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Leibniz-Handschriften zur Mathematik LH 35, 1, 11, fol. 20r

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: 0.88.

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. 17v); this page is its right half.

The machine reads it as

  1. a
  2. Hoc per algebram ita quaeremus. Ex
  3. puncto C quaesito demissa intelligatur
  4. perpendicularis CF (aequalis ipsi DB) occurrens
  5. basi AB si opus productae in F. similiter ex
  6. ex puncto ali ex aliquo baseos extremo
  7. A in oppositum latus BC (si opus
  8. productum) ducatur perpendicularis AG.
  9. itemque ex B in AC perpendicularis PH
  10. AB sit
  11. patet data
  12. sint A CF seu BB esse longitudine
  13. b +
  14. rectas AB. CF. et quia angulus
  15. ACB vel ACG. datus est, datam etiam
  16. esse rationem rectarum A cA. C CA. CG
  17. inter se quae sint ut esdatae
  18. Vou AB CFdet DB CB CA BG. CG AG
  19. ipsas
  20. vocen b
  21. d
  22. erit V aequ. bd
  23. n n X
  24. +7
  25. b d aqu. b ( b aequ. 1 = 21
  26. (3
  27. Ergo per aequ. 3 et 4. erit X= 7 aequ b- Hi
  28. adeoque per A et 5 erit = X + Z aequo l n
  29. Ergo per 2 et6 erit (7)
  30. Ergo CF2X aqua dN + m
  31. (8)
  32. m
  33. et + 1Z aqu. bn - n
  34. jam ob Triangula similia BAG BCF.
  35. erit Bs ad AB, ut BC ad CF
  36. b erit
  37. jam ob Triangula similia ABG. CBF.
  38. seu ero
  39. erit AB ad BG ut CB ad BF
  40. 1b1 X m md
  41. (od. bsmde E. at supra peri
  42. fiet. X aequ.
  43. (10)
  44. erat X aqu.
  45. in a+
  46. M
  47. b- n + m 1
  48. T2m
  49. Ergo aequando vatores exus et 10.
  50. MM
  51. fiet: 4b m - 4 daequ. b
  52. quos duos vatores antrquam aequemafliciter
  53. Ers Ergo aequando hos duos vulores destruitur
  54. incognita m in nominutore et fit
  55. (11)
  56. + 2b. fre- d aequ. b - n + m
  57. Rursus quia CA AG. G CA CG
  58. habente inter se rationem datam ut 9 adY.
  59. erit aqunr aequ. Z9. seu Z aequar
  60. quem valorem sulstittrtu, aequa m
  61. jam ex aequ. 8 est Z aqu
  62. +
  63. 2m
  64. fiet quem valorem aequando valori ex aequ. 12 fiet
  65. fiet: b aequ n + m l eF MM
  66. et ex n fier s Huic aequationi aodatur
  67. ab . tequ n + m ca aequ i
  68. (15)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 1, 11, fol. 20r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067970:0039?run=39