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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 229v

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: 0.82.

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. 230r); this page is its left half.

The machine reads it as

  1. formandus est nonnbil, ut scilicet catulus jam factus possit fieri utilis faciendo qui resta. Quare de
  2. red- inchoemus:
  3. ) b e + ac 0. et de + a f 170. fier ac af seu (Acd - L fb, po.
  4. jam poncndo ab rige + gatr. fient aequationes duo: ge ati e ac 0. et de + afpo. Unde ex aquatione resubtanti
  5. parentresi inclusa fiet acd - fge - fah po. et pro e acd- fatr af. Unde (acd fatd + f ag po
  6. 1 In qua equatione resultante, ad usum calenli ordinarii potes am 9 quam d ponere pa. SedNam adhilitae
  7. sunt tantum ad grdum ultra promovendum, et si rursus ad explices nonas ad pletam nt aequationes
  8. duae (HII) ge tahe + a c 10. et le + ame + a f 0. Unde aequati prosime praecedensae
  9. explicata d, dabit cle + el eam + caem - afhle - aftram + fag po sed satius erit, credo
  10. ad hibere aequationem resultantem pene proximum, inqua fiet: ete
  11. ec- fge - fah. po.
  12. tertius ergo gradus reductus est ad secundum: habemus enim aequationes duas: CC2 tam e + a f p. et tcle + cam p0.
  13. aH aC - fg. - fat
  14. et fiet aequatio resultans tertii gradus. C l’ac - 2 clfgac +fg ac (- Clcamn (+ el fatim, + fgcamm = f9 fatim, -
  15. (F Ca mD) aD emfhla + f h la
  16. a
  17. a1
  18. a F
  19. 10. siuve c l’ a - 2cf9 in qua equatione
  20. adusum accuomnodanda poni sdeben g et lfja. ubi fit: a C - 2a lC + f’ac -f aetom, quae
  21. aequatio debet esse divisibilis
  22. supra
  23. +f am.
  24. famh.
  25. +fVt a
  26. Rectra nn succurit alia ratio, datus duabus aequationibus e + d’e + ab Bo. et e + fe + ac po.
  27. d ivenimus resultantem:
  28. Si ita ponamus:
  29. a b - 2abc + aec + d’ab +sac - d fab - dfac p0.
  30. (7) be + a 70. et c e + a 0. fiet (b = c 10.)
  31. sit ab 1 de + af. fer) de + afe + a p0. n et CC + a 10. fiet: de 2t + a ro explicando b - c,o.
  32. fier: expsiunt ressultantem praecedentem: de + af 10. sive ad e + a po. ergo (fC - C ad)
  33. a
  34. Explicando c siu jomendo ac ge + ah. fier (211) de +ase r a 0 et ge +ahe + a3 0.
  35. et in locum resultantus parredentis pro Cpoundo ge tah. fei: afge + faba g e 2gahe- aeti ad.
  36. et in locum resultandis primae pro b et c ponendo valores fiei: de + af pge a n. sive 1d C = ah po.
  37. sive +ad = ag e + a 10. qua juncta cum dE + afe + a fier: f ad - fag ad 2a dus + aeq
  38. =ph +ff
  39. C
  40. sive: dag fa - h+f - a d- 9, D ad 2 1 t L
  41. af
  42. +h2 - 2hf + f 2H
  43. quod si jem ponomus dag -h + f sive d e + a- h l + fl, func fier.
  44. ex illa aequatione igas. hls + fl. + aht - a f l, (ade ad fgah + gaf rh l- shl
  45. ponendo - h +f B dug a. sine f⊓ d l = gl + ha fiet. fa - a ad. sinc explicando f,
  46. et multiplicando omnia per V, siet:
  47. itaque si luae suit aequationes:
  48. A (d P - gl + hal - a ⊓ (d 1) sive gl ae = ha l + a p0:
  49. de +d1 C + a. qu. et ge rahe + a,o
  50. u aequatio in quae nulla extat e, erit: (g1- hal + a po. l si enuim redire oequaso prior tanteur
  51. Ponendo jum ad H me tan et H pe raq. habebimus ae quationes
  52. duas: (IV.)
  53. pre pro e pon
  54. me + an e + aln e + ao et pe x + aqe + ahe + a
  55. ilende fei ex resullante procedente pel taq hal at
  56. + lm..
  57. - lp..
  58. - alg.
  59. + ah. adeoque: pla3
  60. e + a.
  61. si in aequatione resultante praecedente o12 - hal +a go pro l ponas hatsa fret tae-raehf +sa +ha 1 sa + a po
  62. lende si ponas adpi me tan. et agp pe +ag. fiet:
  63. Unde pro e ponendo ejus valtiem: = a9e- ahe -
  64. dae g
  65. a2m ren.
  66. agl-hal ta
  67. nanc aeh 3h.f
  68. 9d2- 2d9 + 92
  69. dag
  70. fo janer a fe - a. fier: q’er ratim e + a
  71. et explicando resultantem praecedentem: a se + a n a- 2aehf. F m
  72. sive aren aepe + a n C +aq +h0 f p0.
  73. aetishas im.
  74. a
  75. aq
  76. as
  77. tie. hsid np.. =af
  78. amanetan um etan e peran a a m a
  79. qu
  80. aemp.. -2maq.
  81. . ranp. Aranaqu.
  82. p +2age. + aqu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 229v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0458?run=74