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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)
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DHRISTIANI IIVGFNII
DE nora in le s. Trague in EriaHSALS AB D, AD F, aquales anguli A BD, A D
E. Communis auccucsa est ansulus ad a. Frso dicticrianguli
miles erunt, idcoqueo A ad a D uc A D ad A F.
cnisf extra circulum, a ducatur b FI
parallela DE, Qua OCCurrat rectae A D in H. Itaque sccundum jam
demonstrata crit ut D a ad a b, ita a b ad a e, hoc cst, ita a fad
a D: Ideoque rursus proporrionales Crint Af, AD, A b. Ouare
constat propolitum.
astOMITIO XXIII.
It Cyclois a BC, cujus verrex a deorsum conversus sit,
Daxe a D ad perpendiculum erecto; sumptoque in ea quolibet
puncto e, ducatur inde deorsum recta B+ quae C ycloidem tan-
eat, termineturque recta horizontali a I. recta vero B F ad
axem perpendicularis acatur, es divisa bifariam FN in X.
superea describatur semicirculus FH A. Duct à deinde per pun-
etum quodlibet C in curva Ba sumptum, recta Z. C parallela
BF, quae circumferentia FH N occurrat in HI, axi A D in Z, in-
tellicantur per puncta C C  recta tansentes utriusque curva,
carumque tancentium partes iisdem duabus horiz ontalibus
MS, N T intercepta sint M N, S T. Iisdemque rectis MS, N Y
includantur tancentis B F pars OP, C5 axis D A pars OK.
Onibus ita se habentibus, dico tempus quo crave pereur-
ret rectam m N, celeritate aquabili quanta acquiritur de
scendendo per arcum C gcloidis BC. fore ad tempus quo per-
curretur recta oe, celeritate aquabili dimidia ejus qua ac-
quiritur descendendo per totam tancentem DT, sicut est tan-
sBns ST ad partem axis OR.
Delcribatur enim Cuper axe a D Cemicirculus D V A SCconS rC-
Ctam B F in V, _Z C in P, s jungatur a v sccanS rectaSOO, PR,
C Z IN FK _E A. TUINGaNEUL ILCM H F, HI A, H X e A8; qua poltrc.
ma secet rectas oc, P R in punctis A dII.
Hlabet ergo dictum tempus per m  ad tempus per O P, ratio-
nem cam qua componitur ex racione iplarum linearum m N ad
rop. s. Calit. O e, d exratione celeritatum quibus ip la percurruntur, contrarie
de motu x. C, hoc es, e exratione dimidix colcritatis ex B F Sive ex
quab.
Prop. 3. tuj. F. a, ad cetericarem ex Bc, EVC ex P Z. F. Acqui cora celericas ex
Sit jam punctum intersec
EFCLOIDE.