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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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EHRISTTANI AVGENII
equa Lectansulo ab ra, La, mulciplici sccundum
Fc constar quiden es demonstratione praecedenti, alticudines
parallelepipedorum iInsulorum, ut ck, a quales esse diltanciis par-
ricularum, quae iplorum bales lunc, ur 6, ab recta A P. Ouare, si jam
parallelepipedum c x ducamus in distantiam C H, perinde est ac (
parricula c ducatur in quadrarum distantix cir. Fodemque modo
leres habet in relignis omnibus. Acqui producta omnia parallele.
pipedorum in distantias luas ab recta x E, xquantur limul produ-
Prop. L. huj. Co ex cuneo a BD in distantiam L a F, quia cuneus cravitat luper
puncto L. Froo eriam lumma productorum à particulis lingulis 0,
in quadrata luarum distantiarum ab recta a E, xequabitur producto
ex cuneo BD inrectam L A, hoc est, producto extioura a cB in
rectangulum ab FA, L A. Nlam cuncus a BD, aequalis cst producto
extigura a cB in rectam F a F. Rurlus quia tigura a C B a qualis est
producto ex parcicula una c, in numerum iplarum parricularum;
lequitur, dictum productum ex Agura a c B in rectanigulum ab F A,
La, equari producto ex parricula c in rectangulum ab F A, L A,
ulciplici secundum numerum parcicularum c. Cui proinde eriam
aequalis eric dicta Cumma productorum, a parriculis lingulis c in
quadrata suarum distantiarum ab recta A E, Sive a particula unac
in lummam omnium horum quadratorum. Ouare, omissa urinque
mulciplicatione in parriculam c, necesse est lummam candem
quadrarorum aequari rectangulo ab F a, L a, mulciplicilecundum
numerum parricularum in quas Agura a c B dirila incelligitur.
PROPOSITIO IX
Ata figura plana es in eodem plano line a rectâ, qua
Vel socet figitm. vel non, ad quam perpendiculares
cadant à parcheulis snulis minimis es aequalibus, in quas figu
ra divisa intellicitur; invenire summam quadratorum ab om-
nibus istis perpendicularibus; sive planum, cujus multiplex,
secundum parricularum numerum, dicta quadratorum sum
mae aequale sit.
Sic dara Aigura plana a B c, e in eodem plano recta F D; di-
visaque tigura cogiraru in parriculas minimas aequales, intelli-
eantur ab unaquaque carum perpendiculares ductae in rectam
D, lieuc a pauricula F ducta est x K. Oporreatque invenire
rDE
DR CEMEKO
DSCILLA
20n15.
IOUTa A C B
Parricu.
um numerum. 
quod crat demonstrandum.
X PEOP. PFX
ed