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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 81r, page id 00068207:0161
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1
cec
 pr qu  2grad . 9 abe + 2. 9a abid, qu -.
si 914 g grab x 43 abc est nota dyadica
porro hine habemustecum
37) = 9D = pD - 2pCD vel (0D) - OD, : p = d - 20D
(06) = 06 + p6 - 2p06 vel (06) -96,. p = 6- 205
(04) = 08 + p - 2pO vet (04)- O=, p - 4 - 208
Et ita porro. Ope jam harum aequationum generalem
exhribeo determinationem columnae cujusque methodo una
eademque, ut nunc apparebit. Es Columna aequaevis
post d, vocetur 5, et Ob vocetur D. Fiat
6 = 92 ab +93 abc +94 abcd + g5 abede + 96 abedef + 97 abedefgh + ete
D = 102 ab + 103 abc + 104 abid + 105 abcde +106 abedes + 10) abcdesque t etc
C unde erit
(D) - , : p = 102 a + 103 a b + 104 abc + 10s abcd + etc.
sed ex praemissis aequationibus est
(D) - 6, : p = 8 - 20; seu ((1) - 6, p) + 20 - 5 = 0
quam aequationem per asumtas series explicando, feet
+102 a + 103 ab +104 abc +105 abcd + 106 abede tete
+2.102 +2103 +2. 104 +. 105 +ete (=0
- 92 - 93 - 94 - 95.
- etc S
sequentes
quae aequatio ut fiat idenfica seu ut  evarescant, habebimus pro invemendis a
aequationes pro ssuntitiis 102, 103, 104, etc. sequentes:
102 =0 103 = 1. 92 104 = 193 - 232 105 = 19t - 2. 93+ 4. 92
106 = 1. 95 - 2.97 + 497 - 8.92, et ita porro. Sed quia aduc
alia adf duplex est ordo assumtitiarum, seu praeter 102, 103, 104 etc,
assumtae etiam sunt 92, 93, 94, etc. ideo adhuc una opus est
equatione, quam habebimus, si actu ipso valorem ipsius assuntum
multiplicemus per valorem ipsius jam inventum, ut prodeat.
nimirum
Ot seu , ita iterum habebimus ipsas 102, 103, 104 +C, per ipsas 92, 9, 94 et. Constat esse
= Cd F, 3abe -4 abed + 8 abede - 16 abedef t etc. Eum ergo
aorem ultiplicando per patorem ipsius 8, seu per gu abt guabe
+94 abcd + etc. prodibit productum rges en eciem, 
cujus singuli termini aequandi sunt singulis terminis valoris ipsius Od
vel ipsius , seu nempe formula 102 ab + 103 abc =+ 104 abcd + et c.
Hoc productum prolixum in speciem, mirifice contrahitur per
 pre singularia numerorum compendia,
ounibusque, t ordinatis prodit elegans  admodum
abula hujusmodi quantunlibet continud ilis
102 = - O,l.B2
103 = + 1. 3.2 + 1. 113
104 = - 2.6. 42 - 14. 9 - 014
105 = + 4. 10.92 +210. 13 + 1. 5 44 +1.1. 95
107 = + 16. 2. 92 + 8. 3.  +43594 +22. 95 + 1. 7. 6 +1. 197
108 = - 32. 28.)2 = 165613 - 8. 7094 -456.95 - 2 28. 1f - 1. 8.97 -0. 1. 98
109 = +697612 + 32813 +16 2614 +826.95 +4.8496 + 23697 + 1. 9_ + 1. 1.9)
Quos valores assumtitiarum 102, 10, 104, et c. prioribus
earundem valoribus aequando, tandem pro coefficientibus columnae d
quaesitis 92, 93, 94, 95 etc. prodit Tabula sequens, non minus elegans
O - 11 91
0 - 11. 93 + 192
C= 1195 44. 14 + 4. 1. 43
O= 1197 teB, 6 +43.95 +8. 117
O- 149 +. 418 +4697 + 8. 4 1 146. 1. 15
B - 1 191 15G2 1 4. 10. 19 18. 10.B +15 97 + 32.96
ita quivis columnae propositae e coefficiens impar generali methodo
habetur per coefficientibs ejusdem columnae praecedenti competenti
numero in geometricos binarios, et in combinatorios ordine ductis.
prodire bis, exempli grabia 95 = -4. 9  - 4 93 sis prodit, mempe
tum ex ex valoribus duobus ipsius
105, itemque ex valoribus duobus ipsius 106. Nam valores
duo ipsius 105 sunt 105 = 1. 94 - 2.93 + 4. 92 et 105 = 4. 1092 +2. 10. 93+ 15 99 + r195
unde pror. 92 substituendo - 93 prodit e dictus valor ipsius 95. sed
 imatii i u tate m es it e o
idem prodit si aequemus valores ipsius 106, nam habuimus
is aerciorbusis pro caleuli quam compobat