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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 250v, page id 00068201:0500
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Generaliter (2) = 4 = (8) - 8, 1Z sin fiet. () +  - 2 (2 4 - (2) 8, + Y (9 4 8
seu (D qu ((7) - 4) = 8, 1 - RY) sid qu (2) - 4) L biqut (2) 7), quia  qul(2) - 2) est 1orlo,
ideo  hinc biqu. (124) -4) = ∞ qu (1 - 24) id se sed Au (1 - 27)) = 1 et biqu (27) - 2) = qul x). 4)
Ergo fit qua (2) -2) = 4 seu (7) + 2 - 2(2) 4 =8 seu 12), 1- 24 = 2- 4, et quadrando
utrique (2) = 8 + 2 - 244 seu (2) - 4  8, 1- 24 atque adeo et ()- d = 8;1 e D
(L unde quadrando utrobique rediret qu ((2) - 4) = X Retineamus jam aequationem
1) - 2 = 8, 1- 4, quia ita incognitae foefficientes non assurgunt ad potentiam. Et applicemus
ad d et C, fietque (D) = D = C, - D videamusque quomodo id se verum ostendat
explicando: D = p ab + q abe + r abed + 8 abides + erc. Et (D) -D = l, pa + q abetr abe + 8 abed
C = a - 2 ab + 4 abc - 8 abed + esc. Nunc opus est ut investigemus OD,
a. a = 1 a + 2 ab a. ab = 2. ab A 3 abc a. abe = habe + gabed a. abid = 4 abid +G, abede
ab. ab - 1 ab 5abe t Gabed ab) abc = 3abe t Dabed L le abede ab. alid - 6abud + 10 abde + 1G abedes
abe. abe - laver qabed + 19, abidet 20, abidef abc. abed = T abcd + 1 abide + 2a abides F 3 3abidesg.
Et ita porro,
a C - 2ab + 4abc
2. 25 ab 23 abc
hinc OD  = 2D0 ent
- 8 abed + 16 abi de - 32 abcdef
511
2. 5,5
l.bid
(5) -0 = l - 210
4) = 
1.
Ery
 nota
Et eodem modo (D) + D - 2(B) D = g-  ) C3, 1- (9)
-21()
-210
6) ((C))
(4) - 4 = 10062 1-27
4) -  = 1016,
24
1-24
Utique 1096 est vel l, vel 0, sissit 1. adeoque
si omnes nota praecedentes sint 1, manifesta.
est consiquentia, sed si l, vel una aliqua ex
notis praecedentibus sit 0, tunc
2) - 2 = 0, 1- 24, adeoque (24) - 2 = 0, et similiter (8) -4 - 0 et hoc
a notis rem revocando ad res, signiticat, si vel nota addenda nova, vel una aliqua
eu notis p prioribus praecedentium columnarum sit o, notas omnes
sigu
sequentium columnarum post has manere, quod utique manifestum est.
- 22
sed hinc non licet facere
2
1-
Et quia posito 2 = 2a + 22 ab +23 dbc + et Et (4) - 27 = _ l, 21 + 22a + 23 ab VabC
Sed hine jam fieret 0 = 8 -, - 2
seu non licet facere 8 = 1 neculicet etiam furere ex
similiter posito E = 1t a + r. b + 2 abc +   eted et es() - Y - l, 1 + na + 13 ab + 14 abc et
ita
1, 21+22a + 23 ab +h non licet tollere l, si l =0
Noluta diguum est formutam L, 2a+ l, 81a + 82 ab + 83 abc + e4 alio, + et  divisilem
, 1F 12a + 13 ab + etc
15) - D = 10, 1 -2 (6) =6 = 10D, 1- 28
Hinc. (2)
(4) - 7
(27) = 4 = 1096G. et quia quadiutum ab 1- 24 est 1. fial qu (2,  4 = 3 4, divisile per
esse per omnes praecedentes.
Et (2) - 4 seu l, 81 + 82 a +83 abc +84 abcd. divisibile est per
sumnas
l’et omne
1- 2
per  l, 8a +8 ab 483. be tec, et per omnes provitules
columnas
U)
3)
Ha ergo
4
4) +4 -2(4) 4 8 et (2 + 4 - 2(22 =
(
+ 8 - 288 - 8- 2(8)
(15) + P- 1+ seu (2 ) +2+ - 2(2) 2 = 4, 1-14 quadritum
seu differentia duarum
notarum proximatum cocumnae, est puuctum ex priore in ofpititam novae solu oppositar columnae propime prris
∞)- D =
1 - 27