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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 447, page id 851387705:0467
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PFOD. CL XZZ. INELNLTORUM
5. Nempe summa duplicata seriei Primanorum, 0 F 2 a f 2b f 26, _c. Cu
jus cerminus ulcimus 2. L, et numerus cerminorum H. L; exie   2l. BeL. PCOP. 2.
6. Summa criplicacae seriei Secundanorum, 0 f. 3 a 2 f 3 b f 302 _c. cujus ter.
minus ulrimus 3 12 de numerus cerminorum L  F; erit  =3 12 1+
PFOP. 20.
67 3V. per
J. Summa Periei Fercianorum, 0 f a. + B3 + c. dec. eujus cerminus ulcimus 1,
numerus cerminorum L. +. L; eric  L p +. F 12. per Pcop. 40.
teuumisinus summucum aepreguum, (pura = L 21 +  F 3 1. + l. = = 3 1.
+LF p + F E V.) nempe
24 P. 4 2414+ 24 1 + 24 1. + 12 1. + 121 4612 +61. + 611 +61.
Gregati sextans
st Aeereeaum ceiumillacum serierum; cuju s. 28.
Ia + 613 = +F12 +61
c
cus h Ideoque -
24
Cst numecus Frianguli triangularis cujus la.
PRO P. CEXXX
Theorema.
Acus numeri Trianguli crianeularis ad ipsum numerum, estut P act
a +613 + +r12 +6
Adeoque, Dato latere Idabitur numerus Frianguli criansularis, puta
a +613 + 2c13 +6
Daro autem numero Frianculi criangularis non invenicur iplius lacus nisi resol.
rendo hanc aequationem 24 n = 14. + 61 + F2t 2 + 61.
P ROP. CLXXXI.
um crcncts ue cin Theorema.
is
eries numerorum Frianguli criangularium, in praemisa Tabella-
commode interpolari poterit; si iplorum numeris laterasibus, FOF
interponantur medii Arichimerici, quot opus eAt, _ ex iis FOrMENEF
numeri Trianguli criansulares, Der praecedentem.
Pura laceribus interpolatis 3, E, +2, 2, 23, 3, 32, 4342, 5, 53, 6, _c. respondene
numeri Frianguli criangulares 238, 2, 2338, 539 128, 15, 23728735,50728,70, 94 2373
+26, _c. vel eriam 238, 1y 2663 5, 118, 15 728335, 528, 70, 726 7 +26, dc. Vel potiis
3d23 F, 335, 32 325, 3335, 3170,38. 126, ec.
PROP. CLXXXTI
Lemma.
DRoPolicum sic inguirere, quam ad latus Cuum rationem AabCa
lequencium serierum numeri Fisurati pura Frianguli prramida
les, Prramidi erramidales, etc.
Poster quidem hoc prastari eadem methodo qua ulus sum ad ProB. 176, _ 173,
ope propolicionum ibidem memoraTUI REIDC PTOp. 2, 20, e 40, timul cum
PTOP.