Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 447r

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: 0.73.

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. 445v); this page is its right half.

The machine reads it as

  1. Mocnta generli omnium curoum exs ordinaturum expressioned, puta rationali, videtur hinc quique
  2. e
  3. aliquid duci posse ad methodu tamentia invertam sit y b X + g dX etc. AB1)a BPt7
  4. vdXe B. H du ero dy p 1b_t ECX + 3d X etc.
  5. Tot et 7 bex et. Ego XtB bx + Cx + d X eM (H y
  6. et
  7. ab +2CXA3d
  8. Quontuocum: in qua: BP sit a X abenus + ex hoc arto, diordat ut et Dy.
  9. set hac seu VH bX F CxV ou
  10. duidamus per 8. fer. Agy H eB at idem BPF a
  11. ergo d a X dyr, et Ic seu Y p a- x
  12. dividatur per a habebitur series infinita aqualis priorii in qua valires e quadrnt ducitur
  13. in valerem dus quadratum posito finiatur alicubi, hubebuntur ae et aquationis instituendae causa, ut
  14. ossit manere x. comparentur terumini terminis, ita litert b. c. d’et. invenientur quod
  15. didetud methodus Hundeni admac brevior sussane, ut fengentemtnvel perpendicularem feccile sine
  16. illa una incognitatantum ivemiendum, cum flusiana elinquat duas: sit:
  17. ri t A. BB X. F A pD. 4Bg A.
  18. B1 B+
  19. B. CH S V H x A. euit y ABG AC p, Aet 18 22
  20. 0
  21. Hticdralor ipsius y substituendus ubiue in aequatione data. determinand ad duas
  22. adices aequales ut inveniantur A. et D. Hoc in omnibus scaedit d coimis est
  23. qpulum infinitis t pu 9. 3B bx E CX + d er seubetur. A AX+ ex + dX erc
  24. Eoe et piba et de ex. se i sifeni sculi st ap stebuta isisius trotuafio
  25. Hinc generalis calculus pro invenienda diterentiaa
  26. a + b x + cx + d X et A+ A X
  27. e
  28. nava
  29. ande frei.
  30. quaerebatur
  31. rs
  32. f + 9X + hx F l X3n O
  33. 9. - h1.
  34. fiet
  35. 1-x
  36. 4b. 1 + cX 3+ d
  37. at
  38. 3.
  39. 2b1.
  40. 1g +2 t X + 9 CX
  41. e t e
  42. hiei Ar fei D decanint sit signumD et vellim. sit sine
  43. seu et habebimus: d se
  44. D Ox 1
  45. D p eAt 1 0
  46. Ounde patet quo modo sier
  47. regressum invenionda ex data:
  48. e
  49. 0
  50. a 1
  51. 0
  52. Ax
  53. B
  54. aut exacte, aut quando in rationaliter
  55. fieri non potest, per seriem infinitam appopiquantemd quantumliber
  56. aequationes notabiles: b a + b X + CX + d X3 erc. p determinata ad duas radices aequales dat.
  57. b + 2CX + 3dX etc. D Ducatuo hoc in illud fiet D D. Ajo SD n ides (D+D r Z
  58. a
  59. 2
  60. itaque a + b X + CX + d X3 er
  61. a + b x + Cx + dX3 cu 2
  62. per b 4 b + 2CX + 3dX vere S per a + bx + ex L dX3 etS
  63. prorsus ut RX in 1+ 2 +3 4 4 4 5 + 6 etc Y 2
  64. a+ bX+ CX + d∞
  65. Eodem modo suto tesse a + bX + Cx + dXB ek in b 4 3CX + 6 X2 + 10X 15
  66. Eadem res videtur
  67. imo ista diligentius excutienda. Est hoc determinatio ad tres adices aequales.
  68. redire debere, si b + 2CX 3d X etc. ruisus multiplicetur per 0. 1 2. 3. 4 etc. fiet 2C + 6dX + n etc.
  69. hocum dimidium sat numeros hiangulares: ic +3d X +6.. ecc. videndum quomodo ad possit conciliari
  70. cum directa pultiplicatione per 0. 1 3 6. qua initio multiplicari potest: a + bx + CX eri
  71. videndum et si radices non
  72. inminum video mltiplicando plura ex his satis mira duci possunt.
  73. sint aequales, sed differentiam hhabeant certam, quid fiat. Item nreciproce quallesnam sint illae
  74. aequationes, quae tuto possint ad quod determinentur se multiplicatae ordine per numeros quadratos,
  75. debeant imandere nihilo aequales. aliaque id genus quae quaeri possunt infinita
  76. b( + c() rdd- 1A( o
  77. B
  78. b- A
  79. 1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 447r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0889?run=74