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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 290v, page id 00068201:0580
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=580
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X⊓  d + c.
X 3d e X + d sit X (+ pX)  3d e X
orscr
entque. d d 4 a r d3 + r 18Y - 0
s sive d11. B += + Sr c07
fetque (2) = +, 7- c Y
rursus ex altera aequatione dtep
est satis ubitiariarum Si faciamus:
Fp0.
v
adeoque d- v d + v grudo sp
d - a n rd rp dE + p c)
27
sP
ap I = co sive de, ~ + sv st
+SV Cd est autem +Y. VrI sed ad istam comparationem non
Erp
4p
ne p bc
ergo mB
m+ H,  b +C H mb
X + pX2 , 4X + rX + 5X.
sit: X 4+ 3CX + C + b y  N. et X 4X + d + cY ,0. Erit Vr = X - 3rX - d - X = 3CX-1
et fe sive Ax +3lY X , db Y e, tve X 5+ 2bV X +dh. po. aequatio comparanda datae
cc
3eco
-C .. -3e0 - ce
dccc
b-e
b-C
Jin ex prima aequatione eit X + 3co X +C p0. erit Xp sB -c. by + sereby t 7  Co + s bj rolgerdis lo
+ b7
Et quaerendo eodem modo x adhuc semel ope alterius aequationis, singulos terminos singulis aequando
fiet: c+ by 1 d + BV. imo hoc jam tam verum est unde sequitur et CoV
entque: y e c- d. et in aequatione data fiet: X + 30 + db - ce. comparanda cum X ~q+ r. 1 0.
c- b
XH fl + sc r9b 8
xH
rum 2f9 b X
279c
2fgbcc
2f9bcb
fier  v,1-4 et sed haec imania, nam potuit fieri Z cabys.
X, S +st b
lis ebi 
259b 259bcb
2f 9cbc
259b
b -c
2f9 e
259b.C
2529bc b 2f9b2
X fl rsc 496 + gC. X f b + 2f bc +  +fC, +9b + 296
396c22b2
 + 2fgb3 X
+259b
+ 2f9beC
+bec.
fgbc b.
2fqveb
2f92 C5
+ 259b 2b 2f9 Bcc
+259bcb7 2f968c
+ 2f967 +259c, + 2f9bc, c + 2 fgbe b
X
X
X
-
-
+19..
X 3 = 89X - r
X7 - qX + r 3
+
or..
X = 3pX er
X
4 3P X an
X (pX -op X (= 3pr X) +
+3p. X7
+3pr
X + X  + qX + rX + SX + + 
3 + 5py + fy  1ob3y + 5 b2y b
+B. 14 pb +apb
+q +39b
+ qp rpbt
39V +9b3
qu - 
+ q X + Y
4 + qu X 2 - r 0
+r4(V 10 sit de c, seu ex c
 Dividatur haec aequatio in duas
ide nempe X + 3d eX FY p7 0
et v + P ide
+ a + b +, C +c
 a - 6 n e =c erit aB C. et e- c
a +s e c. idem:
t
ab nc A  +  b 4 ub 4 nC
meth
it p  2 anerit: P 2p qa p 9 - 2pr
eit
ive p - 4pi9 C  (29 6pr
p F6pr pIpg, sive p +brpi Apqu
seu 125b
= 125,3
+ 3,5bp 3,5BP + 25
N6 - 29X +   ergo si aequaero tructabilys erit, 9P P
sive X = qX A +r
X⊓ X + b.
sit jam P +etBo. erit bp -p
Sit et 10 b +6xb 139b +Y  sive
( +6p 2P +r 1.
(25
25
es sire 4~p3 - 24p +Y B07 sive. p -  4P +2
Sine per praeparationem videamu an fieri possit
3 - 1528 +  R, antequam accedatur ad destructionem
terminorum,
1et b2 + 3, 25 p b2 +3, 5p b + p, - 15 10b2 5b 1obr p +25 5 10b3 F v.
+3, 25 p b M. patet b
=1, 25p. destraiet prae.
+. 158 0p..
1767)
formaves esse
mutiles
4pb .. 27b.
 6pb
39 b
Ponamus y1 Z. seu  Z b
erit a 2 Z2
+c
Zare V EscZ - 30Z+ 0 Z
430b3 + 12pb + 39b, + 6pb + 12 p b + 3 p4 - 10b - 6pb - 39b + Y. qui si alessent p. et Y fieret 30 b p - 6 ) sin bp s.q
+ 100b1 + 3OPB3 F20b29, + 1b5B +8p b q +q,  b25 b  +ap5 B p +6, 25. 6  +4, 5bp + pY   5 b   ap b + 39b
s trae onae aequationes solvi postent, posser idimpleri conditio posserrs aequationis surdesolidarum rabicum  22 b +
e
+ rb +rb2
+1
50
+
2
N 2. 29 2