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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 123, page id 799199311:0139
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TTOROLOO. OSCTLLATOR
calingula tisurae o op, dirila in tor parriculas xquales, quorconti.
nentur Ceriencis ipisse ibus in Roura ABCD. ITaC au
rem incelligi porsunt teri, qualiscunque fuerit magnicudo ABCD.
sire linca, live luperhicies, lire Colidum. Semper vero centrum gra-
vitaris figurx oee, quod Tic r, eadem alcitudine esse maniteltum
est cum centro graritaris magnicudinis a B cD; ideoque, li planum
horizontale, per F ductum, secer lincam centri AGUER OOD, veL
luc hic ins, aquales esse dictancias SF, F E.
Pottoautem constat quadraca Mctanciarum, ab axc oscillarionis
F, applicaca ad distantiam rE, mulciplicem secundum numerum
Parricularum, etficere lonsicudinem penduli ilochroni =; quae lon- = PrOP. S. hui
situdo polira fuit FC. Illorum rero quadratorum lummam, xqua-
lem esse perspicuum elt, quadratis distanciarum à plano horizon-
cali per F, una cum quadraris distantiarum a plano verricali PP,
Peraxem F _ centrum gravicaris e ducto t. Aequi quadrara dictan- + Prop 47. lib.
ciarum magnicudinis a B cD a plano horizontali perF, xquaneur . euls
quadraris distantiarum figurx oo P ab rectas F. Dua quadrara ((10
sic punctum lupremum Agurx O OP, e  centrum gravitaris cunci
super iplaabscissi, plano per rectam or, parallelam sF) aequalia
sune rectangulo or E e quadrato sr, mulciplicibus secundum
numerum particularum dictxe figurx F, Cire magnicudinis a B CD. = PrOP. 3. hui.
Ouadrata vero distantiarum magnicudinis A B C D a plano F F,
quantumcum que axis oscillationis F distet à centro gravitatis E,
semper eadem lunt: quae proinde puremus aequarispatio z, mulci-
Plici lccundum numerum particularum magnicudinis a B CD.
ltaque quoniam quadrara distantiarum magnicudinis a B CD.
ab axc olcillationis r, ae quantur iltis, quadrato nimirum sr, rectan-
guloorH, e planoz, mulciplicibus per numerum parricularum
ejuldem maonicudinis; si applicentur haec omnia ad distantiam
PElire ST, orietur longitudo F C penduli ilochroni magnicudini
ABCD F. Sed ex applicatione quadrati s + ad latus luum ST, orie- =ProP. P. huij.
cur ipla SF, sIvC PF. Ergo reliqua E C estca qua oritur ex applica-
tionerectanguli OTHF, de plani 2, ad candem SF vel FF.
Ouare superestur demonstremus rectangulum O T H, cum pla-
no2, aequari plano r. Tunc enim constabir, eriam planum L, appli-
catum ad dictantiam F e, efficere longicudinem ipsiE C aequalem.
Ilud aurem sic ostendetur. R ectangulum oTr, inulciplex secun-
dum numerum parcicularum Eixura o. ge, lire magnicudinis a B
cepra incer bina quae que plana, in eadem incer Pe ratione cum (CT- Dn CEVTROI
DSC+ LF A.
mentis dictae magnitudinis, qua ipsis re spondene; lintque Legmen- =10n 1s.