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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 27r, page id 00068049:0053
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X + ab X + aabe dx quaeritur ex suppositis rationalibus vel Conicis. Hoc fiet si extractio fiat vel rationalitr
velfa vel saltem per rationales quarum summatio solas Cogicas supponat, 2taqe
XX + ab  = WV W et XX + ac = Ed C sen XX = 1010 - ab et pX = Eocd - ac. sit jam
ax 2 V eoV + o1a + B.∞ tZ +By h6+ Br3. 125
= B40 StZ + 240148 + 340 588
aco E 150 kb +250 ,  + 3016
at 10V + ua a2 = 20V + 2a a6 -3 ov + 31a a4 = 40v + a ab = 5ov psia
ita eandem formam habebunt XX, et WI - ab vel coco Dac
Generaliter igitur
inveniendo modum exhahendi ratirem ex formula tali qualis per 4vel 5 fit 10W - ab vel cdco- ac
applicari possit, imo ad alia talia quaecunque
adt Xp 00 v 120001 aB + DF. a + 2. 00. 120v 1t2
vetet Bsti ro 46 d2. 1oves..
120. 122 B + 120. 1v. L X +H 8. 121 aa
GB8. 1030. 13d. 10. 31. 136. 1. 31 44
250. 2030. 1yd. 2054. 83. 23, a a
c0 -ac
f’it ergo formula genealis suthritergo per 3
+ 2.00130V 146 +200. 2300 4 126
+2. 01. 130a.. .
+2.120230.
+ 2. 01. 230a..-
+ 2. 120. 1301.
cui forun lae consparanda sit generatis:
30a V t naae + na +    4 sG6 176  auxa
fiat. ipo 2 2. 00 . 3 2. 1, 13030
740aa = 2. 00130aF 2120 250O 7d 2. 00 23 Ct 2. 120.130. 50
281a = 2. 01 120AF2. 1302OY It au E g or. 130 a r az B30. 21 isia  2o. 25 210. 130. 31
703 a- 7 130a 2 20051 a. - 201 30 a, 120 seu 120 18 13. Me a 131 10D
130= +21. 71301. +21. 2. 00 et 2352 1+ 11. 7230
30. 2bi et eodem modo
Aususex 13 et 24 Collendo 120, fet 47126.0 2+ 2. 01. 130. 230110 seu 130, 230= 7120,01 - 712100a:, 230. B1-24100
71212608 - 09. 10. 250, 1 120. 236= 7130. 01 -7 131. 00 a :, 22001 - 221. 00
Ex aeq. 17 firt: iff 7120aa, 00. 31 = 01 30. 10. 21 - 01. 20. 00. 1L01. 10 15 2. 00d. 00. 21- 01. 2, 60. 11 - 01. 10 f. 1. 71c0, f. 71 2136
vel ex 20, 21,23
3120. 130= 230,0] =7271. 00 a :, 2.10.01-2. 11.00
a. 30aa 7130. 21 - 7131. 20. 7230. 11 = 7L31. 10. 0031 - 01. 30
(aa) 7130. 21. n3IcB, rero ic. prs iB. 14 30- 00S1  2 (aa) 00 - ol2o : 0d  
compendio _120= 231a: 68031. 130~7~1O2I = 3130. 21 = 7131. 20 = 71k 1239. 11 ∞ 7 131. 10 = 72  712B 31 121 2
e  7120. 01 - 7121.00 = 2 712(0 7130.01 -7131. 00 = 714 7230.01 - 7251 c0 = n70
00. 11 - 01. 10 = c 00. 2) -01.20,= 0(2 003]-01. 30 = 0(3 Et ex aequ. 27
73(2. 723C : n1 20  2.0(2. 06: 013, 2t ex vy. 2y fiet 71213.713C: 71310 = 2. 0B. 00: o(e
aq. 2g fet : 713(, 712(3 : 123 (0 = 2. 0l. ∞3 :0. Et exagu. 30 td innicam d hy fit 31 e(. 713(2. 723( = 4. . 31Le31
72(3, 7132. 723  :,712(0. 713(= 4. o( similiter ex coteirs  B) 4. O( G12(. 123(  : n1 2 nC
e 8 4. 93= 713 (2. 7. 236. 7126, : 17130. 7236
Y G 10. 1020. in, 120 nu = F2( 120 10 i
(4. 120. 10. 11. 24 21 4 120. 130. 10. 1 1 
220+ 20. 2. 10.3) l170 216. v 31. 1 2
1o= 312B: 206 13021116: 2. _ 230 = 7241: 2. 0
= 120  2 (12. a M. 102t + 2. 10. 130. 10. 10. 21 31 + 10. l. 21.30 +
1302. (i. 3 2. 1B 2. 30.51
210. sed. 1 () 2. 20 21 30. 31
1 = 20. n0a + 2. 130. 23030 2 7120 a 2. 00. 130 + 2. 120 230. 204271304 2,00. 270aF 2. 120.130 =72304
1G 14. fit 60 7130a3 - 200 130a -, 710. 20, 7120a - LX 2,23020 130. 230. 30,
per fit 120 = 7120a = 2. 130.230. 30,: 200a = (per 2) 71304 = 2, 00. 130a , : 2. 230. 20  7 230a - 2. 00. 230a, : 2. 130.)
Ex 5 fit 2120. 230. 20a - 2. 130. 230. 20.30 = 7170. 00a - 2. 00. 130a  fit 24130 = 7130. 00 a- 7120. 230 20d5, 4r0 . 1
Melius puto sic: V = 572304 = 002509; 120. 130 1 = 57 231aa - 0(236a, , 170. 130 10. 20 -
20 = = 7190aa - 00. 130a,. 120. 230 21 = 171314a - 0L. 13C a 5: 120. 230
30 = 2 7 204a 10. 120a, 5130n10 31 = 17 (21 aa - 01. 120a, : 170.230
∞2. 00- 2. 29020.30