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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 75r

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: 0.80.

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. 76v); this page is its right half.

The machine reads it as

  1. uo y rudus + ikov. + 121 dv + 100] = 0q sit v = e et fat r. 120 (1 9 t pay
  2. 210y + 21 dy +220V + 221 d + 200 =0 Ha aequationes expli +121 d βY
  3. mulsipliabur prior aequatio aequatio ex
  4. tat
  5. tera pera . ...... e.F fie d. componendo
  6. ut iam tollamus tant dy quantque, fiat
  7. siat Y = 221: 121
  8. pec licet siu
  9. ide
  10. tur
  11. succe
  12. e
  13. et X -1II. Z2Iaa = 121. 221 aβ + 211 a + 221β=0 sed hoc non succedit, qa evanescit (3. du
  14. ad totendum L Y = 220a: 120
  15. Hoc sid summos terminos cellere posumus, ut y et Z, sed nil non satis hoc pacto fiet
  16. quo valore substituto in y, fet qua coefficiente ipsins y ut tollatur fiet = 10. 22Oaa - 10. 2oaB - m rroad B +
  17. 2
  18. 210aa + 2o Ba + 221 dβa = o, fiet - 110. 22e a (= 120. 22 B. 121. 220d βB + 10. 2W0 a (+ 10. 20() + 120. 221 d β = 0
  19. itaque per quadraturas habetur dβ, atque adeo et β. Et fit B- (110. 220 - 126. 216, :, 120. 22 t 2to
  20. Restat aequatio. ( MI. 220 a - 121. 220 (3 + 211. 1oa + 221. 120 (3) dy + (221. 20a = 121 220a) d Z + 2 ∞. 120- 1dbnlosas
  21. seu compendio S dus a G dque + H dx dq = du + Bx, :a .Hfic valor substitnatur in duabus
  22. fiet 10ay + 120 aZ 2 et B dy
  23. 120 3y
  24. 100 adu
  25. ax
  26. rationib
  27. (+ 200HIa
  28. 10ay + 21 adye +200 adx
  29. G y+ 4202 + 4pay 1400aL
  30. erunt y, Z, et a, quae aequatio sic differentiari potest, ut in ea suit
  31. 121 d βy
  32. vol compaadio 310 y + 920Z + 31 dy + 20d a L0
  33. ita tarum duarum aequationum ope
  34. habebitur
  35. tollndes dus
  36. tollatur Z, maneat y, du, dz, a, dx, eibi pro dz ponendo vilorem dz = Fdy + Gax
  37. habetur aequatio quaesita in qua solum extant setus, una cum x et dx, quae potest solvi
  38. ne procedendo ita, et quaerendo
  39. gratione in qua du et d y et Z golae evaniflant omnia, sei tatur
  40. et ita quaesitum consequemur
  41. un
  42. nes
  43. luffe tamend
  44. y
  45. verea
  46. Ex aeq. X. fiat 210. 41- 1211. 416
  47. et n f. y 1 dy + =c fori coincidentes
  48. = 300 qul a
  49. 3I1. 420 - 320. 411
  50. 311. 420 - 320. 4 ( 00. guL - 311. 400 7 a
  51. 1(310. 411 -311 410) 1 + 310. 4u - 31. 410 dy Y d gro- 3200
  52. =liz =) Fdy + GG.
  53. la2st a . 13. 2B Lra oo Unde apparit evanescere aequave
  54. dina
  55. 311. 420- 320. 411
  56. 31. 420- 320. 41 = 111. 420a + 121. 210 (3 F, 121. 220
  57. a me trrer teaue
  58. tat simpeditus sicessu. Tentunde san liceat officeret constantem
  59. 10
  60. multipliretur +210aay +21aa dy +220aa Z + 221aa dh+ Eebadax
  61. +220βa y +21 Bady
  62. Z et dz. et sunl tollere y et du foret
  63. verte ad
  64. l +22 dBay
  65. uiie
  66. 3.
  67. dem qiu
  68. quatu
  69. ande
  70. ZH. 20

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 75r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0149?run=74