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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 180v

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: 0.85.

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. 181r); this page is its left half.

The machine reads it as

  1. Reneamus jam ad aequationem
  2. gy - 2c9 + XX - 29X = + ff.
  3. YX. AX X 91X XZYX AZ- X, y
  4. VG: YC = LGy. + ZZ +XX - 1ZX): 9
  5. XX XZ = Z-X VYV. sit
  6. V +g v = , Ly + ZZ+XX - 22∞)
  7. vD = gy fZ7+ XX - 27X
  8. y: Z- x = +:
  9. fiet Z- x = by. t 4 vn = gy +: lt) jy
  10. fit v: y = (+ H). + ses fiet
  11. y = tv: sC+H) t (Z-X). et fiat
  12. In: (+H) e =X. Eg Ex aequatione
  13. ad ciculum fit vr- ZZ + 22X 2c9-29X = +f
  14. EF Ft. vocetur 44, fiat axv quo 2c v. 2992+ Egrv +ffq
  15. JueC422+ 453 - 2c, tv + 2922- 2tVZ - 2992 egr = 0
  16. +291V
  17. seu Wo +ZZ - 2tVZ, 291 - 2Ct .x - = gZ = + f
  18. artitrariis aiginairiae f, I til, C, d, ftit artitiara per Y
  19. adhuc artitrariam. Itaque quaevis fomuta in aequatoo localis hujus grodus fonnae
  20. in qua WV et ZZ habent eundem coefficientem, huic identifiam potest
  21. directirem
  22. supra sectionem conicam retulimus ad rectam, quamcurque
  23. per ordinatas tamen normales, et aequationem indenatam
  24. localam exposuimus. Possemus jam matare, eam matando
  25. angulum in obliquum mmente hirectriae, sed pri
  26. nunc aut nunc at relineamus axem et am pro
  27. directriae V. mutemus angulum. Aequatio oealis
  28. Conica generalis id Axem ex vertice, est
  29. KR 10X. + (b: C) XX = yy. pro y
  30. ponatur _ antc Er:g, ut pro x ponatur
  31. 2bZ 2bZ - at. g v 2 b1l. a B + (b: C) 2Z- 2 (b: C) (l: 9) 3n L u (I: 99) (8. ) = 0
  32. 1t
  33. Z = lv:q, et siet
  34. (F :99) XV
  35. Sumamus jam problema aliquo d, quale est maximam vel
  36. minimam ducere ex puncto dato ad curvam sonicam AY
  37. quae so determinata sit MY. Ex Magatur
  38. normalis MN i axem D sit AN, n et MN, m
  39. ipsa autem MY. ipsi Axi sccurrat in P. Ob
  40. 2bX +(b: e) XX = jy fit differentiando b + 1b: C)X, G: y = dy: dx = X B: y
  41. Ergo X P = b + cb. 2) X jam MN: N P = y :, b 4(b: C) X
  42. Ergo sit m. A K + b +(be + (bF er: 2)X - n =. y:, b + (b: C)X. sit b - n = 7
  43. Sit bre = B fin M b + mb: 1) X = ) By + (B: C) xy.
  44. et pro agponendo +v: q et pro X ponendo, Z- (1: 4)V
  45. fict mb F mb.: e Z - mib: esl. qlv = Ht. q)V + (B: est: 9) ZV - (B: C) (+: 9) l: 9) BV
  46. seu (BFl: equ) vv - (et: e9) ZV - rbl: eq) V + meb: 2) Z + db = B- mb
  47. y Ct: 4
  48. Multiplicetur aequ. Q per + f st aequ. 0) per - mb
  49. _ et aeq. D per arbitrariam dtC
  50. productum
  51. ex aequationibus et D addantur in unum,
  52. et compositum identificetur product ex aequed
  53. consentiunt utrobique termini absoluti, nam utrobique
  54. omnic aequabuntur ipsi = ff mb superest ut aequentur
  55. aediaquentur utrobique termini respectiri, qui sunt numero quinque
  56. Opas est ergo aequationibus quinque, habentur auter habentur autem arbitrariae c, 9, f, l.t, sed haesunt
  57. Kuntum alunio ut a.ue pua p t quae mo ti plicadit psam aequ. D. quo s ha quionque un dofitiant sut lanm sperot
  58. Crsiranam mullioqus tartanti
  59. mods quibrevor ante tendano

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 180v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0360?run=74