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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 329, page id 851708439:0353
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le
s
Cap. LXXVIII. A C GE B R A.
e in 2 a a + 6bb +60c +6d a +6cc2
Fee in . . . . 2b + 26 + 2 d + 2c 5 = (2n a a b - ) L. l l 1
FC in .. . . 2b6 + 600 + 64 4 + 6ce2
ee in . . . . . . . . . 26 + 24 + 2e.
Fe In . . . . . . . . . 260 +6ad + 6e02=
=ee in ....
Fe IM ....
ec in..
CFe in ... .
2d
 2C
.. 2 d d. + 6ec
1 = 2 a3 = 2 B3 + 203 = 2d3 = 2032
1 = 2 a + 2B5 + 2c3 = 2 43 f 2C5
e
... 26C =
n = 4 a + 4 b3 + 4c + 443 + 40 = 1
e = 4 in a f B + 63 + a3 + e =
 = 5 maaan f auam F e in 2. aa = 2. bb. f 2. 60 = 2 dd = 2 ec 2
eo in. . . . 2 b + 45 + 64 + 8C5
Ouod erat demonstrandum.
Nocandum hic (quo constet provotitionem hanc cum mea coincidere) quod
naaa + aa a (prOpteF m = n F F, et l = a) idem et eum milh, (adeoque 
illius est = mIII.)
+ce in . . . . . 2b + 40 + 6d + 8cf idem et cum m 1
Et C in 2aa F 2Bb + 26C =2 d d F 2 ecz
adeoque à eju(dem, est = mIII.
Nam (per propotitionem ante demonstratam) 2 a a = 2bB = 26c + 2 d d
F 2 Ce, = Zna a, = 3a an = 3 e in a f b +c + d f c.
Sed a F b. f c F d + e, cst a. = c in 3n, = : n a + = n C = 3 n a. + : a.
Atque hoc in 3e, ct ; n a c  3aC = 5 aa = 3ac.
Ouod additum ipsi 3 n a a = 3aan Facit 3 na a = a a + 3 4 e, (= 2 a a = 2. bb
F 266 = 2d d F 2 ec.)
Acque hoc omne in e, est 3 naac F aac = 3acc.
trem, ee in 2b f4c f 6a = 8 ey seu 2ec in B F26. f 3 4. + 4 0, est 2ec
in B F c + d Fc
Lc = a F e
F a + e
F e
Hoc est (potito e = F,) 2 ec in Pyramidalem numerum, cujus latus est
p = n - T. Vel (Dolito e alterius valoris) in talem pyramidalem numerum
ductum in e.
Falis aurem psramidalis nueruS (PrOuE demonstrari in prOP. 176, 277,
666 + 36b +20
Sico p = n = 2, est  P + 3Pp. + 2P et
Acque hoc in 2eC, sic pPP F 3 PP + 2p in 3 eec.
HIoc est (restimendo n = L PrO P,)
n = 3nn = 3n - + + 3nn - 6n. + 3 + 2n = 2 (= n = 1) i1 3 C cc.
HOc CAt = n e = 2 Me. HOC ettus : MaC = = acc.
Ouod addicum ancedicto 3 naa C + aa e. = 3aec, Caeit naae + a a e. HOC
est m a a en seu  aaa. Duod iptum est meum r = 11I.