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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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CHLkISITMNIAOENIE
Incelligatur  Me IaSao propolica in particulas mi
a a scatCS. Flaeue, Gusa s desue illa Cuspensione idem manci
Olcillationis planum, relpectu parrium magnicudinis; manifeltum
est, Siab omnibus particulis, in quas divila est magnitudo, per
pendiculares cadere concipiancur in dictum oscillarionis planum,
illas ueraque luspentione occurrere ipsi in punctis iisdem. Sint au-
tem haec puncta ca quae apparene in spario ABCD.
Ouum isicur E sIE centrum gravicatis magnicudinis propolitae.
iplaque proindecirca axem, qui per E punctum crectus cstadpla-
num a BC D, quoris litu aquilibrium serret; Facile perspicitur,
Quod i punctis omnibus ance dictis, quae in spatio aB c D lignan-
tur, aequalis graritasrribuatur, corum quoque omnium centrum
gravicatis fucurum estpunctum e. Ouod livero, ut ticri porest, in
puncta aliqua plures perpendiculares coincidant, illa puncta quasi
cories geminata incellisenda lunc, gravicarelque rories mulcipli-
ces accipiendae. AEque ITa CONSIdCTATOrUm, pateE rurLuS CCnErum
Sraricaris elc E punctum.
Porro Tummam quadratorum ab rectis, quae ducuntur a dictis
punctis omnibus ad punctum F, eandem esse paret cum sum-
ma quadratorum ab iis rectis, qua a lingulis particulis magni-
cudinis propositx ducuntur perpendiculares in axem olcillationis
peretranscunrem; quippecum linex ipla, quarum quadrata in-
celliountur, utrobique eandem habeane lonsicudinem. Similiter
etiam, cum luspensio est ex axe per rI, paret Cummam quadratorum
ab rectis, qua ab omnibus punctis, in spatio AB C D Tirnaris, du-
cuntur ad punctum er, candem esse cum lumma quadratorum, ab
iis quae, a parciculis omnibus magnitudinis propoliex, ducuntur
perpendiculares in axem ofcillationis per er cranseuntem. Frgo
ueroque casu, si summa quadrarorum ab rectis quae, a punctis om-
nibus praedictis, ducuntur ad puncta F vele, diridatur perrectas F F
vel E Er mulciplices secundum numerum particularum in quas
magnitudo propolita dirila intelligitur, orictur ex applicatione
hac lonsitudo penduli simplicis, quod magnicudini luspen(a Cx P
vel e ilochronum lic. F. C aurem Cumma quadratorum utroque
Prop. mus. calu aequalist; a recta quo que EF, E H, inter scaequales; e parti-
cularum idem numerus. Ergo, quum e applicatx quantitates, de
quibus illae applicancur, utrobique aequales lint, ctiam longitu.
dines ex applicatione orrae aequales erunt, hoc est, lonsitudines
Pendulorum ilochronorum magnicudini propolitx Culpen(x ex e
vel ex XI. Ouare conltar propoluum.
120
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