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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 112v, page id 00068196:0222
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4
O- 10 + 11y + 12 y + 13y + 14 v
1
Ergo fiet:
6 odx + y di dx +Y Tu ex +77413dx ete  udys + 242ydy + 3. 1B3 7 dys ete
(2)+
Sete
 seu dy: dx = di0 + ydu + y di2 +y d13 etc, :, 1. 11 + 2. 12) + 3. 13y et
jam exdatis
sit -dy : dx = - n 20 + 21y + 229 + 29y) Bc 3:, 30 + 31y +35 +33y etc. Et multi-
30d 10 + 31. d1o y + 32 d10. y = 33 dio y +34 d10 y + 35 dio y +36d10 et
plicando per crucem fiet:
30. du 31 dn 32 su, 33 d1 34 du 35 du
30 di2 3D di 32 d12 33 d12 34d13
30 d13 31 d13 32 d13 33d13
Co.  4. 1. V 23. 1.11. 231. 11
20, 2. 12 21, 2. 12
22.2.
203.13 21. 3
ponmm non ascendi
in dabo ulta 2C et 52
20. 4. 1
aequ
30 d14 31 di4 52di4
24, 1. 11
23, 2. 12
il
21. 4. 1
20, 5,18
30d15 31 d15
25, 1. 11
29, 2. 12
23
3.5
22. 4. 10
2. 8.1
20. 6, 10
30 d16
26, 1. 11
25, 2. 12
24. 3. 13
23.4. 14
22.5
21. 6. 16
20, 7. 1
+ 16
eu
ete
etc
+1I + 12 + 13y. + 14y +159
ubi d per gradum in fium ivenias 1 1, et tollas ex gradu 2d0, utiu
in gradu 2d0 habevis 12 per 10, dio, ad1o; et in graduntio habebis 13
10
per 10, d1, ddio, dddio. Et in gradu it seu ut habebit aequavem
in qua erit sola incognita 10, cum suis aeffectionibus, nempe
10, dio, dd 10, dadio ddddio, una cum X
unde non video
illud tumen norandum, si dx =0
dx ddx, dddx, ddddx
et
sit 10 ut saepponimus rationalis integra jetx
tunc s X evapeset L. differectiae replicata,
et suis affectine
sumimus ut valorem ipsius 10 esse actiorem, et ita
quid lucremum
pri
evauescent
pront
apparebit quid
sit pessibile; si res non succedit finiando in 913. videamus quae oriat
Et ita habebium quid sit possibile
es m et modus altus attollenti
 allummu d 13 sia quo video opu esse atolli
viversitas assumendo ad 14, 15, ete
uneo  modum examinanti.
 31d 1230d131+ 31 d11 1o dnt221. 11y
x 3i 1o +30d11420. 212 y + 30d10 +20. F. n comp quae ae qualio
 si ads it 31 nam fit 31 d13
e
ut coincidat cum ipsa 10+119+ 129 + 139-0 debet Eoc attolli seu
 debuisset 30d10 +20. 1. 11G + 31d10+30l11+21. 1, 1I
cu 10+7,G. ult. pr 40+41Y. fiet 10.40 +1041 y + 11. 41. 1
21d1. 1I et 40 = 31810 +30d11+21. 1. 11 = 10.21. dI1. 113 : 11
ox qu
altique
ii ac
imlliplicari per 40+ a11.
+31d1. y gigari
suet
=e1 41
30. d10 +20. 1. 13 : 10