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Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 41r

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: 0.84.

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. 42v); this page is its right half.

The machine reads it as

  1. erdx tagdus = xydx seu redigendo ad rationes sive
  2. numeros, e ly: AX = X: a = X: yX: a et quia X: g = X. a: y. a fint eg. du = a - XX. a a. a.
  3. siet X: a Z coiZ et g. d Sdz:p. fiet E est aq 2 fiet et dy: a = dz: p et dx: a E Zelo - 0 dz : 23
  4. Ergo ex 2 fiet 22dX:, pZdc0 - pco dzue = co. Z - coco: 22: sAz. p Sed sic locere tollere duo
  5. divellendo nam oportetet facere co: Z- cdeo. 2: A: p = 0 seu X: a - X: a: y. a quod
  6. abscndum foret. Ergo loco aeg. 4 sit g: a= + saz: p + Z. c0. fietque
  7. 4)
  8. dy: a = dz: p + Zdcd- codz, :coco et ax: a = Zdco- codz: Z2, et P 3, 4, 5, 6 fier exe
  9. dZ dque coco + P Zdeo = p codZ,: pcoco y: Zdeo = Codz.. Z
  10. = co: Z = coco: 3Z: SaZ. p + Z. 10
  11. fiet ZE debet poni AZ lcd): coco _ = Z (deo) co: Z - coco . 22: SZ. p + Z: co = 0
  12. seu Z c soz: p FZ = Wd Z Z co sazip + Z - c0co Lb
  13. (2) aco sZ: p + aZ:c0
  14. XXdx, + aydy = Xydx siat X = aco: Z et y = a faz p + aZc0. fiet
  15. (1
  16. dx = a Zdco = aco dZe, : Z2 dy = adz: p + a o dZ - a Zdco, : coco, = a cocod q acopdz- ax polo
  17. XX dxd = B aa coc Zdco = aa coc ac0 dZ; Z
  18. Xy = aacoco sdz: p + a4ZC0,: coZ
  19. + aydy - aco sZ: p aco codque t a ed saripacopdZ- a co sazip az plco + a Z acocodz + a z a co psz- a za zpdeo; c0 p
  20. =X ydx P = (a acoc Saz.p a7dio + aa coco sa p aco dque aa Z0 a z dco a a 20 aco dZ,: c073
  21. Hanc aeq.5 seu explicatam 1. divellamus in duas evan escentee differentiales et fiet (con)
  22. coopus
  23. 12
  24. opaaocoazaco - Z aco SAZ:p aZ Pde
  25. cocop2
  26. aea cattao Chopacoeoun spaz pates - Z a za2 pdeo paaoco suq. paraeo
  27. seu 1o4- co 2 B a s: p - 7 des = c0 Z sai p ao = co Z H = et habetur co: qe per sicip
  28. ergo habetitur X per y. quod absurdum. Non ergo licet sic divellere, si liceret
  29. solutum esset problema, nam tollendo co, et differentiando aeq. sine ed, haberetur relatio
  30. inter ZA2, P dp. verim cvanescentia psius p. oia tuibat.
  31. An sis:
  32. X = co: p et es y a = (dZ: p et fiet da = pdco -codp: pp
  33. etAG= de: P et dy. dx = dZ P: pec- codp. Hi valores substituantur aequ. formatas ex kia, yta loit
  34. lite fiat divulsio, et in una aeq absit dae, in altera absit dexelt ds
  35. adsitque L ap in altera B) adsit deo, ap, de in aeq. 6 erit co, p, deo, dp. adeoque datur
  36. relitio inter co et p, sed in aeg. 7 erit co, p, des, dp, dZ Sdz: p. ubi tollendo saz.p
  37. per differentiationem, f habe bitur Wo, p, deo, Ap, daco, ddp, d2 atque. est ex org. 8
  38. diferentianda dabitur idens co), , deo, ap, ddco, ddp, quarum ope tollendo C0, et P,
  39. fiet aequ: Ope 6, 8, 9 tollatur co, et p, restabit aequatio; in qua erunt
  40. deo, dp ddp, ddeo, dZ, ddZ
  41. Faciamus ddzue 0, et et tollendo x eum sins
  42. effectionibus per B aque ope aeq. 6, habebitur postremo dque per solas de, dap, a adeoque
  43. seu pos de pocendo a
  44. ()
  45. Excmplum sit
  46. X: a = co : p y: a = sdZ. p fiet dx = pdeo - codp, pp et dy = dz: p et
  47. CMa.
  48. dy: dx = dzp:, pdco-codp dy: dx = x 9 :ya ergo fiet
  49. +Cd p: PP,
  50. dZp: pdco -codp = (aa) coc: pp (: saz. p aa et veducta aequatione fit
  51. dZ ps = jodat dq p saZ. p = (x coco deo = p co deo - co p- ( pdco)
  52. feit co dp - p co dco 2 0 ergo dze p sdz: p = - 2c0 ap
  53. et differentando bt saZ. p = 208 dp: p dq eti B. p L -p d2 2c0 da p + co sptes + 20 p p ta (t pli 1
  54. ubi in 5g. 12. fial ddZ =0 ex 5q. 9. different rendo, fiet. P
  55. (d ddp + 3co deo dp - p co dda - p ded - co deo 2pdp 0 ope 9 12, 14 inveniatur eg.
  56. in qua absint p et co, habetitur aq. ystans (15) constans ex deo, dp, ddeo, dd p, d Z
  57. jam e ope aq.)4 tollatur vis uffectio c0, per p. quia ex aeque. ∞ datur co ex p
  58. per quadraturns ergo et deo, et ddco, per dp, et dep; fiet habebitur dq per
  59. dp, dap, d et a adeoque res erit reducta ad quadraturas Quod
  60. accuratius e exerminandum firet eum magni momenti. Ver t
  61. Nam pro de ponas dZN: a et adeo pro dap, dz drr: a
  62. habelitur aeq. in qua extabit dZ II, I, a
  63. adeoque dabitur Z per X, ergo et dp per Z
  64. sed dubito an post subtatas eo, et p, tolli ad huc possit
  65. deoris eo, qua parto deo et ddeo, quin rarsus cedeat p.
  66. So Hinc video non fuisse opus liz eo. sit
  67. ex dy. fat y =4
  68. aqu. (1 nc
  69. sdZ: X et tub ex 1 et 2 sublati s fia
  70. aey. 2. unde tollendo fdz: X, hebe.
  71. bitur aeq. 4, in qua X, 1Z, 3dque, a
  72. lui an

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 41r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068051:0081?run=73