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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)
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ARTTAMETICA PFODCLXXVII.
6: FE summa Perici Secundanorum o- f a 2 f B2- f 02_c. quorum ulrimum est
-
P, ee numerus locorum L. L. L; cric F L P + , P, vet = =  +
PrOB. 20.
1. Per
7. Viriusque isicur summae aexrexaum, (pura  F = 1 f. L = 2 p. 1 1 +
nempe 3V = 31 + 2.P + 21 +1 + 7 213 +61 +4 es aexrepacum dua
cum serierum; cujus aeprepui semistis P + 3 V +
jus latusV. Ideoque-
et
 est numerus P pramidalis eu-
P RO P. CLXXVIL Theorema.
Atus numeri cujulris Prramidalis ad ipsum numerum suum, est ut
1 2d - + 31 + 21
Or ollendicur in praeced.
Acq daco numero Pyramidalin, non innoreleic iptius latus, nisi resolvendo A-
quationem Cubicam 6n = 13 + 312 F 21.
P R OP. CLXXVTTI.
Theorema.
CEries numerorum Pyramidalium, in praemissa cabella commode in-
terpolari poterit; si ipsorum numeris lateralibus tot interponan-
tur medix Arichmeticae quot opus est, et ex iis formentur numeri er-
ramidales, juxta prop. Praeced.
E csosue lois cst
Duta, si numerorum Pyramidalium 1, 4, 20, 20, 35, 56, lacera F, 2, 3, 4,5, 6, etc.
Sic interpolata LInC Z, 2, L3, 2, 23,3,32743 423535336, ec. hisce lateribus re-
spondebit series Pyramidalium 26, 1, 2 16, 4, 676, 20, 24 16, 20, 26 16,35, 44 16,56,
Ac. vel etiam 26, 1, 28, 43 183 20, 767 20, 187 35, 76,56, _C. Vel pOrivS, 183 L, 2834
a8310, 28320, 98,35, 18, 56, eC. 11111
P R OP. CLXXIX. Lemma.
D Ropositum sic inguirere, quam habeant rationem numeri Frianguli-
eriansulares ad latus fuum.
Praestabicur hoc eadem methodo qua prop. 1, 6. Dempe,
T. Numerus Frianguli criangularis aequacur agoregato numerorum omnium Py.
ramidalium, (incellise quorum latera sunt numer inceori, nam de incerpolacis tic
non agicur,) ab unicace ad numerum libi collareralem, inclusire.
2. Est aurem laceris I, numerus Pyramictalio L F 31 F2. per prop. 177.
3. Freo, sumpris laceribus L, 2, 3, 4 c. vel (eorum
10c0) a, b,6, a, Sc. Cumma horum a3 f 3 a f 2 a, b3 L
b = 2b,63 f 302 + 26, 23 4 3a2 + 2 d, ec. exit
Texcuplum asoresati Pyramidalium, (quorum omnium
nUMerUS exiE aequalis lateri eorum maximi, ut patet:
e propterea hujus asgresati sextans erir numerus Pri
Num. Prianguli crians. anguli criangularis, cujus lauls idem exie cum latere
maximi Pvramidalium.
4. Adeoque numerus Frianeuli triangularis est lexta pars aggregaI irium Perie
rum, cousque ab unitate concinnacarum donec numerus cerminorum sC aequalis
lateri numeri Friansuli criangularis propoliri, quod dicaturl: adeoque si iplIS prXe
ponatur terminus alter 03 + 52 f0 (uc series intelligantur ab 0 inchoatae,) fict
numerus terminorum l.+. 1. Fclingularum serierum illarum lumma scorsim inno.
teICet Dex PrOP. 2. 20. et 40.
2a 30
5. LCai DC.
F 3
13 + 322
etC. e. lC.