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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 24, page id 799199311:0040
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PH R ISTTANE AVGENII
ROPOSIIIO
aum p certo tempore a cravi, e quiete casum
 inutum est ejus spatii quod pari tempore
transiret motu aquabili, cum velocitate quam acquisivit
ultimo casus momento.
Ponantur quae in propositione praecedenti, ubi quidem A D
erat sparium certo rempore, a rrari cadente ex a, peractum. BD
vero lpacium quod pari rempore eransiri intellisebatur celerita-
ce aequabili, quanta ac quilica crat in fine primi cemporis, scu in
Finc sparii a B. Dico icaque sparium B D duplum cAC ad a B.
Duum enim spacia primis quaruor a qualibus tempori-
bus a cadente eran(missa LINE A B, B F, E C, GH, quo-
rum incer se certa quaedam est proportio: si corum tem
porum duplacempora lumamus, ut nempepro primo tem-
Pore jam accipiantur duo illa quibus spatia A B, BE, PCF-
acta fuere; pro sccundo vero rempore duo reliqua quibus
peracta fuere spatia E C, C K, Oportet jam spatia AE, PK,
qua Cunt aequalibus remporibus à quiere peracta, inter le
ese licur sparia a B, BE, qua aequalibus item tempori-
bus a GuiCEE PEFCUErCBANEUE.
Ouum igicur SIEUE A B ad BF, iEa A E ad E K; _ COn-
vertendo, uc F B sire D A ad A B ita K F ad F A: Cxit
quoque, diridendo, D B ad B a ut exceNuS K E LUPFA F A
ad E A. Ouum sic aurem, ex ostensis propolirione praece-
denti, x F aqualiscum dupla aB, cum quincupla B D: F
A vero xqualis cum dupla a B, cum simplici B D; apparCE
dictum excessum  E lupra F a ae quari quadrupla B D. Si-
cutisitur D B ad B a ita erit quadrupla D B ad E A: Unde F
a quadrupla erit iplius B A: Cadem veTO F A aequatUE, utI
diximus, et dupla a B ex simplici B D. erso BD dupla A B aqua-
lis erit; quod erar demonstrandum.
DE DESCKNSU
xarrum
PROPOS