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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 18v, page id 00068049:0036
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Dideamus in casibus ubi obtinemue
quomodo demum res otingat:
Mirisicissi
nec andeo
eo fndere
successum
de sideratur
sit y t bege cr aequa yy - bb aequandus quadrato, fit
Methodus
ante
Y= e u+ um = yy 4 - 2ye + ec. fit y = e + bb
seu y =  ec + bb, et quid egc nam e + 2ec bb + b - 4 eelb
namyu - bb =
Hieres omnis
aequalitates
qumir conpotialis
q ec
seu Goryy -bb = re-bb. Sed videamus quomodo hoc influat
in factores.
y +b = eet bb + 2eb
et y - b = Cet bb - 2eb
ita ambo factores sunt quadrati in numeratore
faciamus similiter y- Rodeamus ad nostre
quatuor factores: 7+a y +b, ytc, y+d. sit
RXX + 5X, + ∞dTa =  pxx + 49X + B
y = PXF( 99X + B
Dhex  asx 1 et2:, x x + sx + 
Hoc si quaesissemus Z naa factoru fores
in experimen
reducitur ad
multiplices
y = eet ine nd
netr fit: t ee+ ue f 10
cujus numerator aequandus quadrato
re
+21ae + 20. a 3:, , 7C + 20
Ergo  11 +21 4 = 10 + 20a
seu 11 + 2. 11. 21F 21. 21 aa = 4 18 + B. 10. 20a + 20 aa
ubi faciendo 11 =0, et 20 = 0 fiet 21 a = 2. 10 Yi seu 21 = +a. 10
unde posito 10 =1 fit 21 = + = a vel - 1 a. vel et si a sit (Ib
id est + b verl - b utiue res succedit.
d= Es V + C. i+hh = C ithib - 4tia
4+
4sit
sed si sit aequali
ce B0 +C. fiet.
ec
fiet VD = + cc. it hn
2hh
Di-hh
et ∞ = E  hh + 1 4 tih seu v = = CFC1+, + 1+ i th
h.
quia ergo hoc sensu V includitia vel b, vel c vel d seu est
lambigna, fiet e
y = ee + 10 et y+ v - tee  ove + 10
21C
et  21. v = 10. qui vaon succedit proinde pro duobus at
et succedit solutio pro duabus solationibus i duobus valoribus ipsius v, qui solim
differunt offirmatione et negatione, neque enimi ambiguitas  ex illis orta
ingreditur in valorem ipsiu y.  Verum ut  valer ipsius y proquatur
radicibus valeret, efficiendum essebt ut eum ingrederetur tantum v- fEvx +
 seu ut tolli possit, y ex speciulis sui valores, sed ambiguitate remota
a
sit ergo y + v e y = 10e0 + n e +12. fit y+b = 1o eC + ne + 12
a
C+  C + v2I antiov
ec v 
debet esse   = 11+D2 Ut 21. v. seu 1 + 2. 11. V + vv 4. 12 + 4. 2. v
Quadretur adhm, semel, (CC 1 + 4. 1V + 6p p. VB + 41 V, v seu 16. 12
= 2. 11 V = 11. 11
141212141
B 12. H. 1
4. ll. 11. VD+ 2.11 5 -11 F1 5
destrnamus B, quod fit farends 2nt V quod non licet quoniam sic est.
et destrueretur
uo quam volumus retigere vel postius faciendo,
si jam possemus destrulre V, et residuum e coefficiente ipsi VV
ita inferphelavi ut faciant e I+hih tolleretur V. seu ambignitas e
invemendo n pro v ith substituendo cx deinde per residuum inveni
retur aliqua litera ad huc superctes, cujus rationali nihis hos turbaret
irrationalitas. Sed quia hic res non procedit in aeg. 5. nam tollendo faciendo
4. 21 = 2. f11 = 0, follitur X vD atfaciendo 4 12 = 11. 1 = 0. tollitur
ut unius aqua teminus absclutus; ideo loco aeq. 4 in seipsam dyora ducamus ea in arbitrariam
tiouis arviguis, vv 43, V + 32. fit V + 31V3+ 32 vP = +4. 21 V +4 Y
sublata amtigunte it 3) = 4. 21. = 2. 11 et 4. 21 - 2.11. 32 4 4. 12-11. 1131 =3. 1
seu ∞. 32 + 4. 12- 11. 11=0, et gen
C0)
2. 112
4. 12_VD + 4. 237 V 4. p
11. 1.
 et senique debet esse : 4. 21 - 2.11 31 4 4 12 - 11. 1. -32 = e 1+hh
=II. HI
seu cu
4, 21. - 2. 1)  + B. 12 - 2. 11. 1 E C, 1+ hit et postremo - 4. 12L1LII B= C: hh
seu 4. 12 - 11. 11 = C = CC: tr; per  (12t hibetur valor literae 1.2
es ex
(5) et ex aeq. 1o per aeq. 12. fit 4. 21 = 2. 11= V, C 1+ hh + Y et 10 maneat =1.  sut
sit _2120 et
u
fit 1. .2
est in deferminat
e fiet y-ce Et tctht e gitia  ebes
ih eh
sl
A. ope a
terisseum ie desertntatus
B. v et AtBi Bt 
quid omnibus
radicibus falisfit
reductis onitus
ad id quod oibu
commune est