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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 58v, page id 00068197:0116
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+9. 30.50.56 abvD
= 12- 12, 30aV
2. 12.50. 5b aacV
X30156,56 a abB
F2. 12. 20. 30 +aV
=2, (2. 40. 30 anv
+2. 12 50.60 acV
= 2. 30. 56. 60 a b V
+2. 20. 50. 56 ac V
2 40.50. 56 ab
Respondent in Numerator V ipsi _,
 in Nominatore vn ipsi 
permulatido b, 1
= 203+ tra
a +60Z+56a
20. 7oV f 10, 21a BV + 20. 72 aaV + 20eB a
+ 12. 80a vY + 12. 81 aa V + 12. 82 a
2 40. 8op F 50. 81 avv +50. 82 aab
60. 701 + 6071 avv + 60. 72 aav +60.7sa3
x- C
+ .80 avv +56. 81 aaV + 56. 82a
+12. 12.+0a
 40- 5b. 5bcab
+2 12. 56.60 aac
A20.56. 56 aac
et WV ipsi V
130.d 430. 81aon +30 6dda
+50. 8op +et. ut ru in C
20. 7013 + 20. 2) aBH etc. in, 4a20v + erc
qu (50. 80v7 + etc)
Ve - 2, S5 1et 2 , 12 - 2, 9+ , (7) 18+ 8, a), 19. E
12. 70 = 4. qu. cob cub. (8 +∞) a
30= 2....
+98- 35,., 873
. . . . . , 45: ) 6- 89 15 -98 :1 3 8
50. 36 = Gis 2Z - qu 89- 5 3) p. esH = qu (. 7
a 1. 12. 18. 30 a + 1 s∞. 50Z = 236. 568 - ali s 15) gu 9. 51 147 24
C)omit qu 57 + 88- 5E) 1. du D r
td a sa qu (97 -G 2 + 95)
poneado 50 = 40
Resumamastres aequationes, et videamus quid prodeat en se
60. 60 = Ge. 40 (42) Cqu 40):, 1t0 ( 20)) = 20 a + 2(20 +0, aa: B B fil 40, 40 3  Vo a  o t P 2u ost.  40
Et fret 10. 20YY + . 40Bβ = 20. 40) seu 2 ort 40. 40- 2. 40. 2677: 8
B) 1 37 +  VNC)V- (3
undi 6000 102  7 60.60ββ: 20 20na=
2d. 20: = 10. 20B L-1. 20 2  v  da
EY + VHC-8() -CB est -) vr +y79. 1) . B
ita obtinetur extrahibilitas et fit V = Y(VV-2B)( 160. 204. Hnc 60140 = a Y se. 60= 40a:Y 33
et 20 = 40 βB:  (V+ Se (C) posset fieri  20 = 3β: V et 40 ) + sCYy - B() et 6d = Y y + t- 30): Y
nisi malimus 20 esse B(3, et A0 esse Vy +V. Sevy  BB) et 60 elleas + at VV - (3B)
dendamus jam an aequationem tertiam ubi sit
12 (2. 40. 20aq = 40140 ac - 60. 60773 = 2.56. 60, 2077 - +0sp
Haer tota caquatuo, dividi potest per P+ (∞y- BB) quia hoc in 402 et in 60 et explicando fiet
1 C2 BBga)aa + cvr Best ) pe (Y + +CVP. BC)  2 56a (P By V - pCA = EBY  (NX - 11) A)
in lit 12C ad C ADX + a (Y,. BB) =. 16β3(LYy - 2B) quod totum dividendo per VY. (33)
tit 12 (+ a +(V BB) 4 aV) = 136BB sint 1 unde fat 12- BB, ut 56 = , a (V+  (1 - p. B ))
 ut 20 ~ Bβ et 40 = VY ~ CY-BC) e 60 = a) + a ((y - 39 sit 1) - B (3) = Y. et
fit 1 20 = (B+ 40 = VV + VY
50 = a +ar  56 = +a) + ar-
Tratomus an sit tres aequationes sacedunt. EAqu fit 2aa YYB- aast B+ 2 a a V FerY BB)V
=aa pC(WD+ Vr)  (YDLr = BB) siu ) (2))C eeBt i BC
eV
DB( BB)) quae aequatio est identica ut
Ex oq Ex aeq. deducta ex l et 2 quae est 20. 20)V + 40. 40BB = 2. 20.40)Y, siet sii similiter
yit ppgi p L pe Z e et e AYL- 2β(G8+ (ep ∞Y 1
andem ex aeq. 3 fit  (2p.raa ) V + 2B a VL  B ay Z 2BBaa)3r- BBac)  BBa VVBB
R -  BB) Vaa J.  2 BB)) ad BY  BCVaa YI Et βB) )aa BB) = ( P) Jeua )V-  (() ) a )is B
ae = 2 Y - (YXt 2Xr   - β(C) (B P Y) - ( BB) - β. β) +)
aa  3CD + aat B MA + 4 aa )Y B a A aa BC YY CB
2a). Y Y)A) B(YY Es)
raY. ae
raaBYp agaa BBYY YY4 4aa ((37Y ,(13)
ita succedit calculus, sed nitur inlomulitum fiet enim 1n ad 5b vut 20 ad 50 quod non licet
itaque non oporiet sumer
ta. sisi (d ((
ut 12 = -sβ  20  sed . 56 = 60 faciamus 30 = β. ) + (N- (
=pro + sed pro peo +y12 ot 2 ircha3ga on 43ea  + 1 6967
Y. X+ +Cy. 1B), +a et 
ad missis hut vocarieus tem mentratur qam adminatim
valoris ipsius Z Depronir 1t pe (β (V+ VCH - C1)
et liasque = -Yaav -
Coa
pmian tre)
12. 10. 5Pon .301155. 16(35)   16.56. 56, a V
20. 3a 39 B + 2.30 (12. 20 da 2V 1b. 58 110 
2155. 503B +iacer. 40a
a Cxip vedieo L  t C Non a a + (C. 3)  se
X V1A)  qu (Y L ((.. ))
+30. 50.50bP H 12. 30. a
+20. 50. soC DV
= 2.30.5060hWV
12.56.56 ac
R-3av7 7 2(7 7aa
pobponatur  pro ptonatur3.
inventi sunt valores ipsor
12 et 36, 20 et 40 50 et 56
et v sibi ipsi, pars parti
=40. 50.50bWV
+40.70B + 40. 71 a vb +. 40. 72 aa B F 1o. 13a