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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 51, page id 799199311:0067
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# Lines: 30 recognised, mean confidence 0.89
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ATOROLOG. OSCILLATOR
F A ad CeleritaECI ex F Z, eA in lubdup LM LOMGIFU- DR MOTU r
CLOTDE.
t ac proinde eadem qua L  ult F H. Lt 3 e retoP. 3. lls.
XF A ad celeritatem ex F 3 CIIVUIS L dl s H. IEa
que tempus dictum per m e ad cempus per o e habebicratio-
mexrationibus m N, ad O D, _ F X ad F F. IIa
dinum F A 2
midia celeri
nem compoli
FE ad H 2.
rum vero prior ratio, nempe m rad o P, cadem ostendetur qua
Fst en casses Cycloidis B = parallela rectae. V a, similicer-
que tangens m c e Parallela rectae e a; ac proinde recta M N
aequalis A H, d O P aequalis F R. Frgo dicta rario recta u ir ad
Oe eadem eAt quae A I ad F K; hoc est, A A ad F A; hoc est,
p A 2d A A; hoc cAt V a ad ∞ A F. Fs autCM UE V a ad A P ITA F A + LeMmA PrX-
ad a _; nam quia quadrarum r a xquale estrectangulO D A F, & ced
quadeatum a p xquale rectangulo D a Z, quae rectangula lunt
incer (C uEF A ad Z. a, hoc est ut quadratum F a ad quadrarum AH,
erit proinde ex quadratum v a ad quadratum e a uc quadrarum
FA ad quadratum AIr; acque criam v a ad a e longicudinc, uE FA
ad A H. Ratio itaque m rad o e, eadem erit quae F a ad A H, hoc
est, proprer triangula similia F A H, P E Z, Cadem quX F E ad E
2, uc dictum fuic. Ieaque dictaratio temporis per m N ad tempus
Pero e, componitur ex rationibus F X ad F _ d F e ad e 2, ideo-
que eadem erit quae F X Sive Z e ad E Z. Sicut autem radius X E
ad e 2, ica est tangens sT ad rectam oR; hoc enim facile per-
spicitur. Igicur rempus morus qualem diximus per m N, ad tempus
per ox conttar este licuc SY ad e r. quod erac demonttrandum.