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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 102r

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. 103v); this page is its right half.

The machine reads it as

  1. AB, X Cb, y.
  2. EF, Z CF, V
  3. AG, g GE C
  4. AH, in A n H E, h AHoA D : H ,I:: m: n: h
  5. vel AHim A Ht
  6. Quaeruntur valores ipsarum Z et v, ex ipsis X, y, v, g. , 2, 4
  7. (1mO) B = CK = KF, (2d0) CK = yh: M (o) KF =
  8. HK. n. h HH (4t0) HK A An - AK et 6to)
  9. AX = L -XB et (6to) KB = yn. M. Ergu juventa suat quae
  10. Quaeruntur, et fit AResimo) AK = x gnim et HK = m - X + gn:m et
  11. (9no) KF = muh: xnch t ynnitm et () ex , per 2 et 9. fiet
  12. Iomo) vC gh. m iin. h 4 Xn. h ynritum seu v = th. Mr. timi) Gy A-mi
  13. seu (12mo) v= my (m X) e sch Sed si
  14. (3tio) K F = HK n: h et (ta HK = AH - AK (6t) AH = g + GH.
  15. EX5per 6
  16. EH (6to) GH = em: n sit AH= g. (7mo) AH = g + em:n (8VO) AK =
  17. X = KB et (9no) KB = yn: M et () ex 8 per 9 fit (1omo) MX-
  18. um
  19. X -gn: m. Et ex 4 per 7 et 10 fit HK = g + em: n - X + yn: m. Et
  20. (2) ex 3 per 11, fit (12 m0) KF = gn: h + em: h = Xn: h + ynn :tm, et
  21. B3tio ex 1 per 2 et 12 fit V = yh: m = gn: h - em: h + Xnih - ynnitm
  22. seu (7to) v = (X- 9) n: h + ystit - nn: hm) - em: h. sed f tm tan = tih
  23. sed (15+0) ex hypothesi nm + nn = hh. Ergo ht m 16to fit
  24. (16to) hh-nn: hm = mm: hM = m: h., Ergo ex 14 per 16 fiet
  25. 10
  26. 17 no) D = (X - gn + (y = e) m :h seu fit CF = GnGB + M) β: h
  27. u CF. adhibitis punctis S,B, (3 rectis GB, VB, et
  28. qvia ergo determinabime
  29. ratione trianguli H A 7. Ut oportet eodem modo determinari
  30. C adhibitis rectis VB et ratione trianguli LAh, quod est simile
  31. gno
  32. ipsi HA ,I Ergo fiet Z seu EF seu C= mGB + ng. h
  33. posito G: GE: HE m. n
  34. similitr ergo invertendo figuram Hinc data relatione inter Z et
  35. substitutis valoribus, et explicando GB et VB habetur relatio inter X et y.
  36. non Ronamus jam porro immoto manente plano BBE ABB moperi
  37. in eo curvam CC, q angu 9 reco XFEF; poterunt successive
  38. reterminari loca curvae et cuinclibet in ea puncti. Hinc si duus valores
  39. ipsius Z, itemque ipsius B, investigemus, fiet m M:n vocemque Y, et mot
  40. h = rmmtn h. = hih m hh etum = mm t u: Est nm = 1+ 1: 1
  41. mm:th = mm:, nm + um = 1:, 1+ (1: rY) et M: h = r: Ser+I
  42. nn: hh = nn: mntin = 1:, er+ 1 et n: h = 1: srrti. Et fit
  43. proinde Z= rGB+1)B: fitrr et v= . GB+ rVB,: Sit Ir.
  44. itaque si curva Cc moveatur, et diverse ecudem in ea puncti situs
  45. conferantur, fiet FGB + 1VB,: siter = (Y) (GB) + 1 B): Si + r)
  46. et a 1GB+ rVB: sitrr = 1 (GB) + (Y) (B): Si+Y). Ergo
  47. FGB+ 1VB, Sia r)
  48. C Bs+ 1). sirn
  49. est cnstans. et GB+ rV3, 1+ () est constans
  50. GB + (V B3) FIt rr 7
  51. Ergo t unum multiplicando per alterum inversum, fiet
  52. 1GBF YG6. + 173, 1(GB) + () (2.β,
  53. constans seu fiet deniu
  54. quatuor ret (Y) et,
  55. (r+ V B: 50 8, 1+ B). GB)1) subi to occurrunt: est B. 58, et
  56. 1t AA CB)
  57. 1 + 8Y3: 50Y (Y 1 P]: (60)
  58. M
  59. et _1(). 13B)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 102r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0203?run=74