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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 42v, page id 00068217:0086
# Scan: The same scan as fol. 41r (00068217:0083), where its text is given.
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a b aequ. ab ab  - abc. seu abX - abc
aebc aegu abc a. aequ abc X - 4 abcd
abed aegu
5 abes qu scuabrexus abede
a aque abcecq
ab ab qqu ab a aequ.  abX = 2ab
ab1.
Vigu ab aequ y aequ   ab.
y aequ ab + abCX -4co
c
a in a aequ a + ab
X aequ a X aequ a + 2ab
6 xde
yZ. aequ a
2ab
a rab
X’aequ. a +3 ab +6 abc, seu a 4+ 3 ab X - 32
aeb. rau aba aequ abX - 3 abc
S Ergo ab aequ abX 3abc X  12 abcd) - 4aeb
6abed) -6abc - (6 a l1d) 10gbi de
9 a bed
26abC cd
- 1Babcd = buabede
6
(= 12 abcd)
aeb aequ. aeb 4 aequ aebo x - abc ) aebe rqu abe a rquabex-  rabi rabed
a Ansic brevius omnia investigare licebit ab aqu ab c a  est autem a aequ. X- db 3ab. X +3 Habe
Ergo a b aequ ab XC - 3ab ab X + 3abc ab
ZabC rqu. XabC 2ab aequtabC X-Ga. bcd -20 abede - a bc( a bed). 3a b - babek a bex
et ’abc, ab et ad +de  abc + 3 a bcd +sabcde
rujus baVc aqu. V ab 6 abc, aequ. ab. X 3 - ( a bcd -( ab ede - 3ab - (3 a bcC 3 ab cd) - a b - abc
6ACd.
6 cde
ab
a
9aebed
avx abd
29b
u
cb aequ. jam supra invenimus esse: ab. aequ. ab X - 3abe X + 3ab C. Ergo a bX seu (ex labula) a b + a b  bC aequ. ab X - 3 abc X + habe X
e a
 et eodem mobo: abc aequ. ab cX = 4 abcd. Ergo ab CX seu sextabula) a bc + a bc + a bcd aequ abc X - 4 abcdX
habedx - salede
et eodem a b X aequ. seu ex tab.  ab 1 b +3 a bc  2 a V + 9 a be (9 4 ab 6 abcd, erit  aqu ab X - 3 abCX
Nusus aliter
3abX
 ab aequ ab a aqu. ab X - 3 ae b  abed - Z8. aebc aequ abc 2 aequ abe X - rabid
 2ab seuaequ abX - 3a b  ab ac
3ac3ac
rede 3C
abe
Z aequ. abc
pro seundo gradu A, ab: 4 ab ug.  ab. 4 aqu ab X - 2a1). absrqu ab 9. agu ab X - 3 a b. X). ab s b 
18
abc abrab ZX -  aZa A X aqu. a + 4 a b + 6a b + 12 abc + 24 abcd
ab aqu aeb u iqu a bX aeb
aeb aequ ab
de
b
X- rab
a a
ab
intribus 6
in quatior 
in qualuor 12
in quaeque 20
in duobus ab
in tribus 6
OabEdX- 30 abede
Jitaque tres sunt super sunt literae ab. a bc abc
aequ a + aeb aequ X 3alex + habex. ergo a b aequ. XZ at - 3abX +habCX. equ. Ergo a b aequabX - 5ZX + 4c - 2ab abaju abx - 17+ rabn 8
- 2
(, 16. = 12
=5, 4 t + 8c0
(192591 -20 (- 510, 5) +40
25
aba aqu abX - 3abX - 29
3abX
abe
+ habe
EabX. gabiX 2al. -gabeX +4u
ablaequ. (ab c  a)se eiqu. abcx - 2a bc- a bcd. 2e abcde-
abbd aequ. abed  quabedra aequ. abedx - sabede
20
tab
2a bc aequ abc 2ab aequ abeX - 6 a bcd - 20 abede - abc - a bed 
3e
90
ut  subtrahatur ab 21. relinquat 6.
ita solis numeris, ponendo a + b vel a + b + c. vel a +b+ C + d vel a + b+c +d + C,  et possit eequ aequete ru
posito C tn 2 aequ. a. aequ. b. aequ. c. Mn. progediendo ordine omnes numeros afficientes sine
ullo alio calculo inveniemus pr sufficiebret progredi usque ad  a +b+C+d. sed aus ad 5 nonissime
processi comprobandi causa. In sequentibus enim in infinitum numeri lex o
qi Conclusio hujus paginae.
video n p omnes formas a primo usque ad
quintum gradum indusive exprimi posse per
potentias ipsius X affectas formis aequaliter
in uno quoque motao exemplo compositis
ut a. d. a. ab. a. abc. a. aeb. abcd
a accedente forma abC, seu abcab. quae sola
per illas aequaliter compositas explicari non
ad abed scum psta porius in tulam resolvatur ve
ae ascendendo ad ab, at. Tales igitur
omnes solli non possunt,ut in
a bc aego abc Gabe ab4X = 18 a bcd - 60 abede - 3ab - (6 a b. (- 6 a 1.d - (bed - ab =, a bc
Bacd
aevede
60
aebequ. ab a aqu ab X - 3a VX ∞. -6abc et hinc certa demontratione
TB - 27 -121 6  -487. quodnon proredit riho quia nec ZX valorem hum ingreditur
+6 ab 
250. - 60 - 190 - 30.
25 -5
250 = 120 = 20, - 30 - 20
2s
abab
6 = BZX ratio quia ut tribus non potest cddi nisi Z. id est in truibus unilotem facientibus, 3. debetantem esse 15. ergo 15 dabit 5. mnerur. 15, ut
X2 1ab X, 3Z abc
in dusius ab in duobus est a ab a aequ abX - ab
a
ab aqu a b a equ a b x- glc. 
2lb
ae
52
 1
ope trium saequationum quaerendae.
Rurs aiter a a. aequ. a + ab. aequ X - 2abX. Ergo H a b aequ. + X - a - rabX.. jam X - a3. aequ. 3 ab X = 3Z. Ergo a b aequ ab X - 3Z et supra.
B a x (abe)
quae aequatio quia conerdit cum illa qua inveni a7b. ideo
hino disco tandem erustra quaeri modum tollendi forman abc
ideoque tuto relinqui potest.
sepemuom aded, abc
seu qu ex imro
et in sext ab, a00
Vide et paginam
versam
3abX colligo quod a a valore ipsius 6a  colli libera ri non potest.
6abc
nam si posset deberet ad exprimi per solum Zo nec
exprimi per solas illas formas: eodem modo compositais nam
Sid posset tunc deberet abC posse per ZX neque enim
alia forua superest, neque enim X vel E redire potet quia
redire efiam deberent ab et aV. circa quae tamen per
novae literae accessum nihil mutari potest.
ab + ac + ab+ aC4+ b E + bc
ab a + 3ab +6abc.. - 2abx
ac
ab
ev.
a
stC
18 b8
beab a + ab C + 4 abd, abc LabC
ab abc
ea
ac pa + acb3 +3 aC + 3aC6, (3 a cB 46 abc
auc3
bc 13 bc a + 3bC +3bca Hbca 16abc
bC
bea
bX
4ab
ab3
2ad, quabex. 7a bid. 2 abc- qabede
abc ego ab aequ ab X - a b2
abcc ab. aequ
ab aequiat Ego
abaequabx - 22
fit ab X abc- babC
 -6aVc
27
34b
3ac
ad
abe
abc
-346
-64bc
8c50 =bdabede
o Vere
=abe
baBC
0ab
=18ab10
-9abcd
acb acb
aego ab X-  abc = 3ab - 6a b c.5abc
2, li 21
dissimiliteonsmnes tolli posse praeter abcd, ab, et ratio
est quia non possunt ad potentiam ippius accommodari
nisi iteram reascendendo ad abcd, a seu redeundo
potest. In sexto gradi similiter videntur aliter
ab aequ
bca