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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 110r, page id 00068196:0217
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Sit aequalio data dy: dx = r0 +n9+ ny etc et
assumatur  quaesita: dus: dx =- 30 +3 y: et fiet, aequando et per craccem nultiplcando
dro  + du y  duy d13.5 dx
 +10 +1g+ 12g = 13 y + 14y 415y + 1b 7 etc cujus isse () dgo. d3 
+30 +31)
argey t nsog eabgo ete Untiis o=
C
+203tYt 1 nsty +23.31V  125 3t y etc
erit
 +.1. y + 3. 3y ragy du
Et pantet Gules. in aequ. 4 pro dus. ax substituendo valorem ex aequ. 1. fiet ri. 5.) 10, 1, 12 etc datae per X
+d10 + du y + d12y + d13 9+ d14 9+ d1s y + di6 y
+d307 d31
F10. R. 11 102 12 10. 3.B
11. 1. 1  11. 2. 12,
10. 4.4 10515 10.6.1b 10. 7. 17.
1B. 3. B 114.14 11. 5.15 H. 6. 16
eederi
12. 1. H 12. 2. 12 1P. 3. B3
10. 31 + 1. 31 12. 34
(6) (4. 10
O=
30
aequ.
 no
13. 1. 11 1,. 2. 12 B.3. 13 1. 4. 14.
13. 31
14. 1.1I 14 2. 12 14. 3. 13
14. 31
15. 1. 11 tG. 2.12
16. l. 1
1.31 16. 31
si L 30, 31 quaesitae per X
si indatis non assurgatur ultra 11
n fit suffecerit
aequ. 2 mu laplicari per 40
et habemus duas aegu.
dio + d30 + l. 10. 11 + 1031 = 10.40 +30. 40
et di1 + d31 + 1. 11. 11 + 11.31 ~1140+ 31.40
sie 408
dior d30 + 1. 10.11, 11Y3IC
aequ. q
du + d31 + L. II I F 113I, 10+30
it y + 12y 41313 + 1G L SV L. b in 4 + 41y etc. Ex 093.)
 a
3y
d
si in datis non assurgatur ultra 12, potest
quo tunc fietidio Ld30 F 1. 10, 114 103, = d 1r dy1 + 2. 10. 12 + 1. M I + 11. 31yran etrE S1) 12. M. sY)
lu
et exag. 3 fit 10 ruy r 129  quae multiplicanda per formulam nuius gradus, seu per 40+ a e, ut productum
possit conferri cum org. _ 10
Et ila porro in altioribus semperque eit litera aliqua supernumeraria
30 31.
quando ad possibile est
Dro Tangentialibus resolvendis in lineis ordinariis hac mihi videtur
 extia ethodus : sit e dy: di  10 + ny + 129 etc: 20+ ugrus et
etiam haec pt aduiberi,
Rlian he Asumatur = 30 + 31e +32 e  etc,: 40+ 11 e+ 42e ete el pro e
incognita
substituatur in aeq. _ valor ejus ex datis aeq sis sit per compendium 10+1y + 127 etc = m
et 20+21 9+22y etc _ firi e  m. n et ex aeg. 3 fiet utique
Co 90 edo
(6) 825) 30 n = 31 ne m. + 32 n m ete  usque ad  SCBH. I
_H 40p +41n m + 42 n m etc usque ad. 30 p  m
co
M
ubi est y sine e se
E Porro dm= A10 + du. y + dir y  ete  B + 2. 12 98 + 3. 13ye ete
et du =deo + duiy +d21.y etc + 1.21 C +2 2ye +3. 23yC ete
ed02
ris ita temperanda
1
assurgat in halaeq
quam erate
co-
et ex aq. 6( disfeantundo fit C = 40n + etc 4 30n dn + n d30 t stn dM + n am
sit per compend GC ex aeq. 6 y2) O: D fiet de  D AO- OdD, : D. ubi explicando
 per 6, 7, 8, 9. et tollendo e per 5 seu 1. habetur rursus y sine c. quae duae aequationes
debent coincinere nempe W e 11 et 6
Conferamus pranc methodum cum mea ordianter iltee  aequa
ut
ante e= m: n ubi m et n, dantur per y onfervenientibus numeris quer dantur
sit s 9 ubi q eodem modo per x datur. fit o at a da + dGC dg+ dg. C
unde ex 1 et 3 fit n d4 + m dqu0 sit g 30 + 31y B2y + 33y et c =0. et fiet
dg = d3o + d31. y + d32. 9 + d93. y etc. et +q = 31b, + 32. 2y+ 3335+ 39 4y etc
Et ex 4 per (B6 et + Cit n denique sit mF 10 + 1y + 129 +13y etc. et h= retuy + y et
Ergo 4 explicando fit  20. a30 + 2. d30 y(52r. d30 y + 23. d30y3+ 24430y + 25d30y + 26130y ek
ubi possumus vel coparare
g. 11 et 12.
(11)
20 d31 y + 2 d31 y22 d31 yr23d31 y +24d31 95 + 25 d3l y
20432 21 431 22 d3 23432
et
te
24 d32
etc
int ope aeque sobit O = 7 10. 31. + 11 1. 31. y + (14F3t y (+ 13, L y + 14131 y +15. 131y5 + 161.31
tollendo y secluere
relinua habebimus aeq.
op  erit copair
(12)
dentjica.
10232 y + 11232y +12. 2. 32y 4 132.32y 414.232 y + 19 232 y
 1. 9. 10, et 4q5 tollamus y se
liabitis oe divi et, et
8= 50+ 51r ) et in abeu,  altis asiendat quam gli. s
30
ek
et
eu
etc
et
etc
et Ia ea
+31Y + 32 y 4 33. 9t + 34y +359 4+ 36 y
ex