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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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CHRISTLANI AVOENII
ON CHUrNo CtA COntentIS, DXX - 2 X M =Fnn= + Kk, Hetrora lumma, nempe qua-
20V1S. dLATOLIMFR, FB, FC, FD, x BZZ +nn -+ k h- l. Ouodap-
parec esse planum datum, cum ha quantitaces omnes datx sinE;
temperque idem reperiri, ubicunque in circunterentia lumptum
Fuerie punctum F. quod crac demonstrandum.
Ouod Lipuneta data direrlas graritates habere ponantur, invi
cem commensurabiles, ut si punctum A POnderCF UEZ, BUEZ, CUE
4, Duc7, Corum que reperro graritaris centro, circulus rurlus de-
lcribatur, ad cujus circumterentia punctum, a daris punctisrecta
ducantur, ac lingularum quadraca mulciplicia sumantur se cundum
numerum ponderis puncti sui; ue quadratum A F duplum, BFtri-
plum, cF quadruplum, DF sepruplum; dicorursussummam om-
nium xqualem tore spario dato, semperque cidem, ubicunque in
circumferentia punctum lumprum fuerit. Paret enim hoc ex prxe.
cedenti demonstratione, si imaginemur puncta ipla mulciplicia
secundum numeros attriburx cuique praritatis; quasi nempe in
aduo puncta conjuncta line, in Beria, in c quatuor, in D leprem,
atque illa omnia aqualiter gravia.
tAOFOSITIO XIMI
Thoma pana Sma inplano existens, aliter at que
aliter sun tis, qua in eodem plano accepta
aqualiter à centro cravitatis sua distent; acitata moru in
latus, sibi ipsi isochrona est.
Sit Aigura plana, vel linea in plano existens A BC, cujus centrum
ravicaris D. Quo eodem cenero, circumterentia circuli in codem
plano describatur, E CF. Dico, (i 2 quoris in illa puncto, WEE, C,
velo, lu lpenla Figura agiretur in latus; sibi ipsi, ire cidem pen-
dulo simplici, ilochronam esc.
Sic prima lulpensio ex e puncto, quando aurem cst extra Rgu-
ram, uthic, putandum est lincam e _, ex qua tigurapender, ri-
sidam elle, acque immobiliter ipliattixam.
Incelligatur fgura a BC dirila in particulasminimas equales, a
quarum omnium centris gravicaris, ad punctum E, rectae ducta
finc; quas quidem manifeltum est, quum moreatur Aeura motu
in latus, esse ad axem agirarionis perpendiculares. Ilarum igitur
omnium perpendicularium quadrata, divisa per rectam ED, mul.
tiplicem secundum numerum particularum in quas firura divila
Prop. 6. huj. CH, eAticiune longiudinem pen duli simplicis, hourx iloctronit,
Qua
2I2
ISCFEL A