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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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Cap. V.
COntraCtC KUNNOE1SS5,) dicenda: utpote quae non tam Circulo similem, quam eN cir-
Manifestum autem est, (ex constructione
Cveloidis,) non modo Peripheriam Cirenli
Generantis intepram (propter concinuam lui
guxe supponitur ad rectam r a applicationem)
iphira aequalem esle; (adeoque semissem le-
milli ec. puta curvam Semicirculi a B A, re-
Etx 78, Sc.) Sed e, particulatim, dum Cir-
culus Crenicor, Balin in B contingens, puncto
Tuo lineante delignat Cycloidis punctum b;
rectam rB ( propter eandem continuam cpxpuo-
zlu) curra bB aequalem esle; hoc est, (ducta
recta bB V Basi parallela, qua occurrat in B
Circulo Genitori cirea Cyeloidis Axem consti-
cuTO, Axique in V,) curra aB: Adeoque
et reliquam reliquae; nempe rectam Ba, HOC
eA BB, ipsi B A curra. Ec sic ubique.
Et propterca: Rectam b V, ubique aequa-
lem elle, aggresaro Areus ee Sinus recti, Sinni
verto V A compecentium; puta (rerencis Sym.
bolis propoticionum pracedencium) bV =
BA F BV =- a Y 5. Acque hoc inditteren-
ter, sire sIE V punctum, supra C Cenerum
circuli Generancis, live intra, sire denique in
ipso C. puncto.
Ductisque Ba, bB, rectis; TunE (Per 33.
EI. 6. Fucliais) Anguli Ba A, proportiona.
les iplis quibus insiltune Arcubus B A; hoc elt
rectis bB, Tcu Ba: Adeoque anguli B a 2, hoc
eltus BB7, arcubus Ba Seu BB; hoc elt rectIs
B7. Nempe, (propter angulum in centro
duplum Anguli in Peripheria, per 20. F. L. 3.
VErB recta, hoc est arcus, Bb, Teu aB, act
Semiperipheriam a B A, vel huic aequalem re-
Etam 7 a; Tic angulus bBr, hoc et B ar, ad
A ar rectum.
Dirisa itaque ra in partes quortibet aequa
les, in punctis 8, , s C,E, ec. ductisque, ab
his punctis contactus ad punctum lineans, re-
Atis F, 2C, 8d, 62, EX, ec. (quibus paralle.
Iae sint in Scmicireulo, a L, a  aD, à L, a Z
ec. arcuum arithmetice proporcionalium sub.
ten(:) erunq cum anguli F87, c27, 487, 2lr,
XET, _c. tum, his aequales, PaT, F ar, Dar.
Z ar, Z a r, _c. arichmerice proportionales:
Forumque communis excellus, primo aequa
lis; puta Fp7, rel Par; Nempe, Ca parS an-
culi rectius quae ell Te tocusr_; Teu arcus Fan Semiperipherix a F A.
Diritis aurem hoc meco, cum semieyeloide rectis Le, Ci d5, ec. rum semieie.
culo-
De Calculo Centri Cravitatis.
602.
Fig. 166. Peripheria Tua (concinua ad rectam applicatione) commensurans aequalem rectam
tem rectam (Bali perpendiculares) aC A, Crcloidis Avem.
Crrace Konnois, KinnoISO,) Pocus quat C. ides (hoc elt, Konnociss, Konnoast
culo oriundam, lioeam vel tiguram indicat.
7 ar, donec b punctum lineans, in sublime latum, (adeoque curram suo mocu
describens bB,) cireuien Facto, eandem 2a2 rectam, (in ejuldem altero extremo
7,) iterum contingat: (dum interim Centrum tuum c, rectam c Cic deseribar, ipsi
20r parallelam ex aequalem:) Curram bD descriptam, Lineam Crcloidem appel-
labimus: Rectam ra, Croloics Basin: Figuram curra illa et Base comprehenlam,
2T A, Fieuram Crcloidem: Pjusque semillem ra A, Semisreloidem: Er hilecan.
Crcloidis autem Nomen, quod spectat, Vaur (mihi faltem) Cyclois (hoc ett,