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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 371r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.79.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 372v); this page is its right half.

The machine reads it as

  1. 21 sestetbil: 1693.
  2. nserviunt series ad Tangentium inversas d peras redu
  3. et per eas reducitur problema ad aliud faciliis. Nam cum seriei infinitae
  4. aequatione composi Nam quando y habet pro valore seriem infinilam per X, et ita
  5. repraesentantur ejus affectiones vel per se vel in ipsis e affectiones ductae, componitur inde
  6. series infinita; et si jam addatur terminus qui constat ex solis affectionibus
  7. aliu
  8. is lac
  9. explcata
  10. aliquois non habet valorem infinitum, nec procude in seriem infinitam compositam influit, ut
  11. V. g. si esset ax dx, negligendo de potest intelligi secundo gradui serici infinilae compositae ascubi
  12. ax. I seu seniem re licebit sed ut nos ax evilemus, summatim seriem tantum consideratimus
  13. post X, inciprendo ab X3, et ita quaeremus coefficientitis opeserici incipientis ab Xh quasi
  14. nihil antecederet. Quod si jam series haec a composita ab X tendens in infinitum est
  15. summabilis, utique linea quaesita este stdinaria. Furmmabilis autem est si omissa quantilile
  16. a X dx aequao assumta ad curvam esset dabilis finite ita enim Y hoc series. Itaque et
  17. A
  18. pus
  19. vi
  20. tunc erit summabilis liaet accedat ax
  21. pro aydx ponam bydu et pro
  22. esaus et distrnctus uorem
  23. sit ergo data aequalio differentialis aadus + Xydy +xy dx taq dx = axdx
  24. singamus aadus ehydus, Zydx + aa d F a faciamus aa do + xVdo +Xrdx + ax dx = o
  25. gaes
  26. ypes
  27. schedicusmat dicrsse resolaesi resolui queat
  28. a
  29. sed si jam quaeramus X per _ v, sequitu sequi videtur hanc aequationem posse sumiliter
  30. sed hinc
  31. Porro similithr suitur
  32. resolod, ponendo, XV av +XoAX + avdX = 0 seu ZdV + ZdZ + a d3 = 0. unde sit
  33. v = Z_. alog. Z. sit ergo Z = 10B + 11V + 12 v + 13 v3
  34. (et adz -= a, 1 +, 12V +3BV + 4. 14v + 515V +6. 16 V ex)
  35. 7d0 = 10 + 11 + 12 + 13 + 14. + 15. ex
  36. 7dZ =. 21 72. 2 + 3.23 +4. 24 +5. 25 +. b. 26 et
  37. (6
  38. v =c
  39. 12= 20 +2IV + 2IV + 23V et
  40. per con pend pro 10r utoripec
  41. Erga f V = Z alogs Z t si sit. Erco ex terminis v, v, V, etc. v, et, V, V, etc. quaeratur
  42. series exprimens valorem ipsius Z per V, seu valor ipsam 11, 12, 13 etc. nam 10 manet arbitiaria
  43. porro sed ponamus haec jam ut inventa.
  44. Et ja pergamus ad, aequ. 2, quae et fiet
  45. etfier X et fal 30 +31V + 32 VV + 33V + 24 V et c. et jur quod poo
  46. tiet + apde- A . V + 2. 32V, 333V + 4. 34V 4 5. 35Y
  47. 29(30 +31 +32 +33 +34
  48. X
  49. vx = + B) (41 +2 p. 13 4 14p 15 45
  50. +VYdo=
  51. (8)
  52. = 0
  53. 2 Xdx - 21964g X r41
  54. Ansc
  55. ZX- Gut bosex +St VISiPst t C
  56. itaque ope aeg. 8 quaerendo sed quod morum videtur haec aequatio esse impossibilis
  57. aado = ee tu
  58. qua quoscunque terminos assignes ipsi D, nit reperdes quod ipsi a aequetur
  59. caellies teminiscascrbas
  60. Vi si quater
  61. A = 29 + tube sde + 30 +31V. fort nam ita Vxdo dat h
  62. X = 29 + 2. 29(d0 e 2.29. 30 + 2. 29. 31 +
  63. itaque quia ha haereo nec possum X exprimere
  64. sed puto non scadere quia
  65. fit _ ax - 13 24 - 3. 12, 4. 3+ er Chepdx = a1 242 d 1 eu
  66. fiet: +a Vdx = a 7 X - 131 - 2 12 - 3. 12 - 4. 34 ere
  67. pe
  68. X var = (5 3.1) 31 + 32 + 33 + 24 +35 et
  69. +yxdx =Z,
  70. (Le) . 242 4 3.97 - 4. 41
  71. =a dv - -aa
  72. 1 30 2 0 40=0 a1 -
  73. fiet ad Z = a X 49 H 1 3t - 25+ - 3. 5) eu
  74. Zv- 40r5s, 2 + st + 5 +54 ey
  75. Idq (. 1b v. G 4 -161 - 2 5r 2 1. 87
  76. Sa hac est infinita
  77. ad
  78. sit 238 4 51t 51 +53 ei 00+ e p x
  79. st
  80. ab = a, X X - 1 - 251 - 3. s
  81. 2d- (59+ st + 3 + +, et et
  82. Z (61)- 2.61 9.69 er
  83. nonatur 5o= Bliq et 61 = 0 et 60 2 non iitspai
  84. sit Z. 490+ 501 516152 etc 20- 59049v +60451 vr6ib aeu
  85. Hmo patet omassit temminis uti
  86. vi
  87. 0 se
  88. su
  89. ac ficret aquat i possibilis
  90. 40= 30 4 = 2.303, 42 - 2.3032 +31. 31 437 - 2. 30. 33 + 2. 31. 32
  91. 44 = 2. 30. 34 + 2. 31. 33 + 32.32 et ila porio
  92. 52 +2.50.51
  93. 62 = 2.49,43 +2. 50.52 +51. 51 63 = 2. 49, 54 +2, 50. 53 + 2. 51. 52
  94. 64- 2. 49. 55. +2. 50. 54 + 2. 51.53 452. 52
  95. sed indeo tamen nec sie rem posse u ferri
  96. -
  97. ostenres
  98. seu cntrobius)eodem modo. inveniri
  99. hunc sinterdum
  100. coefcientes. Et hoc est artificiuqusvo naa
  101. tar erti e
  102. non esset
  103. Jam posset eli expumus
  104. 54V + 9
  105. uo
  106. it = et
  107. et 3) determina
  108. ne curva

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 371r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0737?run=74