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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 538, page id 851387705:0558
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CiTCLOIDF.
De Dimentione Cycloidum Concractarum et PTOIALCaLEMI.
Propturates quaedam Cycloidum.
Eper eandem Balem CMI constituantur tres Cycloides genere tees, lcult
D Cet Ca AMI Primaria, cujus genitor est AHID: C0OM Crclois quaedam
Contracta, cujus genicor est OFD: _ GTCF. M, Csclb GuacaM Lrorracta, cu-
jus genicor cAt F. K D
Primo, quoniam Cyelois cujutris generis tc ex moc aequabili in peripheria se-
nitoris, dum interim genitormoeu aequabili cranstertur, Cuver datam balem, donce
punctum generans circulum absolrerir, a puncto contactus incipiens et ad idem
rediens: Ergo utrique Mocus, tam circularis quam rectus, erunt ubique in cadem
ratione. Duare in omni Cycloide, A ducatur Bali parallela d Genirore ad curram.
ut FX, vel HP, vel RZ; erir ue mocus in arcu OF, ad mocum in semicireulo
OFD, ica mocus rectus FX, ad semillem corius monis recti, scilicet femibalem
DM. Similices uc arcus A HL ad semicireulum Tuum AHD, ica H Y ad semibalin.
Idem dicicur de arcu P. R e recta K L
Ouare policis in directum vunotis D K HF, quoniam areus OF, AH, F. R sune
in eadem rarione ad semicireulos tuos, erunt rectae LZ, IIY, IZ, in eadem ra-
tione ad communem balem DM: sunc ergo aequales, de puncta Crcloidum Z LZ
in directum potica unc; rectae igitur X Y Z N F HKD, sunc aequales, de similiter
lectae ee posiia: Sed F D ee OD similicer secta Tunc: erxd recta LLZ N, O AF. D
similiter secta sunt a Curvis Cycloidum.
Sccundo, quoniam aneulus ODF est ad rectum, ut arcus O F ad semicireulum
suum, seu uE F X vel D N ad DM; erEO, ut M N ad DM, ita aneulus M NX
ad Rectum.
Fercio, juneanuur HIA, eique parallela dueatur Y9. Duoniam demonstracum
est Y O canpere Cycloidem primariam in Y: ergo WY cadit normaliter in Cur-
vam primariae.
TheoremA.
Curva Creloidis primaria est quadrupla Diametri: e portioni
euivis assenatur recta aequalis.
TC semiba lis CD dirita in parces aequales um indetinice minimas, et a punctism in.
Dcidant ubiqi in primariam normalicer rectae ma, et in proxime majorem ma recta
mu: ducantur Dn (subrenta genicoris) _ m2, Parallelx iptim à; ilem AB, à 2, a 8
parallela: quare a 2 tansit Cyeloidem in a, de parallela de aequalis est iptim e Og0-
niam isicur ipla ma l quum lins aequales ee parallela lubtenlis penicoris) sune tinus
angulorum