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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 128r

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: 0.81.

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. 129v); this page is its right half.

The machine reads it as

  1. Sit aequilio cubica data:
  2. + PY + aqY + ar 7
  3. b.. 2ac. + aed2
  4. + pV +aqV tary
  5. Multiplicanda per aliam cubicam ardinacio
  6. et exaltabitur ad quadrato lubicam:
  7. + b y + bp .n +baqu. + bar
  8. 4acu. +acpi. + acaqu.. + acaer Y
  9. tad.. +adp. +adaq. +a dar
  10. (+
  11. ubi primum calculi facilioris causa intererit fieri pF FI c.
  12. et aequatio ita stabit: y X aqy aer Y7 acqqγ + acaer y + a dar F
  13. ac... ad..
  14. +à daq.
  15. Jam excitetur aequatio cubica alia ex tribus aequationibus quadraticis sive planis.
  16. tam sive ex quadrato quadratica ex duabus planis excitata, et plana.
  17. jum quadrato quadratica ex duatus plunis exscitata, Y + E taf Y ag) rah
  18. ex duabus planis excitata intelligetur, si modo ponamus esse
  19. nei.
  20. 1g cg l
  21. atque ita quantitates
  22. = fl + egl - g’a
  23. + 4 a l + C - 4 af
  24. ex calculo Huddenii,
  25. pag. 495 eti
  26. e. f. 9. l. manebunt arbitrariae Compendis
  27. s0
  28. 2
  29. autem causa quantitate n utamum, donec ejus valorem explia substituere
  30. per
  31. necesse sit, et multiplicabimus quantitatem 7. per hanc planam
  32. t
  33. CV + am + en 1 0 Nempe
  34. 4 + e V + af V rag Y + ah n
  35. y M y. Fam 110
  36. y+ e y + af VY +aegV + ahY
  37. AM . . Haf. 1 ag + a hY
  38. nan +am un tamem namat. tamug. +amah
  39. 40
  40. 10
  41. Ubi ut appareat primum quid ex calculo faciliore oriatur, ponumus similiter.
  42. (11)
  43. etop et supraib. vel et fiet loco aequationis 10. hatebimus hanc:
  44. Y X1af V taeg y +ah y tamaque) + amh o.
  45. tam
  46. tamf
  47. quamaequationem comparemus cum aequatione b. ope arbitrariarum
  48. C. d. m. f. g. l. quae sunt numero 6. aequationes autem colla-
  49. titiae tantum 5. ipsas autem f. g. l. in novissimum locum differemus.
  50. ac primum ex collatis terminis tertiis, erit 4c
  51. (i f + im - g.
  52. 64)
  53. ex terminis quartis erit: d g - r. ex terminisquintis; f9 + mg - 9 at + nf. et
  54. erit m an = f9 + q () ah + q erit ergo CF at + f ex junctis 12. et 15
  55. 9-f.
  56. s
  57. sugceis denique terminis Restant collatitiae aequationes duae, per quas dr nih ex
  58. ultimis sive d gr- r
  59. 19)
  60. sive aur + fY, (+99 - rq 0) ahd ( 49), sive 5. 4, Y (21) H (7) 1- f, , -9a
  61. 9 f
  62. et ex 18, fiet: 9 - r, Y, q- f(23,
  63. (24
  64. an 44, q. f s h et ex 21
  65. s
  66. ag- ar
  67. ag -a
  68. 15, 4a exs.
  69. 128
  70. a bo X 1a. 4 519 soc C) Fs Hateu, ergo hos vluges peros istus h. ex mibus saciendae aequa.
  71. q
  72. ah, +94. f a, ger

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 128r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0255?run=74