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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 124, page id 799199311:0140
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124
CMRISTTANL AVGENII
DACHVrRO CB, aquatur quadratis distantiarum Arura ab recta X F F, quae per
Saricacis = ducitur iplise parallela; ac proinde criam
Prop. XO. hui. Quadraris distantiarum magnicudinis aB cD, a plano horizoncali
XK, ducto per cenerum gravitatis e; cum distancix urrobique lint
caedem. ACrero planum 2 Similicer multiplex, equale policum
Fuic quadraris diltantiarum magnicudinis a B cD a plano verticali
FF. AC parec quidem quadrara haec dictantiarum a plano FE, una
cum dictis quadraris distantiarum à plano horizonrali per E, Xqua
lia esse quadratis dictanciarum ab axe graritaris per E, qui licari F
ProP. 17. Hd. Paralleliis F. Ieaque rectangulum o x e una cum plano 2, mulri-
plicia secundum numerum particularum magnitudinis a B CD,
equalia erune quadraris distantiarum eju ldem magnicudinis à di-
ctoaxCper F. Sed e planum i, mulriplex sccundum eundem par-
ricularum numerum, aequale polirum fuie iildem dictanciarum
quadraris. Frso planum i ae quale est rectangulo Or H de plano Z
Timul lumpris. Quod ostendendum lupererat.
Erinc rurlus manifestum sic, quod propolitione 10 demonstra-
cum fuit; nempe masnicudinem quamlibet, si alicer atque alicer
suspendatur acque agiretur, ab aribus parallelis, qui a CenErO Dra.
vicatis sux aequalicer distene, sibi ipsi ilochronam esse.
Sive enim magnitudo A D CD suspendatur ab axeF, sive ab axc
Lilli parallelo; par et eadem urrobique esse quadrata distantiarum
ab axe per E, qui sic axibus F vel L Parallelus. Vnde e planum L,
cujus mulciplex, sccundum numerum particularum, aquatur qua-
drarorum lummx, urroque casuidem erir. Hloc veroplanum, ap-
Plicacum ad distantiam centri gravicaris ab axc olcillarionis, quae
urroque casu eadem ponitur, efficie dictantiam qua cenrrum olcil-
larionis inferius est cenero gravicaris; Prgo etiam haec distancia
utroque casu eadem eric. Velur(i, Facta luspentione ex L, fuerie
dicta diltantia E Z, erit ipla aequalis EC; a FOta ZL aqualisCF;
adeoque, in suspentione urraque, idem pendulum Cimplexilochro-
num sc magnicudini a BC D.
eR OPOSTTTO XIK
Imathitudo eadem. c brevius nunc longius (uspen
tur; erunt, sant distantia axium oscillationis
a centro tvitats di sos d contraria ratione distantia
Sit magnicudo, cujus cenerum pravicaris a, suspensa primum
acque axicaca ab areinB, deinde vero ab axc in c; luque in prima
OSCZLE A
FLONX8.
controrum oscillarionis ab eodem cravitatis centro.
T. Fvcl.