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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 387, page id 851387705:0407
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NLEHLLOKCM.
estus ue Dumeri Onactratiet;) Spirali
Erespondebit Parabolocides Semicubicale
cujus itaque currae aequabitur, non modo Semiparabolocideos curra (cujus batie
aquetuT rectarum MI T maximae, ec Axis aggresato arcuum similium Sectorum in
Seriptorum, numero infiniiorum, leu Prienti areus contermini;) Sed ee Recta lines
quam iltius Semiparabolocidis Semicubicalis currae aequalem oltendimus, in dicto
de Foduiss Tractatu;) LBa vero Spirali acacens; dimicla tisura acjacencio
delit aladvident. Li tltaiet adiet.
Lemmas
Tem (per prop. 44.) Data ratione quam habet series una, cujustibet
Poreltacis, (ad seriem aequalium:) reperitur racio quam habet alia
series alterius cujulris potestatis, (ad seriem item aequalium:) inre-
niendo nempe homolosum terminum progrestionis Arichmeticae.
Se Si Ouadratorum sire Secundanorum series sic 2 Teriei aectalium; erit series
Lateralium sive Primanorum ? Periei aequalium: Ouia, ut Series Primanoruni media
est inter seriem Aqualium e seriem Secundanorum, sie 2 (consequens rationis
qualitae Primanorum) est media Rrichmerica inter F et 3 (consequences rationum
Aiqualium et Secundanorum.) Sic cum Cuborum sire Pertianorum ratio SIc = Sire
ad 4, inter quam seriem ec seriem aequalium, duarum porestatum series inter-
jiciuncur; quaerendae tunc dua mediae Arichmetica inter L et A, DuTa 2 e 3, qua-
rum illa Primanis, haec Secundanis convenit. Pt Sic in exteris.
Ec similiter, si quaerenda sic rario luperioris poteltatis seriei conveniens; id
reperitur progrestionem continuando ad terminum qua sicum usque: VI, Si series
Ouartanorum rationem habeat, ad seriem aequalium, eam quae ct F 2d 5 GIVC =
Teries Sextanorum habebit rationem rad: quia in prosreltione arichmetica ubi
terminus (post unitacem) quarcus est 5, ceiminus sexcis exic7, et paricer in reliquis.
eROP. XEYII.
Lemma.
Tque haec regula HOnuS ralebit s exponatur series quantita-
cum quarumlibet (non quidem juxta seriem Primanorum, sed
juxta quamris aliam Fabella seriem, et de illarum Ouacratis, Cubisi
_C. inquiratur.
Verbi Gralia. Si intelligatur ejusmoci series quancitatum quarumlibet secun-
dum seriem Secundanorum (quibus altignatur in Pabella ratio L ad 3) dispolica
rum: harum Ouactracis conreniet ratio L act 5; (quia 2, 3, 5, Pune Arichmetice
proportionales; ee Cubis conreniet ratio F ad7; et Sc deinceps; quia 1, 3, 5. 7
Sc. Tunt Arichmetice proportionales, proutOnicas, Radix, Guadratum, Cubus, ec.
Tunc poreltates proxime sequentes et Creomerrice proportionales.
Nec hoc aliud est, quam quod habetur in Pabella; nam Li quanticales altuM PIa
sinc series Secundanorum, cujus ratio cst 3; carum quadrata erunt series Ouarta
norum, cujusratio Z; et carundem cubi erunt series Sexcanorum, cujus ravioz; ec.
uc dictum est.
P ROl. LCVII
Corollarium.
 R OP. ZL VI
Econtequenter, Conseides vel Py amilles complemento semi para
bolae (circa ipsus diameltu) uxtandum est ad Cylindrum vel Prisma
super aequali base aeque altum, ut x ad 5.
CC7
cireum.