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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 86r, page id 00068196:0169
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+2  + 31 CG (+32Ed I + 33ed8)= 1405  + 4159 (+ q f d V + 43fdes
= 32de l = 33deg
+ 32de V + 33de
+are1p + d338
142fdco p + 43 fdcoe
= q2 + fl - 43 f8 + 42 df 1 + 43 df8
agisa aess tanis is hof e
iea aequando O = D, fiet 32 e( + 33e = 42fY + 43f  quatio trabilis
3oe +3a
o. 42df d42f
-31 e 443d5 = d43f) :, 33C - 43f
u a tiata.sam  pol nduo 2, 3o tiluo dco = +41 F + 33de + dese
ae quatro tractabilis
et fiet 32de t 4ge - 42df- 4225 = 3. 3 de + d3, 0 - 43 df - d435
seu log (32 e - 42f) = log. (33C - 43f) = 1: a
log m - logn = loq (m : n) sit logm - lugn = i: a fit log m: n = 1: a
seu m: n = B1: a adeoque fit 328 -42f7 :, 33C- 43f = b1: a
sed ita bis datur e: F
An ergo sic faciamus 405 - 30e 41F - 31 C = 4 de, et ex duobus valoribus
32C-425 33C - 435
ipsius ded fiet 32 de + d32C - 42d5 daL. f 37 de + 33C - 43f d435 = d
et fial. log (32C - 42f) = log (33 e - 435) = E : a
seu fiet
32 C - 42f3:, 33e = 43f = bE: a, sed hinc tolcendo c: f, et substituendo in aeq. O
habemus difficilem aequationem pro E
quid si aequando aulores ipsius deo, faciamus
32P -425 = β et 33C -39 = )
est deo = 40f - 30C +  d logβ = 4 f- 31 e + d log7)
faciamus 40 f - 20e - 41 f - 31C.  = r_ log (V. (3)
Redeamus ad aegg. 30 V +31G + 32 d  + 33d9 -0
32dco 2p +330 
et - r (log): (B) + d log (Y. (3)
et 400 + 41 + 42 dip + 13 d f =0
42 dc. V +43l0
(Sit aequatio  5e + sign + 50 dA + 5i den = 0 fit A =  b+  n - 9. b
EalsB N + d51 M
E0g s + 51
d50 2 + d5iq
50t  + Sid
50d y + si dC
Nom prodes
 unde vedeo deo esse inutile, et posse poni =d
et fiet 50 = (30 - 32 d 5) 51, : 32 = (+0 - 42d53) 51 : 42
et ebanescente 51 sit evarescit et dB
reide fiet dA = 1 at b + d b dn - Pdt b + d5b
000= 30CY
Set abt t avr sites
Exbinis valoribus e fit 32. 50 +32. 51 13 = 3051 + 32. 51 duo
fiat 30+ 0b
33C - 43f
50 +sidB h= 4 4agdu
3edco Y +33dc0
ardo Y FaSdlo 
31 + 33deo -s 41 +93deo - n habetur d  4 31  +0d t
+32de0. 40+2deo
2502320-41f
30e + 3e + 3slis. 121 q. apti ara arsilpes 4.f ag
3 dco V 331c0g
Habemus ae quationes binas ex datis ductas, 3iβ, + 31C + 32 d p + 33 d es 
addatur et dematur
36.9 50
- 31. 40 4404 (B0. 43
et ex agu duabus  per 30 +32dco, hac per posteriore seu rq. 2. per 40 +g2 dio divisis sic
pncte senaqu
  du + 27d9 +14
472 + ad5g
(3. . +42s o  nste
(33. 40. + 3342d10) d +(0 +42deo) 5
=0 seu -d2 = 630. 43- 35. 47dW) de - o + 32c) n
3240 (432. 42du) 30. 42 ( 32. 92 deo)
dlebet c ut ergovalor ipsius a summari possit, debet esse
(40 +a2 duo)  = (30 + 3r duo) e
32.40 -30.42
videamus an aliqua arte aequatio
32. 40-30. 42
 ~  51dy +61 d = possit redidi solubilis
ubi 51 et Et sunt datae, sial  =  m b et  V ( est; et
ip = hy + KV q= ly + mx fiet sidhis +, dk v + Sihdys +51 Kdv
fit esu = - 6; = 
a t 2
32. B
o-
Sidlu 4+b.dmv + 6eldus +6. m do
n seu log est Hoastans sed ita etium SI: Et foret ostans nom licet
dM
+ 32eduo V F33Cdco G
C = 3t io, f 2dauo