est, ver-
Lrice deorsum spectante, tempora descensus quibus mobile,
a quocunque in ea puncto dimissum, ad punctum imum ver-
ticis pervenit, sunt inter se aqualia; habentque ad tempus
casus perpendicularis per totum axem cycloidis eam ratio.
nem, quam semicircumferentia circuli ad diametrum.
Flto crclois a B C cujus verrex a deorlum spectet, aris vero
A D ad perpendiculum erectus sic, et a puncto quoris in cycloide
Cumpro, velut B, descendat mobile imperu naturali per arcum B a,
sive per superticiem ita inflexam. Dico tempus descensus hujus
esse ad rempus calus per axem D a, licur lemicircumferencia cir-
culi ad diametrum. Duo demonstraro, etiam tempora descensus,
per quollibet crcloidis arcus ad a terminatos, inter le aequalia esse
Constabit.
Describatur super axe D alemicirculus, cujus circumterentiam
Secerrecta DF, basi D C parallela, in E; junctaque F A, ducatur ei
Parallela B C, qua quidem cycloidem tanger in B. Fadem vero
Occurrat rectae horizontali per a ductae in C: Tirque cciam (uper
Pa delcripeus Cemicirculus F E A. 1
l. f
seri
ECigitur; per praecedentem, cempus descensus per areum cy
cloidis B a, ad rempus motus equabilisperrectam B c cum ce-
lericate dimidia ex B O, licur arcus semicirculi F e a ad rectam
F A. Tempus vero dicti mocus aquabilis per B C, EGuatuF rem
Pori descenlus naturalicer accelerari per eandem B C, sive per
E A, qua ipsi parallela est d aequalis, hioc est, cempori descenlus
accelerati per AXCM D A F. ITaGUE TEMPUS PEF aFCUM B A, CrIF F PcOP. 6. C2-
lil. de motu
quoque ad cempus descensus per arem D a, uc Pemicirculi cir- Accel.
cumterentia x ue A ad diametrum P a. quod erar demonstrandum.
El. 31
tocL. 1HACMSB, 1B Loup.