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Leibniz-Handschriften zur Mathematik LH 35, 3 B 9, fol. 2v

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: 0.83.

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. 1r); this page is its left half.

The machine reads it as

  1. Nimirum si centrao A descriptus arus circuli BDC,. Dataque sit subtenso arcus BDC
  2. -1 + X +
  3. -
  4. i-
  5. dentis ex circulo ortae, e (nempe Cycloeidis) quemadmodum orta ex Hyperbole, (Scilicet
  6. et 10
  7. Logarithigica) jam fece observaveram
  8. eo sit X. posita ABA1. erit DLH X
  9. Aaam
  10. SN, R et QLB APerit,
  11. arcus miter at ipsa EC NPB R5 est arcus C M DZM9
  12. sumtis cogo ec R pro numeris, y, secundum
  13. Posita ergo qR b QM it dixip X.
  14. 2C2 2DQ arcu H R
  15. debet et
  16. RS eMQ, positoque
  17. 5 toties contineri in RT, quotie
  18. unitas in numero V. ergo F appellando cd. et RS vocando Z. erit Z HL.
  19. adtoque 3H G:. ram XA(+ I + b. + r, + sendo ergo
  20. a
  21. QL p V B X. B SN
  22. eut aequatio explicans naturam cuvae cireiociis per ordinatas ad basin
  23. 2V5
  24. Posita ordinata
  25. 22) +b + 12-1 +
  26. 8+L-sP-i
  27. la alscissa RS,, Z. ordinata sN H v. radio, 1
  28. constatte quodam arculi eusque sasim subtensa, b.
  29. Si vero pro E0 sumamus non arcum, sed rectam quamlibuerit, vcognitam, vigs. 2. fiet
  30. Ciuva non cycloeides, sed ei proportionalis, cujus omnia puncta quot libuerit Geometrice potere
  31. inveniri, ersi non quod vis datum. Analytice tamen ope aequationis hujus transscendentis comnia
  32. habebuntur: et si faciumus et b7. fiei denique aequatio transscendentis figurae
  33. Cycloeidi proportionalis eu figurae angulerm
  34. 2
  35. Quemadmodui aequatio
  36. 1I
  37. alscissa
  38. + 2 posita matnatu RS
  39. et ab ordinata A
  40. b est aequatio Legarithmorum
  41. Et illud inprimis memorabile est Logarithmicam exegtipris ad refotvendas aequationes
  42. erae
  43. puras pertinere, Agutacegu
  44. partes duas
  45. Vicissimi ubi jam dantur cclculi circa bujusmodi figuras, quemadmodum dantur tangentes Cycloeidis
  46. et Logaritmice, hinc vicissim lux aliqua circa tructanius aequationes transcendentes exergat
  47. emicabit
  48. nempe BC, et ponendo arcum BD esse ad arcum BDC ut Unitas ad quendam
  49. numerum V. tunc posito radio 2. ebite et
  50. BC b. fe er BD X
  51. fier
  52. in
  53. Hinc jam illut praeclaram ducemus, analyticam scilicet enuntiationem. curvae transcen-
  54. 1Z vocando 2, fei et multiplimd a ao,
  55. V)
  56. aequatio curvae
  57. Angulorum, quemadmodum
  58. Co (1) b aequaetio est curva
  59. raltonum sive Logarithmicae
  60. quas nsoledt da radicis sectione in partes opus esti
  61. Angularem autem ad affectas prii gratus regerri, ubi resolutionis causa necesse est rancem secari in
  62. Hinc illudiam praeclarum ducimus omnes aequasionum radices irrationales, etiam quibus interveniant
  63. imaginariae, Geometrice explicari, per sectionem scilicet sive anguli sive rationis
  64. illuo jam quaerendum est, quanam ratione hujusmodi aequationes calculo tractabiles reddi possint

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 9, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068259:0004?run=74