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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 197v, page id 00068200:0396
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Itaque nihil hinc discimus, sed redeundum est ad aequationem n
ndv + Cvan = ndy. si jam B sit rationalis quoad y.  considerari
pt quousque sit assurgendum, ponamus ergo n adsurgere ad gradum e, et V ad gradum 
erit de gradus f- et ndo erit inoe, cujus gradu est n, ejusdem etiam esse y in n
quia si y altissimi gradus ibi multiplicetur per constantem, eam auterri intelligi potest.
sit eogo e gradus ipsius y in n. ergo necesse est ut do sit ejusdem gradus cum dius
seu ut  V sit ejusdem gradus cum y Ergo si v integra non pt esse altior quar
10 10y + 11 et fiet +. 10 ny t 10 ycan + 11 cdn =n du et explicando n, oport et
pudo 10l
aequationem prodire identicam quoad y. s sit Ny + e n = 209 +. 21y 1 22 sit dn
= 20. 2y dy + 21 dy et fiet 410. 20 y + 1021 y + 10. 22
+ 10. C, 2027 + 10. C. 21y
+ 11. C. 20 2y + 11. C. 21
-20 y - 21 y - 22
 et et 11 = 21. 14 2C - . 21 - Bc. 2 et fiet 1 22 Mt E + 211- 10 - toc 11. 20
quae ut sit identica fit 10 = 1:, 1+ rea
et 11 = 21 - 10. 21 - 10C. 21 7 : 210C
2.20C +4. 20cC se 22.2+0 + 21 1 1010c 12C = 22 +22. EC
et 2. 20c. 2d ( 2iet 21 BeC- 1 MCc. 21 = (22. 2. 20C+ 22 4. 20. cc
et fit tandem 21= 4. 20. 22 CC seu 21 = f2. 20. 22  itaque summatio institui
non pt. nisi sit gg 20gy + 219+ 22 quadratus; sec reducibilis Eodem
modo credo reperretur  209 + 21G + 22y + 23 debere esse cubum.
Ita eum levera
potentiae sunt simplices res reduci po ad terminos simplices. nec multo calculo
ipse opus ad hoec quaerenda.
si sit Z
= f.m. dy: y
co-1- ea
con
Rat y =Y et dy =   Ca. v av.
efficiendum ut  co- 1 = eco sit quantitas affermativa
imo non licet  ce = 1 - eco = h C0 = hal: A- C 2+ Ergo non licet
ergo Z-... c0 
yra, vib 
du
per y2 b fit 
i idem per yta fit b
caetla huc reducerentur
nterdum fit, ut duplex cirnitionalis sit summabilis
yta ytb yta, y. b
ta
quaentique tactavil noster, reseius quoo
ta satu
 -HX sar et 1 sa- x -  dx. sac Xx et
Saa tarar-aa =  J: 2aa + a Vax aa adx: 2 Fax - ax
d San- a Pax- aa = - 1: 2 Taa -a fax- aa a d X : 2 la x- ax
1
+b - a
ita  ta =1 Res omnis ergo reducibilis ad e . vel
ita
ad L...... vel ad e,  Y S..
2aa  a fuxoa = avar aa +2 sax