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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 185r, page id 00068201:0369
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AB
Sublatio Terminorum ex aequa
tionibus.
X + 21 =(2) = y
XX + 1X + 12 a = (1) = 0 sit Xt b = y fiet x a y b sit X + b () y vel
X = (3) = y - 41. Ergo ex aequ. 1. siet  CbGbb yy- 2. 21y + 21. 21 = (4) =0. Ubi ut
+ 1. 11 y - 11. 21
tollatur terminus secundus fiet - 2.21 + 1. 11 = 5) =0 seu  me =12 a seu 21 = (6) = 1. 11: 2. Sed
idem generalius praestari potest. sit X + 1X + 12 a X  ete = (1) = 0 sit X + 21 = (2) = y
seu X = 3) = y = 21. Ergo ex aequ.1. per aeg. 2. fiet y +C, - 21 y  + e. . 1. 21. 21. y etc. 
+11. V + 11. e- 21 y +11. e. C-1. 21.21. y etc. =4) =0 sufficit autem uos summos aequationis
terminos explicari, et quidem posito tantum explicationis initio, duobus scil. terminis altissimis
in termine explicando s primi explicatione, uno altissimo in termini secundi explication
et fiet: - 21. C: 1 + 1 = (9t out tollatur terminus secundus seu y adeoque eit 21 = (6) = 1.1li e
quae est regula generalis pro tollendo termino secundo
Simili Methodo quaeramus aequationem generalem pro tollendis terminis
secundo et tertio, assumendo aequationem, compendii causa, in qua jam terminus secundus
absit, quia id quomodo fiat jam ostensum est sit ergo aequatio X X + 12 a X r etasto
it sit  erL)C Q XX + uX + 2 a = (2) =B. Ergo X F EIX. +  aX ) Xv.
Ergo XX t 3X + 21, 2. 4 - (3) - y 22a +21 2t:4 seu X  c tury- na +3. 2 4. Ergo
 aequ. 4 explicando aequationem + fiet quam multi Jam generalis methodus tollendi
pteram duabus aequationibus communem consiptit in multiplicatione quadam per arbitrarias, nempe
si velimus tollere _ X ope aequationum XX + 11X + 1a = B et X+2 - consistit in eo ut unam
quamque multiplicemus per aequationem arbitrariam altera inferiorem, et fiet  3oxx + 3O HX+ 3oa
0 et et fint et quidem priorem per X seu 1, posteriorem per X+41. A ex illa fier
et illa man et prior manebit, ex posteriore fiet XX + 21 X + 41. 41 =0 quam subtrahendo
a priore fiet  1 - 21 - 41 =0 _ sen 41 = 11 - 21 et fist  12a - 21. 11 - 21 = 0 seu 12a - 1. 21 + 21. 21 =0
ptro guadibus XX X, et X, ojunctis, fiet: XK0X + 1X + 12aX + 13aB = 0 et 2XX + 2X + 22a = 0 fet
=0 et similiter
po mustiplicetur per  X+ 31, fiet X + 1X3+ naxX + BaaX
31 +11.31.. +12. 31 a0 + 1331aa 9
postercor multiplicetur per XX + 41X + ara A X 21X B a XX
fiet:
41. =21. 41.. - 22. +1a X
-42a. - 7. 42 a - - 22. 42aa)
ho
t squ
en
1(P 1+ 31 = 21+41 1331 = 22. 42 12a + 1. 3I = ua +2. 41+ 42a 1a +12. 31 = 22 31 + v. 42
XEC a~ 31 = 21+41 11 = 22. 42: 13 fit XF13. 2(+ 13. 41 = 22 42 + 11. 13
a 31 = 41 + 21 -11 11. 31 = 11. 41 + 11. 21 -11. 11 = 22 a + 21. 41 +92 a = 12 a 13. 31 =13. 41413, 21- 11. 13 = 12. 42
13af + 12. 31 = 13a+ 12. 41+ 12. 21 - 11. 12 = 22. 41 + 21. 42
42 - 13. AI = 1. 35. 22 - fn. H 4H 3t, a Ergo 41 =
_I.
cas tres aequationes, in quibus tollendae 41 et +2, ordipemus.
FI. H oraat 2 + o1 2I-0
103a
u
rII. 1120aA
+10. T2aa. 20
dctI 12 t2 a3.  -0
+11. 1.70~
a vel per compendium
51. HI +50. 22 + 52d =0 61. 41 +6042 +62 =0
4 14
vis ea
71. 41 + 3∞ 42 + 724 =
A 42 = - 51. 41 - 52a,: 50 = - 61. 41 - 624.7:60 et  + 516+1 +5260 a = 0
-61.50. 650 62
seu fiet 41 = 50. 62- 52. 60, : 51. 60 -80. 61 et 42 = 51, 62 =52. 61, :, 50. 61 - 51. 60
et fit 50. 62. 71 = 52c60. 71 = 51. 63.70 + 52.61. 70 + 51. 60. 72a = 5. 61. 72a = 0
quam aequabionem inter pretando, prodibit.
obes
egH2 - (11 21 122 42 - st
2
ta
F11. 21 22. 22
11. 1
+1a
+12 a
J.4 +121 2- 19. 21 +(A (22) M a -(ar 13) . 12
L2GI1. 13
Hia)S
= 1. 2a. 22 1). 21.
+ 1. 13a
(= 11. 17. 21
(41. II. IL
- 12. 12a
∞13. 21 a
etL
+12. 2
112. 2
duia ld tiga
=0
F11. 12. 21
F11, 13a
Fstih2. 21
quae duo producta
invicem tollendo
prestat pro
ponere pro, 11, 12a, 13aa
porere na. naa, 1a
Et pro
21
2
+12. 21aa
+ 13 420
a, 23ga
1230
ta o
calcul
erit ordi
natior
Re sumamus a sigio N