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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 250r, page id 00068201:0499
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dgndica
dgadicarum
3 Su puta summet duarum notarum est in eatem columna nota differentiae
ut
n et in sequente columna nota producti
Indyadicis a +b = ab (+a et a +b + C = 2ab +a. et ita continuando
b
ab
rabc -2ab
+4abc
Columnam altimam esse a ∞2ab + 4 abc - 8 abed, et it a porro codudum
inveni, quaeritur modus inveniendi columnas sequentes.
Esto columna prima O, secunda D, tertia F, quarta , etc. ad dendr erit
 nova nota dyadica  et provemientia in respondentibus columnis sint
(0), (7), (5), (4) et ila porro. fiet:
 (() = C + 1 = C + l - 21 et (D) fiet ex D et addito ) unde fiet
(8) = d +O( - 2tOD et ad 6 addi debebit 1CD, adeoque fiet
8) = 6 + 10D -21008, et ita porro atque adeo habebimus
+ es
+c
+deros +LSDS + 1OD
+
+ IC
=21 X2 - 10γ - 210d6 - 210
(2
(4
Hinc quaeramus duorum proximorum relationem inter se, verbi gratia
relationem inter (2), (4), 2, 8, ne opus set ad unamquam que novum
notum haberi praecedentes omnes. (2) - 2 = lC168, 1 -24, et similiter
(8) - f = 1035, 1 - 28. ergofiet (4) -2,:, (8) - f = 8, 1 - 24,:, 1- 27;  nisi quando 16) -
quia autem quadr. 1 - 24 = 1, itemque quadr. 1 - 28 = 1, quoniam si 2t est 1, fit 1 - 22 - -1
cuijus quadr. est 1, et si 4 est 0 fit 1 - 22 = 8, cujus etiam quadr. est 1. ideo
qun quadrando fiet quado ((4) -2,: L. 7) - Y) = 4 vel extrahendo
atrobique fiet (2) -2 - ++  F  + CY) + E, (+)q Et eodem
consideremus jam quod  notae velut O, D, 8 etc. componuntur ex formis
tentos
modo fiet: (8) - D = + (0) + 0, (+)C
a, ab, abc etc. una cum certis coefficientibus, quos habemus jam in colurmmo
ubi sunt nuneri progressionis Geometricae duplae affecti signis alternatis
haerul
itaque (0)O erit:
Esto Ergo C = a - 2 ab + + abc - 8 abcd. erc. fiet
et ad unum gradu
l - 2l a + 4 lab - 8l abc, etc = l, 1 - 2 a + 4 ab = 8 abc = l, 1 - 20 itaque tundem
ubi tantum profor promoventur formae ad literas una plures
fiet (3) - D = + l, 1- 20, (4)O seu (3) -D. = + (+) l, 0 -20  adeoque tandem
nisi L sit 0. Sed ne tunc quidem idetimaquaio prodire odetut  quod mirum
et
(+.) (0) si jam D
(7)0
fiet utique
Esto jam D p ab +g abe +Y abed +s + etc.
5) = p (ab) 9 (ab C) + Y (abcd) etc ubi formae parem thesi incluse sunt promotae ad
(5) -5= a F 2ali +. 3ovc r ex -
lteras una plures, et unum gradum novum. et (2) - D erit p la. + gt abq + r l ubedt et
(ab) ab - la = + (F) lC eritque p a +9 ab + r abc + ere = = () a 2 ab + 4 ab c - d abed, etc
abi) aber lati est autem p - 1, ergo f.  D = ( ab - rale + 2 abed - 0. abida p  abede f +8 abedetus - Habude syhi ( ete
lad (a) l
(∞) - D = l - 1t a +4 la - 8 abe t etc. = l, 1 - 20
et 4(0) + 0 = + 1 - 20, quod debet duci per (4)O, jem fit +(+) l, 1 - 20, , jam 1 - 20, 0 = C - 20 --0
ergo + (+) L f- 20, 8 = 4 (+) C 1 ex (D) - D = +l, 120, 0, fiet (D) - D = + (4) 10. itaque explicando
(D) - D = la- l ab + 2l aba -0. abed ete 
fiet la = ab + 2l abe = 0. abed, etc =  (=)B + (+) , a - 2 ab + 4 abc - 8 abed ex
seu a = 2 ab + 2 abc -0abad = + (+), a - 2ab + 4 ab - 8 abeid eic. videndum an non hoc succedat
itaque ut evitemus ambiguitates rediamus ad aequationem generalem, abi differentiarum
etsi non comparentur coifficientes Hele in  mt
abi quaoratum a ratione ifferentiarum aequatur  notae, qu seu qu(_(D) -D) =  qu () 0)
seu  os l. quE a 20 seu  Vel etiam seu (D) + D - 2 (∞) D =0, (C) + 0 ∞ - 2() seu
() + D = 2(D) D = O = ((6) = 0, 1 - (() sed quia (D) - d est 1 vel - 1) vel 0, hinc ejus qu. est
1 vet 0. et Ergo sed quadvatum ipsius, () est 1. Ergo it gr proinde qu (2) - D) = iquadr (D D.
jam u jam qu (1- (0)) = 1. Ergo quia biqu. ((5) - D) = cd. C, qu (1 - 0) fiet tande
(5) qu ((D) - Y) = C seu 6) + D - 2 D(D) = O, et (9) - 2D () = 0 - oD
t a 65)
110 = B. alo= N O+3. Cd in 1 3  B gr
rab