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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 449, page id 851387705:0469
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PFOD. CL XXXII. INFLNLTORUM.
Propolicum sic inquicere, Ouam habeac racionem series finica Ouartanorum, (ab
Oinchoaca,) ad seriem coridem maximo A qualium.
T. Character numeri Priansuli criangularis, ( per PrOV. 180: ) est
21 +61 + xr 1 + 61. Et Frianeuli prcamidalis  F 10H + 351 + 505 f 211
DEF PrOB. 182.
O2 f 03 f 0+0
a +6a  + 4 482
24) B F 6b3 +
ct +6c3 f 226 4 60
14 f 613 F FF 12 = 61
1. f 101. + 35 1. + 5012 4 241. Aer eeacum.
120
20 a Aivs 1OM
2. EHt aurem, (ue Paxius
dictum, est,) numerus Fisura-
cus unius gradus ( in praelenes
tabella) aggregatum omnium
Praecedentium in gradu sibi
proximo: Adeoque numerus
Friansuli Prramidalis, clt a8.
Pregacum Friansuli criangula
rium. itt e
3. Ec propterea, sumpris la-
teribus 2, 2, 3, ecc. vel (eorum
I0cO) an B,C, _c. (quorum maximum dicatur B,) e Formanis inde numeris Frian-
Sulicriansularibus; tlorum axeregatum exie numerus Frianguli pyramidalis ejul
dem laceris, nempe F101 = 35 13 + 50 V f 24. l.- ∞ ∞3pen0 ciy 1a 3u1i
+. Summa aucem seriei 0 = 6 a + 6B + 6c _c. eA (per PrOP. 2.)
2+67
5. Summa seriei 0 = TZ a2 = rF B2 = FY C2 _C. est (Der PrOP. 20.)
E 1X22+
6
2x p = 2213 + 211, 21 1. + 121- 221 +338 +721
6. Summa seriei 0 + 6 a3 + 6B3 f 603 _c. est (. per Drop. 40.)
26P + =6p -612 + 51, 67 +61 612 4 121 +61
. Ea creo lummae in unam collectae tune
51 +61, 221 + 331 + +11, 622 + 1213 + 67 9 1 + 4013.  60 f291
8. Si igitur ex riginciquadcuplo corius agoresari, auteratur summa irium serierum.
Nempe A ex 5) 13 = 1014 + 3513+5012 + 24. 1.
autcratur 6) 912. + 4013 +6012 + 291.
Hoc est, Si ex 30) 813 +601 + 2701- + 3001 +. 244. L
auteracur 30) + 45 11 + 2001 + 3001 + 2151.
Panebir summa
Seriei quarrae, 9uae 30) 615 = 15)4 = 1013 + 001 = +1.
Mst Quarranorum e
Hoc ectus
HOC ett,   = p+
30
613+67
+01+05
1+ 3 p + + 2p 1+
Oux est ixicur summa seriei Ouarianorum cujus cerminus ultimus est J. nu.
merus terminorum I F. L.
Vel; s Pro numero terminorum J F F, substienatur m et propterea series
aequalium m I; eric serieo Quarcavorum = m 12 F 3m 13 = 5 m 12 = 2 m I. (A
nempe cerminus primus (it o, sccundus r:) vet  V , 3m 12, m 1. m1a
L.
261 361 301
ec. ad
Addica.
O. Adeoque