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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 103r, page id 00068198:0205
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data 1c + n e =0
mna it posita e = dyidx. sit  quaesita 20 + 2y =0
nam altius assurgi um potest, f differentietur, et fiet d2o + yd2 +21 eo
et tollendo e, fiet: 11 d20 + 11. a 21. y - 10. 21 20 seu y = 10. 21 - 11 d 20, : 1 d 21 = (per 3) - 20. 21
et fit 10. 212 + 11. 20. d21 = 11. 21. d20. Ubi cum 20 et 21 sint rationales per X, exhaurientu
tandem differentiando. Et, si quidem ponatur 20 non esse ultra 1omam differentiam ire nec
2) ultra nonam, continnaliis differentiationibus licebit tandem invenire valorem ipsius 20, si placet
nam assuatu fiet 20 1. 21. d20 - 1a 21: 1 d et et Nempe d20 = 10. 21 + 11. 20. d21; 1
quam disferentiando prodibit dd+20, d2o, 20, in aeg. (10) tollatur deo exaeque 10 perou
habebitur , inde rursus quoratur ddd2o, et ita porro, tandem in altinia totlantur
va ad. quae ∞g. 0 tollantur valores omnium differentialium pracedenum
quine jeum dati, et habetur quaslaqu valor ipsius 2c sempliliter. Vel
vel pote  aeg.  10 reperta tollatur ex ea d2o, ope aeg. 9. ita fiet aeg. (11
in quo solum dd2o et 20. atque ita poro. Hoc g. H si differentietur
videndum au ex eogitair queat id habetitur aliqua (12) in qua erunt
dad2o, d2o, tollatur a20, per aeg. g. fiet ae g. (13) in qua ddd20, et 20.
quam differentiando prodibit daddro, et ita poro, donec finire placeal. Reperto
quam galcre ipsius 20, oportet eum esse integrum seu sine
A acpone, quam in rem galebit ipsius 2) explicao. Quod si non sit possibile
eum esse integrum, nec potenit solvi aequad in ordinariis non altrus assugentibu
possumus famen, et explicare in ay. 8, 1o, H, ex datis, et 20, 21, C generaliter
per assamtilias secundumx et tum videre an es explicari possint et ssumlitaae
ut proditat ideaticae aequad
S.I  10 = 30 + uX + 32 X + 33X + 34 x + 35X etc
H = 40+ 41X+ 42X + 43 X eu
20 = 70 + 71 X + 72 X +73X et. 2 = g0 + ∞IX + 82X + 93X eta
et d2o = 71 + 2. 72X + 3, 73X + 4. 74 X et d. 21 = 81 +, 82X+ 3, 83X + 4. 84X etc
21 = 8D + 2. 80. 81X +2. 80. 82X + 2. 80.93X F 2.80. 84X, ∞ 80. 85 X +2. 80. 86 X
+ 81. 81 X +2. 81. 82X 2 81.83 +2, 81. 84x + 2. 81. 85 X
92. 8Z. + 2. 82. 83X + 2. 82. 8YX
c83. 82
10. 2 = 30. 804 2. 30. 80.81X + 2. 30. 80. 82Xt2. 30. g0. gX + 2. 3. 881X + 2. 30. 80. 85X+ 2. 20. 80. 06
+ 31, 80. 80
+C30. g1.  X +2.3081. 92. 4 2.3081.83 r230. 81.94 +2. 30 81 85
16.30. 92. 92 +230, 82. 83
4 2. 38. 87583
42.31. 80.81 +231.80.92 +2.31. 8083 +23) 8084 +2.31. 80. 85
F31. 81. 81 +2. 3181. 82 271. 81. 83
1. 31. 82. 82
+32. 80.80 +232. 30.81 +3.32. 3082 + 2.31. q0. 83
35. 80. 80
ut rectanus. LA, plus rectanus. AC ad quadrat. AE. et gdibit V1. 2. d20 = eodemmodo ut 11. 30. d 21. dummodo pro Z et 8, ponatur. 8 et 7.
32. 81. 81 2. 328187
2.33. 80.81. 2.33. 80.82
33. 81.31
2.31 81 8Y
2. 31 82. 83
+ 2. 3C. 80. 
34. 80.80 234. 80.81
42. 73
43. 72
240. 7982
32 82.
2. 33. 80.83
35. 80.80
40. 75. 81
H1. 74
2. 33. 81.82
2.34.80.82
134. 91. 81
2.35. 90.81
2. 32 81. 8.
(I. 20 = Qu. 70 +41. 21 X 143. 72X + 40. 73X + q0. 74 X 4 qu. 75 X P. 7b X
41. 70 +41. 71
41. 72
43. 70
41 73
+2. 72
vn
41.74 41.45
G2. 73 42. 74
Ni 21
si aisit lantum 30, 31, et 40.g
36. 8c. 80
40. 76. 81
41. 75
43
 
3.40 2sq.d2
3.90. 29 3
4. 40. 73.84
5. 40.72. 95
6. 40. 96
4578) 172. 92
fiet 30. 80 440. 7081 = 40. 71. 50. _ 2. 30 g0 21 + 31. 80+
+40. 71. 89+ 41. 7 81 +2.40. 70. 32 = (40. 71. 8)4 41.71. 80
1240 +2, 40.7280.
40.74. 81
41. 73
42. 72
43. 71
44. 10
W. 20. 431 = 40. 70.81 + 40. 71. 81
41. 70.
+40. 72. 81
40. 73. 81
11. 42
43. 30
11. 2120. deem
~itp. 72. 8
2.42 10
3. 40. 71. 83
41. 70
4. 90. 70. 84
2, 41, 72
3. 40. 72. 83
4. 40. 71. 87
3. 40. 70. 85
140. 73. 32
iltaqi
3. 40.73.85
4, 90. 72. 83
4170
S. qu. 2. H5
41. 70.
6. 40 70. gb
2. 40. 70. 82
240. 71. 82
2. 41. 70
3.40. 79.83