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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 28r, page id 00068197:0055
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∞ OD in OQ in D4 = 00D) P
sit ax = CD et ax + ab = O et _x +ac = DC
finte On = C2 - ab = 52 - ac et B = _ a (b - 5) ab + OD: 0 = ac + C),: 1 sit abD + BV -acCteoF
faciamuse C = 1P + Na, a :, 30V + 31a  et D = 2.V + Va, a:, ZoV + 31 a
fill - 10. 100V + 2 10. 1aV + 1. 1aa, 20V+ 2a, a = +W. v. 20, V + 2. 18. 1. 20aaBP + 11.11. 20a B + 1(11. 21 a
=+30 pV 4, 10 2 av 21. 2 aa, 1oV AIa, a = - po 2020  - 2.
on - 2.11. 20. 2 3∞ - 11. 21. 21a7
= 30. 30 vrt 2.30. 3lav + 31. 31 aa, 20v + 21a, - aa b = - 20. 30. 70 aB - 2. 20. g a. 31 aa vv = 20. 31. 31 a
21. 20. 20 aavV - 2. 27. 3031 ar
ut destruatur V, fit 30. 30 = - l0. 20 (10 -20): (10-20) Ergo 30. 30 = 10. 20 et parifua 3HH. 21
et pari jure ut destruatur V, fiet 31. 31 = = 11. 21, Ope prioris tollatur _19ope posterioris tollatur . 11
pyt 16 2 - 30. 10: 20 in aequationibus praedituris, ut sint  coefficient ipsius v, et ipsius V, aequales nihilo. Et in duobus
istis coefficientibus _ etiam est asenomia, ut scilicet unusfiat ex altero per mulando 10, 20, 30, cum 1, 21, 31
itaque habita unius prostatio destructione, facili habetur et alterius destructio
2. 30. 30. 1L. 20 . 307 2 + 2. 30130. 31. 31. 20 11. 20. 20 _-2. 2051 + 1130. 30- 2 20 3031 14191
seu +2. H. H. 2020. 50.30 + 30.31. 3] 2 20 20. 30. 30. 31. 3 t 11. 1. 201 + 2. 11. 20. 3831-1 1. 2020303. + . 1. 20. 7 X p
peli ando 10 et Ul.fito - 4 2. 130. 30. 21 31. 20  + 38. 21 + 2. 3010. 20. 21 + 31. 31. 20. 20 2, 30. 4 - 3 1. 113070 - 2. 20 3031 - 1. 2130, 20
Iir Verulicando
10 et 21 fiet
seuo 2) 28. 30. 31 + 307 21 21 4 (2s. 35. 20. 25 +  25t. 31. 31 - 2. 20. 21. 38.31C 20. 20. 3050. 71 31) 2. 28. 1 30. 3(=20 26. 21 21302
12 (202 1  36)  - 2. 31 (20.30, 20 496) + 30.30 (20 +30) = 0 et divisis omnibus per 20. 20 + 30. 30
ep  destmendo,
Et prorsis eadem prodibit aequatio ex v destruendo
21 sed hoc non licet, nam ita fiet D quantitas constans. Quin et si conjungamus
31.20 = 30 = 0. seu 31: 21 = 30. 20
nc huic aequationi binas priores 30.30 = - 10. 20 et 31. 31  = - 11. 21. fint 31. 31: 30. 30 = 11 21: 10. 20
sed 21: 20 = 31: 30 Ergo fiet 31. 31: 30. 30 = 11: 10, 31: 20 et fiit 31: 30 = 11: 10, 1el 31: 11 = 30: 10. Ergo
etiam C desineret esse constans. Haec ergo via non procedit.
Ergo pro explicandis (3 ut 9 assumamius literas binas: C = DaV+ 2+ 12a
v + B0Z + 56a
fiec + ()3D = + l0. 1ovV + 20. 2572 + 2. 10. 20vZ F 2. 19. 12 ba + 2. 25. 12 Z a +12. 1 aa, 300+40Z + 3+a 3f a
Fiet (- 99) = 4301oVMt 40. 407 Z+ 3. 30 40v2 + 2. 303qua + 2. 90 347a + 34. 34aa, 10V + 40 Z +12a, - a
O= +acO = + 50 50 vn + 60. 63 77, + 2. 50. 60pZ + 2. 50. 56Va +2. 00. 56 Za + 55. 56aa, 18v +203fna, + aac
l- abD = 4 50. 5ov P. + 60. 6077 + 3. 50. 60VZ + 2.5056va + 2.6056 Za + 56. 56aa, 30 + 402 +3 4a, = aab
Hic tentemus tollere Z,  Z3, VZ2, aZ2,
+20. 20. 4∞a = 40. 40. 20
d346. 40. 
O2 1210. 20. 40 a
+ 60. 60. 20c - 60. 60. 40b-0
265 50. 10
D. = 30v+407+3+ a
a 500 +60Z+56 a
A2. 30. 40. 20) +250.60. 205
Unie 40. 40 - 20. 20C
etE 260=20 laib
60= 40_c o 10- 20l(.
20. .  1660 (roc 40b)
- 60. 60.3076 = p 20. 39 (20- 2.40) .10. 40 (40 -2. 20) a
- 10. 40. 127 +50.60. 12 7c
- 2. 40. 34. 20. +2.60.56. 205
-2.50. (D. 40) 7 60. 60 (10c - 30b) 4 3. 50. 60 (20c - 40b)d
= 60. 60. 34 7b 29 L20. 34 a β2- 2. 40) 460. 60 (12C- 346)
=3. b0. 5h. 40d + 12. 40 a (2. 20 40) 2. b0. 5b (20C- 406)
Ex his tribiis aequationibus prestitis, haberi videtur valo. ipsius Z rationaliter per v
+20. 20. 34a
in aequationibus prima et ultima, absunt 10 et 30, quae possunt reservari mediae
Z 11. 20. 42 toa
9o. C 20 toa I prima et secunda absunt 12, 34, s quae possunt reservari ultimae
Aqui sut (60
sed in  nihil ab est secundae et tertiae, adeoque prima nullas proprias habet.
20. 40. 40a +60. 60. 2c  media fit 30 = 10. 40 (40- 2.20) + 2. 50. 60 (40b = 20c) = 10. 60. 60C,:, 20. 204 - 2. 20.40 a - 60. 60 b
dicidinosset in
60. fol, 20 10a =
Sidil f. ret =C
X ultima fit 34 = 12. a (40 - 2. 20) + 2. b0. 56 (40b - 20c) = 12. 60. 60C3:, 20. 30a - 2 0 +o a - 60. 60 b
nhis pro b0 substituatur valor ex aequ. 1. qui est 60.60 = 20. 40 a (20 -40):, 40b - 20c
20. 40 20a 460 sid indeo trevis procedi quaerendo solas 50 50 ex media, 5b ex ultima, 60 ex prima equatione
 doibe = +  fit ergo ex media 50 = 20. 30 (20- 2. 40) a + 10. 40 (2. 20 - 40) a + 60. 60. (0c 20b), : , 2. 60 (40b = 20c)
Aru saibe - 14
si firiol 20- qu, a m oc adbd et ex ultima 56 = 20. 34 (20- 2. 4) a + 12.40 (2. 20 -40)a + 60. 60 (12c. 346)3 :, 2.60 (40b = 20c)
oc fatei quia ergo tot literae sp superfluunt, videamus an liceat sevare in numeralonbus
sit roa + 3= qota + b) prima audem et 60. 60 = 20. 40 (20 -40)a :, 40b = 20c
2020, (a +C:, a + b) ipsorum C et D solas 10 et 40, et destruere 20, 12, 30,. 34, fiet
e40 = 241 + c): (a + b
et 2C. 40 = 4 60.50
(sed ita C fieret
et 60 fiet etiam d
50 = 10. 40. 40a + 60.60. 10C, :, 2. 40. 60b et 5b= pd ita fit et 56 =0
itaque ante omnia conservare demius 20 et 40, ita stabil 60: nonplicet simul rejicere 10, 12, 30. 34, sed
videmur posse tuto rejicere 10 et 34, fiet 50 = 20. 30 (20- 2. 494 - 3060. 60b,:, 2.60 (40b 20c)
t inisii sit es ti, et 56 = 12. 40 (2. 20.40) at 12. 60. 60C, :, 260 (20b - 20c) et 60.60 = 20. 40 (20- 40)a:, ob. 20
ita tpplicaro bosit 50 = 20. 30 (29 -2. 40) (40b - 20c) , t 12.29 4u ( quiae - 30. 20. 40 (20-40) Ab, : , 2 qu (tob- 201) 60 
1 11
seu 50 = (20. 20. 304065 () 20. 30. 90. 40 (b (= 20. 25. 30. 40 ab t 20. 30. 40. 4 cab) + 20 30 (20 r2. 40) fC, : 2. u( goba
et 56 = 12. 40 (2. 20 - 40) (Geb - 20c) _a + 12. 20.90 (20 -40) ,: 2 qu (40b- 20c)604 seu
SH = 12. 40 (2. 20- 40) 40F -12. 40 (2 20. 20 12. 40. 4020 a  fF 12 20. 40. 20d C 1. 2040. 40 4D;, 2qu (gob- 201) 604
fit ergo 50 = 2 30 20 (2.40 -20) aC = 40. 40 ab, 262 2 qu (40b - 205) 2 1 (20. 40, 20- 40, a :, 40b - 26c)
et 56 = 12 +0 ( 20. 42) (1ob. 2oc t 2 (20 (2. 20 - 40) ab - 20. 204c, 12. 40: 2 qu (90b - 20c) 1 (20. 40, 20- 40, a:, 40b - 20c)
dea: si esset 60=(0, fieret ex 1, 204 20=40
 ati adtuo unb acehonao o peletaee   disi o oa t
u te tius pari tndo dun lict lactre ab 40 ito pec lalea  s d 250 simal uee lace totu
 3A; vot 12 et 30 4
o rondorai u
H1 = 26b H. b) lbc -20 C guat)