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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 57r, page id 00068197:0113
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C) D in CQ in D4 = 005D92
sit ax = 0D axtab  ax + ac = G
fiet pro ax ponendo valorem OD fiet OD + ab = 04 seu (= 6D + ab, 0 et rursus
(D + ac = DQ et G= OD +ac: D quos duos ipsius e valores aequando, fiet.
OOD + aC O = ODDF ab D seu +0OD -ODD tac C - ab D = 0
sit jam C) = 10D + 202 + 12 a
50v+ 603 +56a
et D = 30 +40Z +34a B.evioris calculi
gratia videamus an non res succedat, si 10 =0
C) 20+12a
50760Z + sba
et D - 30ri 4oZ
50v + 602+ sba
50v + 60Z +56a
et 34 =0 et fiet
ODB = 20. 20Z7 + 2. 20. 12 aZ + 12. 12 aa ∞ S 40Z, (B.. .
D-O1 ( 30. 30 vv + 2. 30. 40vZ + 40. 9027 21 a 
 ut qu3.. + a
eloZ +122. . 3 - a
H tac  50. 5ovv + 2.50. 60V7 + 60. 6023 + 2.50. 56aV + 2. 6056az +56.56 aa, 
e0e
(- abD L 50. 50vv + 2. 50. 60Y7 +60.60 ZZ + 2. Sc. 56 aB + 2. 6056 a Z + 56. 5taa, 300 + 40Z... . . ., - a ab)
Ex hac aequatione excerpamus et destuamus terminos afectos per Z, vZZ et a
20. 204 2040. 40 + 60. 60l = 6016ob = 0
60. 60: 20. 40 = 4-20, a:, 2c - 406
H. Xc. 40. 50 a  2. 20 30 40a + 2. 20. 50. 60c- 2 40. 50 tob, J V7 2 = 0 seu Meonoson +oa -101lo. to b 2 0
=1. 10. 60.6065
+2. 12+20. 404 = 12.40 40a T1. 12. 60. 60c
+. 20. 60. 56C - 2. 40t 60. fsb. a 72 - 0 se
in 4o (2. 20-40) a + 12. 6. 60c0
Si Aequationeml. divellamus in duas 20. 20. 40a = 40. 6060b -0, et 2 . 40a + 20.60.60c = d, fiet
60.60 = 20. 20 4: b et 60.60 = 40. 40a: C, et 40: 20 = l (c 1b)  et 660 = 2 1o 20, +04. BC
sin aliter divellas hoc modo aequationem 1, sin duas, 50.60c + 20. 2040a  et - 4d. 60. 60b = 20. 4d. 4da, 
fieret 60. 6 = -20,40a: C = - 20. 404: (, quod non licet, nom fieret b = C  utemur ergo priore divulsione
si in aequ. 2. pro, 60. 60b ponas 20. 23 a , fiet 29. 20. 30 2. 20. 2d. Aos 20. 203 a) + 2 102050(a ib)
20c = 40b = 20c 20b (C ib) fefro20. 30a) = 2. 20. V Sola ) (t: b
.  sb
1b) 1C.=
quae aequatio dividi potest per 2o.0 (C: b), et fist = 2. . 30a + 2. 4.50 1aC = 2. 256 ab =0, seu fiet
SC 50. 30 = Va:, sc = +b
Eodem modo si in aequatione tertia pro 60. b0c ponas 40. 40a, fiet inde 
50 +c - 30 fa + 5616
(12. 40.40a = 12. 40. 40 a) +2. 12. 20. 20 ~(C: b) + c. 20, 20. 5bC (a. b) - 2. 20. 20.566+ (a. b) tc: b) =0
seu dividendo per 12. 20. 20 AC. b), fiet 12  56 1b 12 sa + 56sC   562 ta: 1b -c
Sed paulo ante fait 56 50te- 3ota,: 1b quos duos valores habencto aequando, habebimus
12 Yab  50ebC 50c = 30 ab + 30 tac si faceremus 56 + 400 A 12  te 
tieret l = 50 +c - 20 Va seu 50 - 30 a + a b ide 00 mihi est unitas.
Habemus ent 60,  40, 50, 56. manetque 20 et 30 rmbitrarus Cc
Hinc 56:12= = 50:30, cum differant signis tantum
o ab, ponamus ββ, et pro ac ponamus V7
 50 = 3 a : 1) = β
5b = 12a, β.
Et 0 = 202+ 12a.
) _ cbof be rlstust t 30a v + 20 a  12 9 a
fiet (1  20Z + 1a, BE.
+a(tIB. b + ( Ce 3os + 20d2Z- 12 fac
obq = (37 7) (ser
(+) t -. E 60160 =
30v + 40
30 2v +20 22.
et fiet 60 = 204: β. 40 = 20 . p
et D - 10b + 20γ: 3) Z BE
20. 2037+ 3. 20. 12 aZ + 12. 12aa
3 (P + 20EZ = 12a β
30. 3. B 2. 30. 4030 + 40. 40pV, aa.
3040pp VV. + 2. 20.3β217+ 20. 20222
post fiti 3o- J. (i= 12 20-C
et sic o. B2 n 61 n S ev e
pro 207. B compendio, onat 18
Z.... .-, 30v1402
oraa, a
leussi Absti neamus sivulsionem irtius aequationis, per quam in impossibilia duci imaginaria ducimur si
sit deca sint lvel C negativae, facium ex aeq. 1 60. 60 = 20. 40 40- 40, ic b. Et hune
valorem in aequ. 2 el 3 substitucudo, tum ex aeq. 2 fiet  1. 20.  (29- 2. 40) a (roc- 406) + 20 . 40 a 90. 40),  9u 20c. +o6)
=  50. 60
Et ex aeq. 3 fiet B12,, + 1. 40 (R40 - 20) a (2oC, 40b) (6 20. 40a ( - d) :, 2 qus 20c - 40b) - 56.60
seu ex aeq. 2. f. et 30, 400 - 20. 20 10 ac ( 20. 1040 ab, +, 20. 10. 40 ac -0. 40. 40ab (+ 20. 4040 ab = 20. 20. 40 ab : 29u for dob) 50
t ex aeg. 3 fict 1, (40. Gu. 2049- 40. 40. 40 ab -(2, 40. 20. 20 ac +2. 40. 40. 20 ab f20. 40. 40 a F25. 20. 40aC),: 2 qu (20c- 40b) = 56. 60
en 5. 00 = 2:. 20, 2 20ac + 40. 40 ab - 2 20. 40 ac, :, 2 qu (20c- 40b) ex aeg. L
Et 56. 60 = - 1B. 49. 20. 20 ac 4 40. 45 ab = 2. 20, 404b, :, 2 qu (20c- 40b) ex aq. 3
Cxamus quist liat. si sit b3. NO aa = 20. 40 49: firt ex aeg.  120. 40a9 = 20. 46a, 40 -20, :, 20c - 40b seu fiet)
2019-. 1019∞. 40aa - 204a. Seu 20: 4c = aa + bg, :, aa +c9, et 40 = 20, aa +c9, :, a a +b9, et fiet
 rotmeoimi
lt 5
sititer
ad 20 aeire. o
 et C= - E fit
Frett 40 2 ient E  F  Havulla
E 40-20= 6060
 G 4o posio q esseimajonam quan se  esse tam pat sipra 1, ut P ad ha
quao Bono
  o  
 s e e rosa biteo
19 penteus e artir  8e b0