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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 55r, page id 00068198:0109
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C= 2 =O: D
 sit aqualio data -dy: dx = 1 = 10 ruy + 1yy+ 3y CtC: 20tuytngy rasse
ote quaesita 0 =3 = 30 + 31y + 3299+33  + 34 y etc, quae differentiata dabit.
0=4 = dx (430 +y 43, + yy d32 + p 433 + etC) + dy (1.31 +2. 32y+ 3. 33yy + 4. 3477 etc) = 5- dx 4 dyt
unde - dy: dx = 6 = 4. t 27=O: D adeoque Ot = 8 = D2 Atq adeo fiet.
. 10. 31 + 2. 10.32y + 3. 10.33yy + 4, 10.347+ etc = 9= 20 130. dyy + 20d3ryy + 20 d 3y tet
+1. H1. 31
2. I1. 32
3. 11. 330
2. 12.32
21 430 21. d31 21.432
Haec aequatio aliquam est identia 22 30 22. d31
23. 430
sed regulariter hoc postulandum non est
itaque coincidentietur potius alteri aequationi, factae ex ductu quaesitae e in artitrariam, formulam
1. 13,31
quae sit 4 +a2y + 43yy + 44  + etc. Unde fiet productum
Lu
30. 41 + 30. 42)
odro
F31 41
+30. 43gy + 30. 44y7 + et =10 =0 et prodeunt aequationes
2. 10. 32+ 41. 31
1. 11. 31 47. 30
coltii
1e 3,102) = 3l. 1
2. 11. 32-
1. 12131
ponamus aiquationem datam esse
29 430
coincidentiantes quae scquantur
plitatobus 10, e 11, 12, 13 C 14, 15, etc. et
sed et et ex issis 24 2t, 22, 23, 24 ete habere solum 20 et 21
edrete
prodibu aequationes A1. 30 = 2d30, 41. 31 + 42. 30 = 20 d31
 eu ordinet habere slum lite
13. 31 +48, 33 + 42. 32 + 43. 31 + 44. 30 = 20433 +22431. Sed placet ordine exponer
41. 32 +42. 31 +43. 30 = 20. 432 + 22430
141. 30, .3
on
2. 13, 32491. 34
41. 32 1.13. 31 +4133
20456
3.t . quus
videamus jam qua
ratione res possit
finiri, ut quam
4+,  sit 0 et 30 sit constans et
prima aequatio habetur, A1 sit constars et erit (d30. 30 -71Fdp. 20 si jam 42 sit 0. fiet
30 et
vidanus an licent fatere =0 quis qu 
loganthimi eorum
 differant constente N  sit 43, et 94 et 20 et fie in
n+ = 38.  vel certe habebitur dotem vodo, ut in summando
41 32  aequ. 20d32 + edjon Aihoo seu 20. 4g2 aequ. 20 d3c + 41. 22 30, et haberi
3, 35, 36, etc =, et
potest 32.  ex  dende B. 31 441. 33 = 20 d33 + 22d3) et habetur 33.
43 44 3144 45. 46 etc. ilidem esse 0. Et ex aequti Et Maeter ultimam aequationem
ponamus in hoq caso non assurgi ultra
35 feur 33 G
et adeo esse
h.B3. 33, = 22433 seu (d73: 33 3 sdx. 13: 22
et habetur 33 absolute. Aequatio genultima dabit 2. 13. 32 +42. 33 =22 d32. ubi 33
nil turbat. Sed aeq. antepenultima est l. 13. 31 + ( 41. 33. +  E2. 32d32 - 2 (13, 33) 32 qu. 20d33 te2 c 31
nulla prodibit alia Ex ex ipsa siet 
fi, 22. 13. 20.32 + 42. 20. 852 22. 41. 32 H22. 42. 31 + 43 = 22. 22. 41. 30. Et exk aeg. 4
seu antesenult. fiet 20. 13. 31F 20. 33. 41 + 20. 42. 32 aequ)20 d33 + 22. 41. 31 + 22. 42. 30
sed video nos pro 6 649. habere 30, 31, 32, 33, 40, 41, 42, Quod subicit. Ex perutli Tertia aeq.
ia aequi
Ex 1. Aer. 4r = 2t 20d30: 30 et 20 d30. 31 + 42. 30 = 20. 30d31 et 42 = 20. 30d31 -20. 31 d30; 30
seu pen antep eagltima fit 241. 32+ 20. 47. 3) aeg. 2 20 d32 4 22. 91. 3 ex
Exaeq. 3 est, 20. 30132 4 30,  31. 20. 30d31 - 31. 20. 31. 430 = 20. 38d32 + 22. 30d30
supersunt adunc duae aeget. pro 30, 31, 32 nam 33 per ultimam habetur. Et haum cum sint
et d32: dHC et d si possemus aequatione
Tollamus omnes
iacnit disfe entules rationesduae  d3i: de
ote te cetu aetise tentus sen tt
Et ita porro
minimum ascendamue
1. 10.31
4. 16. 34 Y +1133
3. 11. 33 42. 3
2, 12, 32
l 13. 31 44.30