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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 39, page id 799199311:0055
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IOROLOO. OSCILLATOR
DE DESCENSI
Lu n
i 22 Led A
eloidem taneat
Circa axem cxcloidis A D delcHIDaIL CirculuS geNIEOE A F D,
Aio in Cycloide puncto, rectam per illud ducere qua
tem duccte oporteat.
 ducatur B E paralleta vast Ccloidis, quae dicto circulo occur-
TaE In E, _ junSatuF A E, cui denique parallela peF B aGaCUF E B
N. Dico hanc crcloidem in B contingerc.
Sumatur enim in ea punctum quodlibet, a B diverlum, ac pri-
Sic crclois A B C, dt punctum in ca dacum B, per quod rangen-
moVtS IeTIOTa veluE H, _ per e ducatur recta basi crcloi.
dis parallela, qua occurrat cxcloidi inL, circulo A E DINK, rC
etae a E in M. Ouia ersO K L est aequalis arcui K A, recta auTCM K
AE MINOF ATCU KE, CrIE RCCta M L MInOF ArCU A E, hoc CA, recta
E B, Sive M H; unde apparet punctum e esse extra creloidem.
Deinde in recta e e Tumatur punctum e inferius B, e per H
agatur, ur ance, basi parallela, qua occurrat excloidiino, circulo
A F D in O, rectX a E producta in P. Ouia er5o00, aequalis cAt
arCUI OR; O D AHECM MajOF APCUO E; CFIE P O MINOF aICU F A,
hoc eAt, recta e B, live e H. Vnde apparet rurlus punctum v esse
extra creloidem. Cum isitur quodlibet punctum prater B, in re-
eta  B e sumprum, sic extra crcloidem, constat illam in puncto
Bcrcloidem contingere; quod crar demonstrandum.
Fluic demonstrationi an locum luum hic relinquerem dubita-
vi, quod non mulcum ei ablimilem à claristimo VVrennio cditam
inveniam in libro VValtilii de Crcloide. PoreA aucem _E UnIVer-
Caliconstructione propolicum absolvi, quae non crcloidi cantum
Sed e aliis curvis, ex cujullibet figurae circumvolurione genicis,
conveniat; dummodo sic tigura in candem parrem cara, ec ex iis
qua GCOMETTICR VOCAREUT.