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# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
# Folio 77, page id 85138403X:0085
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DE CTCFOTO
De Dimensione Creloidum Contractarum e Prorractarum
Proprietates quaedam Creloidum.
Iper eandem BaLM OML const EUAntuF tres C ycloides genere
ditte: entes, scilicet GaM A Primaria, cujus genicor est P. LS: FI8. 20.
COOM C.rclois quadam Contracta, cu jusg enicor estO F D: 8
ECF M, Crelois quxedam Prorracta, cujus geniror elt P H D.
Primo, guoniam Crclois cujulris generis tic ex moru aquabili
in peripheria genitoris, dum interim genitor mocu aequabili
cranSSerEuT, Suver daram batim, donec punctum generans circu-
lum ablolverie, a puncto contactus incipiens ex ad idem rediens:
FrgO uerique Mocus, tam circularis quam rectus, erune ubique in
eadem racione. Onare in omni Crcloide, si ducatur Bali parallel a
aGenitore ad CurrAI, UE F Z, vel H Y, vel R LS CTIE UE
MOEUS In AECU OF, ad mocum in semicirculo OF D, ica mo-
TuS reCtuS F Z, ad semissem corius motusrecti, scilicer semiba-
sim DH. Similiver VE aECUS AE ad semicirculum sUUM
AHD, ica HI Y ad semibalin. Idem dicitur de Aecu P I ex
recta KL.
Ouare posiris in directum punctis DKEI F, quoniam ArCUS
OF, AII, F K sunc in eadem ratione ad Cemicirculos (UOS,
CrUHE recta FZ, HIY, R Z. In eadem ratione ad COmuneM
balIII DM; sunt ergoxquales, e puncta Cvcloidum ZY Z
in direCtum POTICA TUINE; reCtR IGITUE Z YZN, FHIMD, TunE
aequales, ee similirer sectx e pottxe: sed FD et OD similitee
sectae sun: ergo recta ZYZ H, OAFD similiter sectae sunt à
Curois Creloidum.
Secundo, quoniam angulus OD F est ad rectum, ut areuS
OF ad semicirculum PuuM, Peu UE F Z vel DN ad D M:
erGO, Ut MN ad DM, ita anculus M N Z ad Rectum.
TerrIO, jungANEuE FI A, eique parallela ducatur X O. Ouo.
niam demonstratum est X C cangere Cycloidem primariam in
L: exgo N Y cadit normaliter in Curvam primaria.
Theorema.
Curva Creloidis primariae est quadrupla Diametri: es
portioni cuivis assignatur recta aequalis.
IE semibasis GD divila in partes aequales mm indetinire
minimas; et a punctis m incidare ubique in PFIALIAI NOE-
maliceE