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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 77v, page id 00068207:0154
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abula valorum punctatorum ad Casum Maximum
Pre II. Nominibus
Pro III. Nominibus
a potterim esfecta
Ergo pro 1 Nominibus
Z= c. Ergo Z-
Pro 1V. Nominibus
tabulai hi lalores ad1B
fam Valores punctatos
Fuit O+p -280 = (())
Ergo (6)- C = a -20
abcd - 5. abc = 10 ab. -10
2b. - y =0. Ergo y -0
a OD+PD -210 D = (0D)
. - 2. 10 44. (0 -8. 5. +Z. 1. = 1.
Ergo ad vlenm
F-9 - a 4-7 -0 ad  ,
Pro V. Hominibus a - b ab -15
abcd = 15. abcde =b abedet=
a -2ab. + 4 abe - dabe t 116 abede - x abides -0
102 - 150 +80 - x = 0 182 -1
ProZ. ad VI. Nomina abcd-aubede +Z abidet - 1.
Atque haec Methodus etiam expeditior videtur priere Methodo. Sunt tamen utrique
suae seorsim commoditates d Praerogativae
Tertia Methodus est quae Columnas invenit independenter a toto systemate Columnarum
de tantum dependenter ab una vel paucis columnis, quam Verbis Leibnitianis ita explie
Sit O = n a + 12 ab + 13 abc + 14 a bc d + 15 abcde
2. H. a +2. 12 ab + 2. 13. abc. + 2. 19 abed + 2. 15 abcde et =0
Ergo 11 = 2. 12 = - 2.11. 13. = -2. 12 14 = -2. 17
Huic seriei si addaz Ap. +12 a p +13aba
venit Valor (() ad unum Nomen ampli
PTheor: II. Ergo (8 C-n Hira Hhab
d inde EOR 1. Coefficiens Membri cusquis in Colu
Ergo 0= 1a 2ab. + 4 abc -8abed etc: etc:
una elis duplus est praecede
tis Coefficientis cum Signo contrario.
D) = 22a + 23 ab + 24 abe +25 abcd + 26abe de +27 abcdet) (03)- D - 122a + 123 ab H2gabe +12s abel H2balud
+20D =   2. 12E ab +3. 123r4 + 2. 124,  + 2. 125, 4 +2. 126 a a
fit D - D = p D - p0
Ergo 30- D = 9 -6
C = =1a + 2 ab- 4 abc + 8abed -16 abede + 32 abcdef
22 - 4. ) 23+2t22 - - 2 (24 +2. 123 - 4 (25. +2. 124 - -8
+207 = + 2. 122 1 1 + Z. 12311, + 2. 124 111 + 21
D=  4  - 2E ab = C3 abc =29 abed 425 um
2.122 = =23 +22. 123 =4, -24.) 2. 124 = -8 -25 2.125 = 116-26.
N 122 -0. (2. 122, = 22. 4 1 23] 2123, 23 -129. 2. 124 - 29. 125
et 2.= q 2 f 1]- g, 8. 25 per 5 20 = +16- 16
P∞0 - + - 123 per H2 - 23 -124 P, 1t9- 24
Ergo 125 = 1. Z
Ia per saltus alternos utrigque, Dnae  odnae coefficientes ordine nt
CD: p = 122 a + 123 ab + 124 ab5 + 125 abcd +126 alu de)
D.P = , - 22 e = 23 ab - 24 abc - 25 abcd - 26 abe
Haec ultima Aequatio identificatur in singulis menibris
ja - 2 ab +4 abc -8 abid tibabedo (=0. Inveniendi autem Valores 2. 172. 2. 123. 2. 124. 2125.
= D = a  2ab - 23 abc-24 abccl - 25 abide
Excalculo ad dextram fit THEOREM A II.
Coefficiens D fit si summa duorum Coefficien
tium proxime praecedentium duplicata
statuatur affici signo contrario
ut pro D incipio oa + x ab sunma Coefficc: est a.
duplicatur cum Signo - Fac. - Z abc
tam ex hac Aq Aequatione quam ex priore DX
sic. 2. 1227-23 2l _Z. 127 = +2. 24, 2.
Hom Z. 123 = -24 +4
_ Z. 123= +2. 23+ 22. +2.22
ergo - 2414 = 2. 23 +4+2. 32. facit 24 = - (2. 2212. 23
Hem 2. 124-= : 25- 8.
2.124 = + 2. 24 -8 +2. 23 Fac. 25 = - (2. 23+2. 24)
Pergo 1 ab - Zabc Suma 1- 2 = - 1. Duplicata cu Signo contr. fit +Z.
Pergo -2 abe + 2abcd Suma Coessice = 0. Facit - 0. abc de
Pergo +rabe d = 0 abede Suma Coeffucc = 2. Facit - 4. abedet
Pergo vabede  abcdef sua Coefficc = - 4. Fac. +8 e sic porro
Et sic porro 26 - - (2. 24 + 2.25) 27 = - (2. 25 +2. 26) et
Ita jam Columna Dna ex se ipsa elabo
rabitur per Theorema Il. in calculo
Pro Columna OD ex se ipsa inveniendâ. Capio - 123 = 2. 122- 22 ex Aequatione V2
THEDREMA III.
Coefficientes Columnae sal fiunt ita: Duo proximi
coefficientes additi et duplati hanc summam subtra,
5]-8- 0 10D Seu 000 -8 - 8D - 0
=08- 2028
Explico 1ZZ. ex WX = a. fit - 123 = 2. 122-1
fit Hem. 124 = 1 23 eBZ. Seu 123 = 1-2.122.
Explico - 23 ex VX fit - 124 = 2. 123+212
Htem ex V2 125-= 24-2. 124.
hunt a Coefficiente Columaae Solis que Minori additorum respondet.
. 5 por. 202s. Calculus pro He
(OD -S
Ergo x - 32. & - x - -3
e Sit D - 22 ab. + 23 abc +24 abed + 25 abede +2o abede f etc: sit OD - 122 ab + 123 abc 4 es abdl 412s abido
(0 -03: p. +20D - D-0
Pone (0) -0 =0
4. -2.6. + 4. q = X. 1. =0, fi
a, 20. -12 -X =0
(1) - C +20 - 1. = 0 Ergo (1)- 0,: p = 1. + 12a + 13 ab + 14 abc + 15 abid +16 abede etc
Fuit D +pO - 2p0 D- (D
Ergo (D) - D +26D-0-
d
Explico +24 ex VN fit 125 = 4. -2. 123. -2. 124 etc.
Inde fit THEOR: III.
Sit 8- 44 abed +45 abeder a 6 ab. f et 50D - 1247 abedesgue +124V abunh eti:
Ergo OD5: p = 1247 ab . f +1248 ab ag +1249 ab h.)
Op oi ee abe
000 - 5D - 8D-80) = Hrab a asab. udl B rsale xirabf a quabig  +g abucta 20
00+. 00.0. 0 00
Sece 12g= -2, 2. 1E,. 2. 1
(+0D = 123 abc + 129 ab, d +125 ab, e +126 ab f + 127 ab. 1g + 128 abuh
SD9D =  a    n  246 abif 127 ab. 9 + H ab H.)
Aujus autem calculi prosecutio inopinatam prolixitatem offert
pro Columnâ otis ex solo ore de OD continuanda
fali Theoremate 2 49 = 2. 129 + 3 121 + 2. ei +  eM unde Regulam non ausim
Ergo hic labor in altioribus colamnis nondum succefit
2. 410 - 3. 411 - 2. 41E - L 413
Pro V. Nominibus
Effectusyabede. + Zabia
ab -2abc + 2abca =G abcdef - 2.
Proy. ad VI. Nomina - 15 + 2 - 1. Ergo Z - 16.
Systema ad VI. Nomina