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Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 22v

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. 23r); this page is its left half.

The machine reads it as

  1. sit filum trectum
  2. duo
  3. GE, EF
  4. sit articulas rectolinem GF, suspendeneplibu catenam
  5. Em
  6. FA. sit cenlius , in N et centum cntenae a FBC
  7. sit in P. erit AP = sX san gus: 5 sdx di AH, X. FH, y
  8. st AM = + AB m. HI et HN = L_ eA X -X, : 2.
  9. et AN = p - X, : 2 +X = N+X,: 2
  10. sit G. rentum grav. totius eFAFC fiet pg. F = Nq. EF
  11. Aq = Ap + PZ et P NP = AN = A B et PZ: Np:
  12. ii EF: EF+ FA sErgo pu = NP. EF: EFAFA = AN- ApDEF: EFAFA
  13. fia AQ minimus, erit seu AG = X Saxtadu + Z r+Y. EF; EF+ FA, ubi sola Efi
  14. varians
  15. Et sbtique noinam, et d Aq = = EF +FA i vix = SX Laptatus B E rt X. EF ubi imior Loanssere EF
  16. Tigum FF cum inde dependente chorda A FAF pendeat ex
  17. artienlis GCF. sint Z EF et FAF ponderosa. Debet
  18. manenles distania punctis GG et distaum =4 si disponi
  19. lolumut centr. y. mux une descendat
  20. Dideamus an non possit esse uius maximae et
  21. minimae ad determinandam curva parametium investrus ata
  22. am speco in qquam catena curvasri debet: Et hoc videtur
  23. samino debere lonum alaquem habere
  24. Curvae naturam esse invenimus ut posita A, HE, y et OHia
  25. af.IY. Scax tx sit y = as, dZ. (Z2- aa = nc et
  26. sit (Sd q + diu = syn - aa = AF
  27. Ponamus jam dari HF seu y et A AF
  28. Quoritur ergo datis punctis, F et H, et aequatione 1, naturam curvae
  29. exprimente, qualis sit parameter a, seu BA, ut centrum ipsius
  30. AF quam maxime descludat,
  31. A3= Z Saque dus: R=
  32. dz = du = Z4Z: se- aa
  33. Efficeedua este rvantur
  34. vaeritur data suqaa dataque as, dz. _7 aa, ptalia quae nam sit a
  35. et Ay = (ZZZ: X2-aa: ut txna B
  36. ut fqaadus. Sat aa fint omniam possi bilium minima.
  37. 33-a4:77-aa fiat omnium possibilium minima
  38. Equidem q non est constans
  39. e
  40. Sit (ZZ- a a = f
  41. et y = C, nempe in casu dati puncti F
  42. et 532.2: 122 aa: f = Min im
  43. Sed difficultus est, quod hic caliulum de maximis et minimis non videtur commode
  44. fiet CL a5, dZ: 122. aa
  45. 2 Sq aa.
  46. Si aequatio 1. esset cli absolute calculabilis, seu
  47. relationem confineret inter solas c, Z, a, ejus ope Utique ejus ope daretur relatio
  48. Z per a et C sed ex aequ. 1. datur hy per a et f
  49. licere applicare.
  50. hos duos valores ipsius Z, dabitur d per c et f datas, itaque
  51. video admissis aequationibus E, 2, dari aEex c et f, adebqe et sine
  52. nicet cut
  53. ergo jungendo
  54. Et proinde non dari applicationem calculi
  55. maximis et Minimis, si utrumque datum ponamus, c et A, sed si datum
  56. intercedente. aeq. 3.
  57. it alterum tantum ponamus ergo dari C, non vero dari f. itaque
  58. et AP AZ = (AP+ Pq =) (AP. ER+ AP. FA + AN. EF (- AP. EF): IE riA
  59. et AP. FA = Tx Sax + du et AN. EF = . V. EF + = X. EF. sot
  60. filu EF
  61. ut S2
  62. E
  63. ly + yd
  64. a
  65. .
  66. pt

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 22v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068056:0044?run=73