Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 7v

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1. sint ergotres aequationes 111y + 12 dy + 1L1Z + 122 dZ + 100 =0
2. Companto i1 dy +2 dz + 101 -0
3. Compendio
4. 21 dy 4 22 dZ +20 L0
5. 2119F212dy + 2213+222d2420020
6. ubiduae pudus aequs sunt datae
7. tera assumta
8. Tollenda du et dz
9. aZ = 10. 21 - 11. 20, :0 11.22 = 12. 2 et dy = 10. 22-12.267:9 12. 21 = H. 22, quae duo mutatis
10. 31AG + 32 dZ +30=0
11. signis habent eundem denormoatorem. Ergo ex aeq. 3 fiet: 10. 22. 31 = 1. 20. 31 -. 10. 2(. 32. 4 11. 20,32 F12. 43 1 2c 3
12. fiat LIII. 222. 31Yy A 12L 121 222311Z +100. 222. 311a Jum 1223
13. D(- 21I. 122. 311 9 - 221. 122. 3117
14. O= = III. 211. 322y
15. + 211. III.3249
16. + 121. 211. 311y
17. = III. 222.3119
18. = 121. 211. 5227
19. = 221. III.3227
20. + 121. 211. 3228
21. = 200. 122. 31 a
22. = 100. 2II. 322a
23. + 200. 111. 32a
24. + 121,211, 300a
25. = 111. 222.3272 = III. 222.300a
26. 411 311 y + 421. 3117
27. 412 3227
28. 422917
29. per
30. dix (P.31y
31. je.. y.
32. (6 322y
33. I1.22 - 12, 21 =
34. 111. 222= 1224
35. + 431 3ua =0 fit quae aequatio
36. 432. 322 a
37. 439. 300a
38. diferentiata
39. dabit d41. 2u y + 411. 311 dy 4 d421. 311Z + 421. 311 dz +14 31. 31 =c
40. 4I1. d3H y
41. d412. 322 Y
42. 412 d322 y
43. 412. 322 dy
44. 421. d311X 422. 322 42
45. Hanc aequationem possemus appellare
46. a422 311
47. 422 d3117
48. compendio SI y +512 dy + 521Z + 522dz + 500 =0. Eamus
49. 431 d31
50. 4432. 322
51. 432 d322
52. d430. 300
53. 430 d300
54. conjugedo quam cum aegq. 1 et 2. inde facere aequationem, qualis O, et cum ea coincidentiare
55. sed quia taman postea ob nimias, arbitrarias instituenda divulsio est, destmerim
56. prius dus et du. sud veres hoc quidem si liceret. Sed si liceret si adderemus hun
57. aliquam ex datis vel summam datarum, ad conservandam legem justitiae
58. Et ita videtur res processura, sed video ipsam malecalculatam et omissas
59. sed multiplicat
60. esse 8312, 321.
61. prius pene arbit
62. Et tum assumamus relationes inter binas quide,
63. transcendentales simplices, et binas alias ordinarias simplices pro effi
64. crendis qualuor aequationibus. Et ex ordinariis assumlis quaesita, tenta
65. scirvabunque s trauscendentales suas simplices. Et ita tentemus efficere quae
66. situm.
67. s
68. bona
69. sed nu imnia fabricanda est nova aequatio C
70. 4102L + 1II. 222. 311y
71. = 122, 2I1
72. + _ III. 211. 512y
73. k 11I. 211. 312y
74. + 1II. 222. 321Z
75. = 122, 211
76. + 1II. 222. 300a)(+11. 222 fAy +11. 322 321Z +III. 222300a
77. = 122. 211
78. -4 121. 211. 32Z
79. =127211
80. =122. 211
81. L - 122. 21)
82. +B100. 211. 382 a) = 111. 222.312y -121. 238.3137 = 100. 222. 312a
83. 4g 11I. 221. 31Z =41II. 20. 3(2a + 122.211.312)+ 122. 221. 311Z + 122. 200.312 a
84. +4I1I. 222.312y -121. 222.321Z
85. _100. 222. 37a
86. 42
87. + III. 211. 3229+ 121. 211. 322Z +700.211. 322 a
88. = 1H1. 211. 392y = 111. 221. 3222 = 111, 200. 322a
89. 12 dgo- 112 dy + 123 dy + 1. fiet =d7 = 112 dy +109: 122 Ergo dy = = p10. 312 + 929 )20 pr du - t0 25 2. 120
90. 4 L F122. 2V1. 312
91. 4 122
92. 0- 212 dy 4 222 d +a
93. o 312. l9 + 321 B t30_
94. AE
95. 4112. 222 3Iy +H2. 222.3212
96. =122. 212
97. = 122,212
98. -HI. 232. 3121) = 121. 272.312Z
99. +122. 211 312y 4 122.221. 312Z
100. 4 III. 21 322y 4 121. 2]. 3322
101. = 11. 211 3329 = 11X371. 372Z
102. = 212 dy + ∞10, : 222
103. 2. 222- p2. 21
104. quos valores substituendo in aequatione 3tia seu initio assumta fit
105. = 112: 222. 300a
106. = 122, 212
107. = 100. 222 312 a
108. 122. 200. 312a
109. + 100. 21. 322a
110. = 112, 200.3224
111. compendio
112. +1222, 311y 4 1222321Z + 1222 300a
113. = 1122. 312y D- 21223127 -0022. 313a
114. +11I. 322y + 2112322Z +0012. 322a
115. quam d
116. =1222 d311 y
117. + 1222d321
118. L +1222 d300 a
119. =4122. 312y = 1122. 312dy = d21 22. 312 -2122. 3Bcy =d0022.312a
120. = 1122 d 312 7
121. = 2172 d312
122. 2 = 0022 d 312a
123. +d1112. 322y + 1112.322dy +2112. 322 +2112.3224Z +-d0012, 322a
124. =(112 d322 y
125. praestat ergo tollert Z112, 432
126. dz v
127. 20
128. quam aequationem differentiando
129. fietc: +d 1222. 31H + P1322. 311 dy + d1222. 321 Z 4 1222.321d7 41222. 300a
130. D-
131. 4 0012 d3220
132. quodsi haic aequationi addas datas
133. binas arbitraris multiplicatas
134. lice bit deprmere dus et de, et
135. ia regia per eorum valors, uti numeri non pisi cogniti. et per set
136. habebumus binas aequationes, in quarum qualibet sunt 31. 312. 32l. 332. odeamus, an 312 et 3EZ sic explicari liceat, ut sotum
137. in una aequatione restet 311, in altera solum 32I, et habebitur quaesitum. Itaque hoc jam examinandim in genere
138. sunt binae aequationes differentiales simplices primi gradu, tinarum quatuor literatrum variantium, vidiamus an hacu
139. harum binas sic interpretari liceat, ut in una equatione una lterariliquirum, in altea altera restet quo
140. dus ( - 102 a. myn defly = 1e2 + idZ fiet y= cps BSudx ((ax, watrczfiredq = W0 ((et dx, 100 + 2 Z e de
141. posile spes erit
142. Agn. 2ec + 2119 4 2417 1222 dZ hrty = l sit bsitu b. = Adx, 0d00 + 22i Zt 2224
143. ubi sin sent datia
144. Syt 312 dy + 321∞ + 322d3 4 300 20
145. fiet 12dZ+10, : 11 = 22 4Z F 20, : 21 seu 12adZ + 10, 21 Z U. 22 dZ + 11. 20. Ergo
146. quod superest coincidentiare psi
147. aequationi C, sed ita spere
148. duae aequatione pro coincideo
149. tiandis Z y et Z aderunt duo
150. aequationes quarum quaelibat
151. habet amb incognitas prorsus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 7v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0014?run=74