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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 30r, page id 00068255:0059
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omnialesumuntur et distinctius exponuntur pagiriss sequentibus hujus plagulo
Additio dyadica Generalis
a, b, c, ete se habent
eodem modo in
 M
l et v ∞ sohb permps
met le quodem secund
n et lmo (modo
P et Imnv) colum
tC et
sam n et iloporro
lerminus primae colimn est sucmm
lv. 2m B.c 12ab eb
Merri
v = dl: 1 - 2l = dm:, l, 1 - 2m = du: Lm, 1- 21
quia autem quantitatum l, m, n, etc. quaelibet est o vel 1. hinc sequitur
sivsit et sil sit 1, dl esse negativam; sin B, sl sit 0, ol esse positivam. Si v sit 0, il esse 0
Si v sit 0 trit dm estv
e
Sivsit1 et si M ht 1. am est negativa
si vsitt et si n sit 1 dct est negativa
sin Vit I etm sit 0 erit dma l, adeoque dm positiva:
sin v sit 1 et l sit o erit dmza et in =b vel am pritativa
sin Bsit P et R sit o erit dn = lm adeoque ampositiva
o vl substituendo valorem, sit v - db: 2 fiet M = v - dl = 2dm, : 2P- 2de
L Si  quaevis, a, b, c, etc. adeoque et V sit = 1, fiet
Hince Talternis D et 1, nam si l= 0 fit (1) seu (= l = 1. sin l= 1 fit (1) seu 1- l =0
M alternis est. 0, 0, 1, 1. Nam si M est o fit (M) = l si e  se m est 1 fit l+.
si l’est 0 pt (m) = m si l est 1 fit (m) = 1 = m. Hine bina in M b9 0, et bis 1
A iptio = 0, em et la  hinc cum buoc mox l = B p (I) et littend
si una ex his let m est 0 fit (n) = n, sin omnes precedentes linea et columna
nempe hic tam L quam m sint 1, fis (1) () 1 - n. seu oppositum pr
podemque argumento pro (P) prodit octies semper idem manere, ac tum demum fieri mulo
ninere in quale erat, et tunc mutatum rursus mantie quater qual
ab = 2abc + 4 abed - 8abede eu q liavel
sed ita ut primum sit ab ecundum quae
C involvunt, tertium quae dpe
nempe ac + bc - 2abc, otertium
a vat itde
M = vl-dm.:  1t0 iel, et
si urae ex hic l. t m est o, fit (2) = A, Si  an  it  (2) n
ffine cum solum in uno ex quatuor praecedentibus contingat, 
a - 2ab + 4 abc-8 a bid et
sed il, ut primum
si v sit o et de et0
Pt 2 et sn sito, esit anZ ort R=ovet dupositiva
honic quia in quatuor vicibus non nisi serme contiagin ut omnes sint
Iu primae columna prodit
lio quae
vit
persium quae d involvunt, nempe
aet bercet de - 2abe -race - 2ade - bce - 2bde - rcde + 4 abre + 4 abde + 4 acde + 4bc de - cabede  = D
ad + bd + cd = 2 abd - 24 cd - 2b cd + g abed = C
qartum quae e involvunt nempe
itaque tota secunda columna erit A = 2AB + 4 ABC = B AB Id, etc
AD + Bd + CD = 2ABD - 2ACd = 2BCd + 4ABCd, et ita porro
et tertia columna erit (A) - 2(A)B) + 4 (A(BC) - 8(A) B1C)() et ita porro
et si militeret
et (C) erit
AB est 2abc - 2 abc = 0 AC est rabd + abcd - 2 abd - 2 a l cd - 2abed + 4 abid = a
Labde- 2abide+
A seu A + B + C + D et est aequ. primae columnae
C = a - 2ab+ 4 abc, d D = a - 2ab. + 4 abc - 8 abcd, e -
AE est AD .st Cab e + abet tabee + abde (2 abe( 2 ab ce
M B M l= a. - 2ab + 4 a bc = 8 abed + 15 abcd e - 32 abedes + etc
seu AD = abcet abde - 2 abede
B = a - 2ab,
m = A - 2 AB  a ABC = 8 ABCd + 16ABCDE - 32ABCDEF + et C (du) - mdrm) - biti)
A) = AB (B) = A - 2 AB, C (9 = p - 2AB+ 4 ABCD (D) = A - 2AB+ a ABC= B ABCD, E, etitu
in ( 2)Q + 4 (D (B) C) - B(A)B) GId) + I6CNDCB)CC)CDNE) - 32CA)CB) CC) Cd) (5)4) + et C hitebmutus dem
nachadanio
(AD = (D CB (X 1BD = 1 . 2 (ACBC) ( () = 14)- 2 (418 + 2(12) 8) C3D)  stmcdus. sii C suiptis (tet
int prosest iet
2
ritis abinatio
a protermiforu
(AI 2
AAD = 2 (CA(CB) + 4 (AD (3) (C) = 8(RDCB)) C1D(CD) + eA
min tuom corlasse plemna sabicoe ( pora B. di ge i) id on alle sne at abe esasint Foril ed
es senatiu
6. ue ct iutis sua
() = S posito intipi a nihillo
(1 7 4t = l l + d1 -(1) m+ dm -(n), E
(d1, sam), An) etc. angent quantitatem, nem
et suam columnam, et scaventes sinistro
e) n) is ) euc
siat ou
x
rementa ps columna
am dan Rtc
rementa in
Jae a, b, cyd esc
ecunda  A, B,
Ut pibic orc sunt ouet
per  ita etium
A, B, C, et et (), (B) G
(dm) = 1(a Con) -M Cam
et ita porria 1 dabed
taboest abedehabide
etc seu 
quodsi vellemus absolvere
theoremata geperalia, et
promovere quantum licet, exa
minandum esset, ordine quid
peret duendo.   ade pele
 ab in ab in abe in abeo
o ur