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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 37, page id 799199311:0053
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TOROLOG. OSCTLLATOR
ED DESCENSU
oR aYLUN.
EROPOSITIO
A F cara circulum quad
X Y
Stocircalus ABC, diametro n C, cui ad anculos rectos
vero 0
currat a termn ait acata
quidem necessario secabit circumfe-
 sitF
rentiam, puta in B. Dico arcum BD, lineis OF, AF interce
ptum, minorem esse recta DF.
lungal e, l euut ea fultu cunsens circumte-
rentiam RCta B C, guX necCCarIO OCCUEreFReCtA FC inteF F  D.
F.ltigieur asutus b a C in circulo aequalis angulo E B CF. quare
d ansulus FBF, qui una cum E B C constituit angulum rectum
FBC, erit aequalis B C a. Ouia aurem limilia lune triangula A B
C, A C F, erit e angulus e aequalis angulo a c B. Frgoidem an-
sulus e aequalis angulo F B P. Itaque ilolceles eA criangulus P F
B, habens crura xequalia P E, E B. Addica ergo urrique corum
recta E D, HeE F D, aequalis duabus BE, F D. HTalce vero duas
majores esse constat arcu B D, iildem cerminis intercepto, e in
candem partem caro. LrsO e FD eodem aecu B D major erico
quare constat provolitum.
eROPOSTTTOXIIT.
I(dem positis, si recta a B occurrat ipsi D C intra circulum;
aDico arcum BD, rectis C D, N B interceptum, majorem
esse recta DF.
lunsarus enim D C d ducatur arcus D B lubcenta B B. uo.
niam ergo angulus A B D aequalis A C D, Hoc ett, angulo A D
C; angulus aurem D = B major angulo AD F, AIVC A D C; erir
ii