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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 251v, page id 00068201:0502
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(D  sit = D = 1 ab 4 12 abc + 13 abed  14 abede + is abedet
fiet () - D = L, na + 12 ab + 1abe + 12t abed = l, 0, , - 2. 11 ab  - 2 12 ab c = 2. 13 abcd - 2. 14 abcde
itaque 0, in 1 - 2- 1 ab - 2. 12 abc - 2. 13 abcd et c debet faciere V a + 12 ab + 13 abc + Ct;
jam C =  a - 2 ab + 4 abc - 8 abcd + etc
( in + 2) = a -r ab + 4 abc - Y abid +1b abide - 32 abcdef + 6+ abedef
 in -  + D. = = a +, ab 62abe + 4 abcd - gubede + ibabudet
C = a - 2 ab + 4 abc - 8 abcd + 16 abide + 32 abcdef - etc
si sit D = 1 ab + C 12 abc + 13 abed + 14 abcde + 15 abcdeF
2006 -08 3 -1: 1 24
oportet ut na + 13 ab = 13 abc + 14 abcd + 15 abede + etc. prodeat matiplicando C per 1- 2D, et cum
que
aequatu pademens debent  dentica invenientur eo ipso incognitae 11, 12, 13, 14, et.
terminabuntur
 Et quia habemus  = 1 ab. = 2abe + 2abe +0 abid = 4 abed + 8 abcdes - 8 abidefg +0 abidefyhi + 6 aui-nrantt
o
osd
huno similiter si jam fiat 6 = 2rabe + 23 abed + 2t abide + 25 abidet, etc
habe oportet ut 42 ab +23 abc + 24 abed +25 abide etc prodeat maltiplicando
C = 1a = 2 ab + 4 abc - 8 abed + 16 abc de - 32 abedef + et 6) - 7: l- 50 = 0 - 20D, et 0D = 0 -8; 2
= () 3 = l. 0, L2d (5) 6 = t, O, D, - 20
ael 9 = 82 ab + 23 abe 124 abed + 25 abite + 26 abede f. + 27 abedefy + et (1. 8, l2d  t 610 = b gt+
5 = 33 abc + 34 abid + 35 abide 1 36 abedef + 37 abcdefy +38 abidesgh + eu
 = 44 abed + 45 abide + 4bubudeft 47 alidefg+ 48 obuasgh +49 al defghit ea
Prodit 22a +23 ab + 24 abc + 25 abed + 26 abud et etc. multiplicando O per 1- 23, quod at fucerdat invenientur 22, 23, 24. et C
33 ab +34 abc + 35 abed + 36 abede +37 abidef tet
3 4 abc + 4g abidta babide t47abedet + 4Y abedesu ea
exc
ex
CD per 1-26 seu 0 - 5V, 4 - 5 invemtntur 33, 39, 35, etc
DS  1 sen L0 - - - 7, per  
utea
s
(5) - D,: l (6) - 8, :l (4)- Z.:l (4)- 2, :l
5u = O per 1 -23 2 = 0D par 1 - 26 8 = 0D6 per 1 - 28 7 =0984 per 1f22
5V
si 2 =0 fit
O=151 + 23 + 4787
si 4 =1 fit
O = 15 + 22 + 43-8I
et ( + 97 = 15 + 22 +4
si. 2
dD = LO - =5V 4 = C3 - 20D8. fit 6D6 = = CD,   3)8 = 2C -  8- 7
B = 4 -  V - =A - 20808 fit 0D64 =  6 - L 5V - + 3 - L B
et eodem modo fiet c2360D68 = 160- 16s - 4 7 =  3 = 7. Et ita porro
1+. X Ethug
Unde prodibunt theoremata aequationes, quae ut fc succedant incognitae assumtitiae invenientur
quidem talia, ut nunquam nisi duae series in seinbicem ducantur. O= sa
est
S =  que 2O, per  -8 2 = +cd-  de, per C  6
Scribi poterit utique
8(1- 2) I = 5P+ 2 7r 93
Se = O, per 1 - 2D 3 = +0 - = 5e, per 1- 26 3= =0- +  - + 4, per 1 2 8 7 - 20 - 1 5 - 4 7 - 2 3, per 1 - 28 f
S+ = LC per L-D + - 40 + N, per  - 8 3 = 
Seu 51 = O per 1 - 2D 27 = O - 52, per 1 - 28 43 = 0 - 8 - 22, (er 1 - 28 81 = C - 51 - 2 + - 4 3, per 1 - 2 2 f5t ita pon
g
Quaram aequationum ope, ut fiant identica, lite qcoefficientes assumtitii determinabuntur, qui simul reperiuatur in N et 2,
item in 6 et , in Q et 3, in 2 et T; nemper per pimam harum determinatia aequationum determinabuntur
coefficientes 22, 23, 24 etc pro Columna 2da; per secundam 33,3435, etct pro columna 3tia; et ita porro
sed et aliter rem tautemus hoc modo: + - 6D, 26 (2 - 4,:l  seu 7 = 0d84, 1- 2+, C+
A(4) - Z, :l sen 5 = 038, 1 - 8, et fiet 036 = 3 3:, 1 -  = 2: 7(.- 21) seu
9, 104, :, 1=24 = 7: 3. sed quia quadratum ab 1- 24, itemue ab 1 - 28 est 1, ideo
quadrando utrobiu fit  = 77: B3. ubi notandum est 77 non esse  = 2,, nec 33 esse = B
fiet
nec habent, semper 
netae dus adjue Fer alia
hotamum diut eyadicarum, possunt
genotae dyadicae
quia et quia C S, , X, 7, etc. non suit
latus aequale quadrato, cum enim sint differentiae duatum
Eodem mobo dehebit esse C = quia (∞) - 6,. l = 1. fiet
ses sest: 1 = O seu ses =  (1) - C vocemus 2 fiet O = 505: 2d.
esse 0 vel L vel - 1
investigemus jam quid sit 2. quia C = a - 2 ab + 4 abe - 8abed, ete fiet (6) - C = l, 1 - 24. + 4 ab - 8abe + CH
Et 0) = l, 1 -2 Ergo (6) - O, :l seu 2 = 1 - 26, et firt C = S2S :, qu (1 - 20)
sed qu. (1 - 213) = 1, et constat ergo fiet tandem  Se se = C
Tentemus experimento: L D = 1ab =- 2abc +habe +3 abeo = 4 abede + 8 abcd ef -  abedesg +0 abcdefyh
tonteo experianum in fit X = 1a - 2 ab + 2 abe +0 abc - 4. abid + 8 abede - 8 abidef +o abcdesu
Ex Experianum in simplicissimo, ubi solum a, fit sus = C nam 1.1. aa = 1a. pugpedianum ad b, et fiet
As = 1a + 2ab + 4 ab = 1 a = 2ab sit X 22 a +27 ab + 24 abc distamuus in his tri sistamus in D, et
V 1a - 2ab+ Tali dat. 8
+R. 22. 23 ab +6. 22. 23 abc _
16. 3. 4 abc et 22. 24 abea
oasit. - d aib  et qui,
et quadremus prodibit 22. 22a +,
L 16 cy abc + 9. 22. 25 abco
fit 22 = 1. Hic ob ab sit 2 + 4. 274 23. 23 = -2
seu 23. 23+ 4. 23 +4 = -2+2 Et 23 + 2 =0 sen 23 = -2
ob abe fit - 12 + 6. 34 + 24 - 12. 24 +24. 24 = 4. seu fiet
24. 24 - 6. 24 + 9 = 1 seu 24 - 3 = - 1 sin 24 = _ 2
+ 1. 23. 23 ab + 6. 23. 13abe + 6. 23. 23 abid
+6. 33. 24 abc + 24. 23. 14 abe
+ 12. 23. 35 abca
F1. 24. 24 abC + 12. 24. 24 abc
+ g. 24. 25 abcd
+G. isusabio