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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 67, page id 799199311:0083
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TTOROLOG. OSOTLLATOR.
vero lequicur, ex cycloidis prOpriCEaTC, CU CIECUIUS SENIEOE MLK DE LIBEARuM
cangebat reculam in x, punctum de scribens Fuisse in e. Itaque,
recta x F Occurrit cycloidi in e ad ansulos rectos F. Fl autem R P = Propol. 15.
ipsa B Kproducta. Ergo Patet productam B X occurrero cycloidi
ad ansulos rectos. quod crat demonstrandum. A quB
PB OPOSTTIO
Emicycloidis evolutione, à vertice caepta, alia semicy-
Lclois describitur evoluta aqualis ( similis, cujus basis
est in ea recta quae cycloidem evolutam in vertice contincit.
Sic Cemicrelois a B C, cui luperimpolura sic alia similis A EF,
quemadmodum in propolitione praecedenti. Dico, si linca Aexi-
lis, circa lemicreloidem a B C applicara, crolratur, incipiendo
ab a, cam describere extremitare lua iplam lemicreloidem AE F.
Ouia enim ex puncto a cgrediuntur lemicrcloides A B C, AFF,
in unam parrem insexx, e ambx in candem carx, ac praecerea
ita comparatae, ut omnes tangentes femicrecloidis A B C OCCUITAME
Temicreloidi a e F ad anoulos rectos, seguitur hanc evolucione
haccis 2.
illius, a termino a incepta, describi t. quod crat demonstrandum. = Propol. +.
Ec apparet, si dimidiam creloidem, ipsi a BC gemellam, con-
crario litu ab altera parre linex cc disponamus, velur C N, ejus
erolutione, releriam dum filum, jam extensum in CF, circacam
replicatur, alceram semicreloidem e Nr Aili exrremicare descri-
Deum iri, qua limul cum priore A P. F inceram constitaE.
Acque ex his, e propolitione 25 de descensu grariu, mani-
Feltum jam est quod supra in Constructione HToroloeii de aequa-
bili penduli moru dictum fuic. Paret enim perpendiculum; inter
laminas binas, secundum semicrcloidem inAexas, Culpensum agi-
carumque, moru suo crcloidis arcum. describere, ac proinde
aequalibus temporibus quaslibet ejus reciprocationes absolvi.
Non refert enim uerum in Cuperticie, secundum crcloidem cur-
vaca, mobile feratur, an Filo allicatum lineam iplam in aëre per-
currat, cum urrobique candem libertatem, eandem que in om-
nibus curra punctis inclinationem ad motum habeat.
qui
LOSELIC
Tolois linea sui adissstde aramerit cirnt ciors
Ls