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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)
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Calculo Centri Cravitatis. Cap. V.
Polsunt etiam ex Crcloidum Secundariarum (Contractarum scilicet 8
Crotractarum) Tansences exhiberi; carumque Curris semtpe
aequales; d partes partibus respectire lumptis.
COmpto, in SeMmeyeloidis curva R7, puncto quoris B; aIICL WHLCHIZACUII Bai
18. 177. Vra, Parallela bB, Circulo genitori, cirea Cxcloids ase La Coc, 
curreus in B: Junetaque Chorca AB; ducacur hiuie paraltela, per punctum b, recla
Sbh. Dico rectam sbh,
Semieycloidem in b comringere.
B
Sumpiis in recta sbh, supra b, puncto 8; ec, intra, puncto h: ducancur, ipsi
BB Parallela, recta 8 x X C, hd HD, Semicycloidi occurrentes in X, d; Semicir-
culo in Z, D; chordaeque AB (producta) in G, HI
Otentum est (S A. prop. 20.) arcui BA, aequalem elte rectam bB; adeogrie de
(propier parallelas) sG, e hHI. (Trem arcui Z A, rectam XZ; e arcui D A,
rectam dD.
Cumque ibidem demonstracum sit rectas BP, (tic. 167, 20B, 288.) areubous
BX, ubiqueminores esse; rectasque B F, arcubus BD majores: Similiter osten-
detur, (Hig. 777.) rectam Z C minorem arcu B X; rectamque HI D, majorem este
arcu BD. (Nam Cimilicer, hic, ducitur AB, ab A; atque illic, a B, ab a.
Adeoque; propter cotam p CE rectam, tori B A currx aequalem; e ablatam ZCI,
ablata XB minorem: Frit reliqua X 8 recta, major quam reliqua X A curra, leu
recta XX. Erpropterea, punctum g, extra Cyeloidem cadet.
Icem; propter hE rectam, ipsi B A currae aequalem; de FID adjectam, majo-
rem adjecta BD: Frit cota Dh recta, major quam tora curra D A, leu D d recta.
FC, propterea, punctum h est extra Cycloidem.
Cum iraque, cum 8 (punctum quodris supra b,) cum h (punctum quodris
intra B,) sic extra Cycloidem; (adeoque unicum b punctum Cycloidi commune;)
recta sbh Cycloidem in b cangit.
EIIque (propier parallelas) b8 = BC, bh = BHI, gH = CH; e (producta
b8. donec tangenti verricis A P OCCUETat in T,) bY = BA = C = V 2VR.
PFODEEE AV, AB, A~ hoc cllu V. c. 2. R. continue proportionales; ut CaepC
dictum est.) Irem, (ductis BXO, bBV, hDC, ipsi F A parallelis, AXi Aa
occurrentibus in O
C rectam VO, vel CO, incercipiencibus; quam dicamus
B;) eri uE AY = v, ad A B = Y 2~R; siC VO, vel CO, = B; ad BC, vel
HC; hoc Cst, ad b8, vel H8,-
8120 =B,
FiB. 177, Si ieaque intelligatur recta A a = 2 R, in partes aequales numero infinitas, di-
ridi, quarum una incellisatur VO, vel OC; adeoque omnes AV, hoc est om-
nes v, eo spectantes, arichmerice proporrionales: Oux his respondene subren(x
toridem AB, hoc elb, toridem V 2V R correspondences; (series urique Tubsecun-
AanOruM;) Tunt ur coridem rectae Vp semiparabolam AP P a (H5. 278. ) com-
plenres; cujus cum AIS Ao cum batis a P, (adeoque de lacus rectum,) it
Rectaeque b8, seu eh, cangences; hoc est, (in parcibus intinice exieuis) ipsa
DX
1d.