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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 174v, page id 00068198:0348
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=348
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sit eL O ingrat d = InZ + ag  = pu t ati
sit E 4 +d 5E +d sit 42=
O= saztas D2 Caztag G= Saztan
OD= ataaque +a YZ2+ s + 59 0D = a YEZ+ F1Z+ sh
aX = imOD + n OQ +  pDG tagZ tar de
an s. an fh
ramr trur +rapr
a’en aten aep
aem. acn.. atcp..
aequ apg.
2aegr.
acq.
ZOn. H o st e attH OD+ asiosQ ta st Q ras 2Z + a5
ratd
sd
ras 2atd raud
Haec yparanda, idemque ad huc simel
empe bis novse
Habemus 15 aequationes et arbinaria,
at
a P dk
atY
at er
ab
+ as sg
at
ad au q
2ade
teb 829
042 +  sn + 9B
ax =arop Z (0D mp2OQ +mn Z  rnphOS mptamnf 9Q tamZZ + anf Z +and s_
Ag. nq. rap9.
tbc
at
e
aetfh
a gh
at
a valore ipsius X habobium 5, a duabus ruditibus 10, et a valoribus 0, D, e adhuc 3. summa 18
Aliter sit  ax = mOD + nOQ + pD E t et ax+ ab aequ. quadruto atlae 110 + uD+31G
et ax +BC vg. qto ab 410 + 51D +61Q denique ait ae aeqgto ab y10 +81D+918. Ductis jam
aleibus hou tium fis tubus 10 + 218+31G, 410+ 51D+61Q, nO+81D+918 in se invicem, efficiendum erite ut
destruatur CDE fittantem 11. 51. 91 F 11. 61. 81 + 2. 41. 91 + 21. 67. 71 + 31. 41. 81 + 31.51. 1 = 0
Habemus aequationes comparatitias ter 5 seu 15, cui addabur destructitia ipsius CDe sunt in universum 
aequationes 16. arbitrariae autem sunt m, n, p, gr. 11, 21, 31; 41, 81, 61; 71, 81, 91; f, 9, h adeoque in summa 17
itaque non despero rem posse effici hac via, que videtur simplicissima et praecedente nihilo vadetur inferior
superest ad huc arbitraria ex ipsa explicatione ipsius X. illud dubiu si 11. 21 = 41. s1 1. 31 = 41. 61 21. 31 = 51. b
an 11 = 41   et ia et 21 - 51, et 31 = 51 ? quod matum foret 11 = 41. 51 : 21 = 41. 61 : 31. fit  51 31 = 21. 6).
ergos 21 = A31. 51: 61 = 51. 61: 31 et fiet 312 = 61 et pari jure  212 = 51 et H = q, hinc
foct faceo possumus Saextab = W FL O + 21D +312. saextae = 1O =D +3Q et Saxta = 11Ot2. 31G
faciendo scil.  11 = 41 = 71 et 21 = 51 = + 81 et 31 = +61 = - 91 seu si = 2i 81 = A s2F 61 = +Y 3s 9- a
en
quaevis radix cuiquis val radicis valur habet unam negativam tres affirmativas Caeterum, ut
aqe sit = 15 + 21 + 3 = 41 + Si +61_ = 7,2 + g1 + 9i succedit ex jam inventis sua sponte. postremo fit
ar+ ab ar tab = 1BF 11f +219 +3h, sed hic demum prodis absurditas, nam peret art ab= artaec =aerrae
 Face videumus an res melius, si faci pro _X+C
tq V C W + D. pet IY KX et X+d adhibeamus ex + C et KXt
Fortasse licebit viteamus eriam an pro XX tab et XX + ab, se prodedere licelt ambo aquando quad vatis
ut far cianuu
X = _m 9 + nD + PQ ir ita exx +ab aequemus Bto ab g∞ + r9+5 et KXX + ab aequamus Hto a tO + vD WC
ar + exX= EmnoD tmpOQp D tmmaz temmas
de pe
a epp a
C =1a iaqu rars Ha q az ae pas
qeyagr = ema g= emniar =emp: 2 5 fu Sn = Yp. et fit rosn: p
ruisus r = enp. a5 fietque epp = a 55. seu 6 = pp se. a
Sed video rem non procedere ob absurdituim ultimo leumrno
sit  ax tab seu ameD rand  apd  aq
aqu. Dto at 1Btu BNI seu 211. E1 2 113 221. 31 + 1aZ 10
Sit si at
aex+ aC = yto ab 4 0 + 51 D +6,9.
ats +a d = quo ab nO +BD+ 91 8
en 21 =  91. 51 eH. 31 = 416) C.V. 31 = 41. 61 fit
tiet ae a4 = C. 1 a S = erY a61 = e31
aCx =
aCx =
Sit a v = ut dx
d
mendo
sig
av
pro min, p, 1 fia