Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 88v

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: 0.78.

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. 89r); this page is its left half.

The machine reads it as

  1. vdvia deo ergo
  2. e
  3. aequ2t Quta eteo fit co
  4. (ax Sb.4 +BE BY
  5. Aob: 4 =AAVV
  6. sit do = - taeX: XX F 2rX + IV et C
  7. ditrum
  8. Dco-
  9. sit v= ta : 2X +21.
  10. D XFExt
  11. 6X+ 2b 2X + b er
  12. cettaa
  13. aabbx t abbx +aLI
  14. ubi debet fieri b b f ab b eethaa = 4bdr. et recidimus in idem absurdum
  15. KKFa
  16. retenta ergo aeq. 38) faciamus P= BX + at, EX + 2Y et erit ob b + ee B
  17. 9
  18. ed exC Ldx. βx+ eY ta: X+Y
  19. (31) pBX +
  20. Cd =
  21. X+x+
  22. At
  23. bb - BB
  24. n eat
  25. X +ib YX + b2 BV (7(+4 beq
  26. e. +2eeBX + ceaalt
  27. b X + 2AbrX + 4abb 1Y
  28. aaAB.aBat X aatt
  29. afieri bt eeaat
  30. Ergo
  31. orrda t
  32. =+b reeBat
  33. debet ee (+qeβ at
  34. BBaat)
  35. et fit bbaa H + PBr +2bb r Bat. et facindo t= 0 fet ( + a bba
  36. et habebitur rrB, at BD sc. fit bb + dB - + 2bb
  37. 4, 26
  38. Debel
  39. faci videamius an compendii causa ob aequationes 13, ( 15, 16. liceat facere
  40. qu
  41. pp: 4 = ag = 0 est autem p = 2bbr - 2Bat, :, bb- eβ fietque pp. 4 = aq2Z
  42. B2 2bbpat + BBaatt r 4 baalt + 2bbBBbb rr abb BBa βbF + BaC
  43. ((2 - 2bbr Bat + (BaF) ( b + ba C + Bbr BBa +) 20. quae aequatio
  44. coincidit cum aequatione 35, quod memorabile est, si faciamus r. b quae
  45. aequatio propemodum caincidit cum aeq.35, et si sit + = +, seu in casu Hyperbotae
  46. fit r = b s adeoque ex aeq. 35 fit aatt + β3bb = 2b Bat. Unde habetur at: βB = b-r
  47. sed in casu Ellipseos, ex aeq. 35 fit bbaatt = - 2bbr Bsat - ββ . Et ex 38) = 2bbiBat - (36Y
  48. atis
  49. Ex quo patet in Ellipsi necessurio ZBF esse quantitatem affirmativam, et fieri β = 4bat: r. 1. bb
  50. quem balorem substituendae in aeq. bbaatt = 2bbr pat - br, fiet utiZ
  51. r6 - 2rb + rb = cr 8br - 9brb - 16br seu 25b7 -10br + r - 0
  52. seu 5bd - rr = 0 seu Y = bS5 adeoque in casu Ellipseos fit at: β = b 15
  53. itaque tam in casu hyperbolae quam Ellipseos fit at: β = +r. Itaque ae dimensionem
  54. X
  55. e + LSXtS.
  56. a Curvarum Hyperbolae aut Ellipseos reduximus ad summ. gd7
  57. Pelibea antams quae summa constat ex duobus membris, quorum unum quoque quodque est summabile
  58. per reductionem ad rationales.
  59. X+C Xx

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 88v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0178?run=73