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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 85v, page id 00068207:0170
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pro tollendo ZB respecta aequntionis 1, erat 2. 14. 31. 42 + 15. 31. 42 - 0
2. 19. 41. 42 15. 32.41
quae a queatro manet permutanda a2 et A adeoque 4 et 4 5 et 3 adesque 4 et. 9
s Ex hac aequatione fit similis pro tollendo ZV respectu aequ. 2, permutando 4, et 20
Et fit 2.24. 31. 92 + 25. 31420
2. 29. 41.42 25. 32.41
tins quaeramus 32 et 42, fict Eips d fint 3+ = 2. 19. 31. 32 4 2. 19. 41. 42 a th. 31. 42, , 15. 41
Ex 11fit 32 = 2.24. 31.37 42. 29. 41. 42 - 25. 31 42,, 25. 41
Quas duos valores aequando fit 2. 14. 25. 31. 4Z YH + 2. 35. 19
Hinc quaeramus 32 et 42. A  eF aeq. 8 sit - 32 = 15. 31. G2 +2.19. 41. 42, 14 131 + 15. 4+
item 31. 41
Cq t
et ex aeq. l - 32 = 25. 31. _t + 2. 29. 91. 9t pi, 24. 31 + 25. 41
25. H1 + 2. 431
quos duos valores aequando fit 1g. 24. 3 A +
2. 24.15. ∞. 31 (42) 31 + 2. 24. 19. 41 (97315+ 25. 15. 51. A2. 41) + 2. 25. 19. 11 (12)41 =
2. 14. 25. 71 (42)31 . + 2. 14. 2941(9731 (+ 15. 25. 7342. 41+ 2. 15.29. 11 (42)4
Et fit -3
22. 1. 2 seu 14. 19.25 41. 41 Bl. 141 29. 31. H 4+ 24. 15 - 31. 31 =0
=1. 29....
2C+2.1924
+ 24. 19
quae n aequatio manet eadem, si permatrntur 41 et 31, itrm 09 et. 4
lxX + myy + n GX -0
seu AxX + lmyy + lnXy =0
fit Uxet InHy +. anyy = _ ua
aequ. nngus - 4 lmgg: 4
fit IX + Zny = Ly +Cun-alm)
seu p. -nft  Con. aems al
lxx + amX + aan = 0
Exaequo. 12 fiet 41. 1B) 4 14. 37
Ex aequ. 6 fit 40 =
quae duos valeret
-14. 25
42 ) ex priore permntando. A et .9
21pr 3 126 F00. 12. 3
triy (00.3
1. 15. 4IfL1.25. 315
(224. 31 2 D9. 49)
L1. 25. 41521. 15. 31)
225114.29
 ioth it 9
+21 224. 334 00. 22. 31
= (ex eq. 9) 1. 25. 4130t00 23.41
2. 2941+25. 31
2+9 30731. 31 p f15. 30231. 41 +4. 1. 29. 30 pr h1
aequando fit 2521. 00. 2
(2. 14. 31) (2. 2941 18
Uxx tamlxtaaln =o
+YCqu (   35
2, 124. 15
p 1. 15. 4100 00. 13.
2. 19415. 31
22 D0 29231. 4. 
J. 1. 230
1. 00. 13.25
22. 312 (219. H1 1- D1. 31752. 29. 91Y) v0
28415E15. 313 E 1. 41521. 25. 31))
Hic valor, sidem manet, si permutentur 1. et 2.
et tent valor ipsius 40, per mutand 3. et 4., item 12 et . 3.
aequ. 16) ex aefn. 15
40, et 30
Uxx tam HXrEaamm C Htabemu ergo +1
adeeque + et. 9
verb. gr. n paraboa.
=aamm- qualus ia quia in omni eonica polli simul potest V et Z; idet etsi praejodicio harmo
niae toltemus  in omni vero Conica potest tolli NZ, et altera simplex velut av,
tx lxa am a smmlu)
et terminus absolutus; ideo id potius sequamur
seu X = D- m 4l (an- a ln)
e
pxX +, aq taar=s
IexXKI
= - q + seaqu apr
aequentur
R. 19 +LYq=
itaque omissis aequ 6 et 9 adhibebimus ipsas 7 et 8, item 10 et 11,
Et quidem ipsis 8 et 1 jam defuncti sumus, earumque ope invenimus
42: 32
ope aeq9. 13 et 14
: 31 et
1s - p s. = A qmp Addamus jam aequ. 17 et 18, quae sunt
mpet prDa
Ha t OD = qu (lq- mp) 144. 30. 30 + 15. 30. 40 + 12,00. 30 + 10. 00.00 -0
13,00.40
a AtLO
24. 30. 40 4 25 ∞p. 40 + 22 00. 40
 19. 40. 40 + et bolt
Et 18 fit ex 17.
permnfando 1a et 2.
(0. 38+ (1. (00. 30 + 5200.00 =0 60. 38 +61 00. 30 462.00.00 =0
aapD - 4(1qu mu) 4 _ Ep aequ. 18 fiD
+nalo
+. et 158. 6Z = qu (450. 62)
29. 40.40
Inp -qs d 1O + PD) Iu sed hoc loco 50 = 14 v0. PK 15. 40+ 12.00 et 00. 0052 = 19. 40. 40 + 1300. 10 + 10. 100 00
.61602. 1
60=24
+ 14525.40
00.  = 25. 40 + 22. 00 et 00.0062 = 29. 40. 40+23. 410420 0000
15.4075 29. 40.4
(t  12.603 2e
c22. 9032
-l25.402 [19. 40.40
od 212. 00F l (22.005 13.00. 4
10000b
C29.40.40
F+19
A0. 0u l 20. 0000 qu.
24(19. 40.40
13. 00.40
00 vol 10. 004c
f.13. Er. 19
m7
19+ (mp .l91) -t0- pp D
scuquetemp. lus) Hotins fet
taque in m. 13et 8 P1 tg
Er a4.4. 25 + 1524 d etrt
etle quad vatu)
et ordinande + 14. 15. 25. 294
14. 19. 2525
- 19. 192
24 (15. 402
8d. by +14. 15. 23. 25. ∞0 :14. 1). 25. 15
 13. B, 24. 2C
Zr. 15. 24. 49 12 19.24 25
- 1.4. 14. 29. 29
6. 15. 2425 12.14. 24. 19. 29.
19. 22. 24
 uiq
+13. 14. H. 10
i idi