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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 421, page id 851387705:0441
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PTOP. CXXYII.
PkOt. CA=YLI.
Theorema.
T expOnaTIE (MMIILA) series aequalium mulctata serie (ataloe2
Primanorum, Secundanorum, Tertianorum, etc. Residuia ipsa.
corungue Onadrata; Cubis ec. Fam rarionem trabebunt ad exxo-
licam seriem aequalium; quam habet Cnitas ad numetos in subjecta
Tabella indicatos. Lrempe.
Retid. ) C. )Cubis Big. ISupers. ) Sext. 1
122 1 28I e
6 ab l 384 I 56 I 
13 1 18 1 162 l 104 2 1 3 bo l 3b
13 3u  3bqu l Sraa l 132685 l 3943 13
150 l 130 ISI 31SoB  prer 6 E
IIvrs Sela lesto 1o
Et Ec deinceps.
Sequitur ex praecec.
SCZYOF ZV M
Verum quo pacto inrestigabitur, quam habeane rationem serierum illarum A.
potomarum Radices Ouadratica, Cubiex, _cc. ad seriem rocidem carum maximx
aequalium: Ilic labor, hoc opus est. Nihil enim aliud deelt ad Circuli e Fllipleos
quadraturam. VTCx PrOP. L2C. jam pacec, ee ex propoticionibus aliquor secucu-
ris ulcerius patebit.
P R OP, CZXVTTE
Theorema.
T errnatur leries squalium mulctata ferie Subsecundanorum:
Residuorum Ouadrata, Cubi, Biquacrata, etc. ad seriem toridem co-
rum maximo aequalium, racionem tabebune copnicam. Nempe
R- VC
VR = Vb
IR = VC
ec. ad
Cubi.
X. LdL+dtra. 3210+36VR - bV
1R = 2YCR L C) RVR - 3RYC + 3CYR = cVC
cl. ad
_c. ulque 2d
VK- VR R = 2VRRFRRVR = 3kVR F 3RVR - R YR
AVR ZAVR AR, ZAR FEAR ARVRS ARVK + Z ARVR = ZARVR
Scriei
(Primanorum
Secundanorum 13
Tercianorum
Ouartanorum
Ouintanorum
Sextanorum
Ouadrata.
 Lda LVaZaVat3ad aa
 S dB
2
Lt lic demecps; nempe cam rarionem quam haDet lad uueros criangulares, lire
agoresata numerorum Arichmetice proporcionalium (quousque sradus porolta
iis pottulat) ab x continue unitace exelcenrium.
10 1