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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 913, page id 851387705:0933
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PFOPXXX. DeCalculo Centri Cravitaris.
CA = R,) ut x ad s, sic R ad = R = A F = BO.
Si itaque sumi intelligantur, uc (in fig. 208.) CV Ceu _ arithmetice prOBOT
tionales; vel, his aequales, Vu criansulum C. Au complentes: Sumpris ubique
nc _ ads siC R ad quartam; erunt illa quarta, series toridem AI, hoc cAt, toci
dem BO, complencium R B A O fipuram tangentium.
Sed (neglectis aliquandiu terriis R) perpendamus quid fucurum FE, EI, prO R.
Substimerentur cocidems: Adeoque sumerentur ubique, ul n ad slic s’ad quar.
tam. Frunc urique illae quarcae, rocidem: Hoc est, (propter, in ti8. 209.
YB4 = CB9 - CY4 = C A9 - CY 9 seu P = P. = ~,) cocidem  ; seu
rocidem = - v.
Sune aucem (propiex  arictmetiee proportionales, ab ipso C puncto, seu 0
ordientes; ee P2 eandem ubique quantitatem;) Omnes = Series ReciprOCA pri
manorum (per deL. 2. hujus.) Tndicem habens = r. Adeoque ad seriem coridem ulcimo
aequalium, hoc est ad cocidem RZ, in ratione intinita, (per prop. P. Vel 7. hujus;) e
Dropterca, magnicudinis intiniea. (PAque rerera, Spacium Hyperbolieum exierius,
Curra ec Asimptoris interjectum, ue ad prop. 3L, post oltendetur. Pademque l’igura
Secantium, sinibus versis Arichmetiee proporcionalibus conreniencium; Proxter
proportionales, in f8. 209, CV = v. C B = R:: C A = R CY = =.
Scd Omnes v, sunc series Primanorum; adeoque tinicxe magnicudinis: Nempe
ERE Seu Z AR, (Der PrOD. T. vel 7. hujus:) cancundem scilicet acque C A u Pri
angulum, quod complent rectae Vu iplisx aequled.
Fx prOpterea, Omnes = - x, mgnicudinis acttiue infinica. Nam sinicae mueni.
tudinis ab intinica detractio, relinquit adhuc infinitam.
Verum, quam jam consideramus, Fisura Pangencium eriam achue major ct:
Ouippe Fansences Lingulae, sunc (non quidem cocidem = sou =
- sed
coridem : Adeoque, (Propter R; ubique majorem quam sy) Series Omnium
seu Fieura Tangencium, major erie quam Omnium ; adcoque mulco ma-
sis erit magnicudinis intinitae. Adeoque mulco adhue magis, Spatium Conchoci.
dale, seu Semiconchocidale C AOOHI, (ex quadrance Genitore, et hac tigura
Fangencium, compolica,) magnirudinis exir intinica. Quod demonstrandum
TuscepimuS.
Verum quidemete, in Conchocidibus Secuncariis, iplas BO, non elte cansenres Fie. 2a5
ad radium C A, sed ad radtium PC. Hloc tamen intinitari figurae non derogat
quippiam. Si enim P C major sic quam CA, sigura R B AOO in eadem ratione
auSetF, (uE SD. oltensum est,) non minuitur; adeoque non minus erie intinira.
Sin PC minOr FE quam C A, minuitur quidem figura RB AOO; sed non nili
in ea ratione minuitur, qua PC minor ett; Hoc elt, in ratione finita: Ouod au
rem intinico non nisi inrarione tinita minus ell, etiamnum elt intinicum; adeoque
Plani intinicudo non destruitur. Salrem, nil incellisatur ipla PC venitus cra
nECCerE (UE P C quam C A sic intinicies minor) coincidencibus P C punctis; quo
calu Conchocidale spatium degenerabir in Ci AR quadrantem.
Ouod aucem Planum hoc, utur magnicudinis intinicae, Momentum respectu F
Regula suX C FI HL Finirum habeat; adeoque Ingulas quae aciem habeant Regu.
Jam illam, Solidaque circa illam convertione facta, magnicudinis esse fInIra
(quod nos, ni Fallor, primi docuimus, in cubjunctis Tractacui de Cyclocide;) lic
Oltendimus.
Guodnrats
u L. L. L. Z