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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 17r

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. 18v); this page is its right half.

The machine reads it as

  1. de pressio formularum per explicatione
  2. Ende terminatae.
  3. PXF 99
  4. e formula 9 + b = fint y = pX + 993 : X + Y. fit O = bX + bt 3:, X+Y
  5. pro tollendo termino rimo fit p2 -b si srimumet secundim simul velinus sollere siciet praeterea
  6. Y =C - 99: b et 2 O=0, nieoque y2 -b
  7. sit semper y = px + 44,: XtY et formul:
  8. +9 +Bbp
  9. +bp XX + bpYX
  10. + b 99X + b 9gr
  11. + cC XX + 2CCY X + CCYY
  12. seu fe
  13. gy+By + cc = O et explicudo
  14. xraere
  15. 3 FX- EYX+ ir
  16. seu p = 4-b+ C
  17. uet tollatur terminus suemmus pmmus
  18. fit p2- b + 1 Hbb +cc
  19. ut tollatur primus et secundus
  20. fit: r b92 + Sbb Sacc bg4
  21. si compendii causa bb - 4cC Pocemus et,
  22. fiet q p = =b + L e
  23. (1) C x + 94
  24. X + 299
  25. e- b
  26. 2bb - 2B bb - 4cc - 2cc
  27. et r- De.
  28. Zee - 2te
  29. B299 c8
  30. C- b
  31. Nam si p- b+e fii pep - bb + 2bC + bb - 4cC
  32. seu g = X + 299
  33. e-b.
  34. 40) e
  35. e b = 1. Exgre seu y=
  36. XL 2
  37. - b
  38. go duo termini primi simul tolli, non possunt, quin eadem
  39. epera ex odianta indeterminata y fiat determinata
  40. contra propositum.
  41. si processisset haec via, licuisset
  42. formulas indeterminatas semper reducere ad rationales quoad
  43. inde terminatas simplici explicatione adhibita. Et continuari
  44. Termingea posset perpetua depressione, quod tamen non
  45. est admittendum. Nam ex formula Nam pro formulu
  46. y + p y3+ qyy + r y +5 = C, ponendo y
  47. Px+ 49 feret
  48. X4 Y
  49. ( = P: X +. X +. X ita opus esset solum formulam uXX +. x +. p
  50. LIX+Y
  51. aequare oto, quia anminator jam est qtus.
  52. Illad vider licere simul tollere terminum summum et infinum nam
  53. sed tunc fit: x3 +. X +. X verum, ita si rursus velimus pergere tollendo
  54. L X+Y
  55. possumque quidem frere X = 1. Z
  56. facere X = 10 Z + 11. 1 sed ita Prodit fomulae aequoata
  57. 12
  58. et ila poncndo. X +. p2, . x = D. fiet D = 202 + 21Z88. sed hanc
  59. (2) Z+12 7+ 12
  60. non statim est in pte aequare gtd. sumamus. 20Z + 2Z =
  61. et si sumamus:
  62. 203+217
  63. R+ 12
  64. =9
  65. ac si 20Z + 21Z +12. 21Z esset aequandus quadrato, quod aeque
  66. c3
  67. + 13. 202
  68. difficile est ac Xha X + X) et nihil inde
  69. lucrat sumus
  70. idem est si in x = 3IX +32X pro X poneremus 1: Z. fieret sane
  71. 20 + 31
  72. +32ZZ ubi 30+31Z + 312 aequari debet quadrato.
  73. Quodidem est ac si dicamus 30Z+ 31Z2+ 3223 debere oqumi yto
  74. ustio
  75. termineat
  76. tollere possumus. Sed s quia pulla hinc rascitur de pressio ideo
  77. si altimum provenientis ad huc semel tollere, velimus. one
  78. peceunt tot fecmini quot ante
  79. Sed sed si velimus uliam summ
  80. euriam tollere, id sime fractions none possumus fit enam ul y -. 40i
  81. fit O = +PPxX + 2p49X + 9
  82. eg

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 17r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0033?run=73