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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 64v

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: 0.87.

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. 65r); this page is its left half.

The machine reads it as

  1. doctrina de Aipplicatis
  2. ad Loca plana
  3. rectam, et circulum:
  4. Atrae nempe exhibentur:
  5. aequationes generales.
  6. tam ad circulum
  7. is duorum si in Triangulo ABC. detur differentia lateris AC et AB, item
  8. lateris AC et BC; deturque praeterea angulus aliquis ut c. invenire
  9. Triangulum
  10. quia datur angulus dabitur et ratio rectarum BC. DC. Bd
  11. sit AB aequ. X. BC aequ. y. AC aequ. 3. Differentia inter
  12. AC et AB sit a. firt 2- x aequ.a diff. inter quam ad
  13. (3) Bd sit aequ.g-
  14. sit AD aequ. e. DC aequ. f. fier et fae9. 3.
  15. Ob rationes trium rectarum datas id est easdem cum rationibus rectarum
  16. datarum l. m. n. faciemus. y: g: f:: l m: n.
  17. e it tamen mint nn ego U. uti gg+fs aqu’yy
  18. faeqo ny
  19. denique quia AB Ft aequ AD F + B D 1. fiet _ Xx aequ. ec + gg.
  20. ob 3 er 8 est C aequ. Z - n y. Ergo per 9 et 10. Xx aequ7Z + nagus -2n q1) + mmgy
  21. Est autem Z aequ. a +X ex aequ. 1. f ex aequ. 11. et 12. fiet.
  22. (XX) aequ aa(t xx)t 2ax (t un y) + mmyy - 2nay,
  23. multiplicetur aequ. 15 per x+y. fiet: xx-yy ubx+by
  24. (16
  25. aequatio i3 multiplicetur per 2. eique addatur itus = -c7
  26. 0 aequ ina + 4 aX + 2yy - 2nay - 2 n Xy
  27. 16 fst 0 aequ. XX
  28. summa
  29. - b x - yy - by Xay +
  30. +ax
  31. 1c y
  32. XX +2aa - 3ax + yy - n a y - 2 n Xy
  33. 0 aqu
  34. Xago lvtDZt
  35. yugo PVt9Z+
  36. + bx.
  37. habita.
  38. + b y
  39. + c y
  40. +y ZZ tay1
  41. quae est ad circulum
  42. redam
  43. non obstante Xy.
  44. Itaque aequatione 19 ad circulum, et 15 ad rectam, intersectione
  45. rectae et circuli solutum erit problema
  46. a XX ayy Xy
  47. XA yy xg.
  48. Ex xy ...
  49. X..
  50. yy eraequis
  51. per 1 et 2. fiet: atx aequ. b4y seu X - v aequ. b. a
  52. aequatio (18)
  53. fres
  54. AC et BC sit b. fiet Z- y aequ. b.
  55. Ob analogiam 4 est g aequ mey
  56. per 2 fiet
  57. nic addatur
  58. a XX + byy + cxy + dX Fey +f aequ. 0.
  59. L xx + myy turu APX + 9y + Y aequ. 0.
  60. 1. . . . . . X .... X .... X .... X.
  61. X +s X + FXXF Y aequ. 0
  62. sit aequatio _Y + coco +Z 1pCo + 4 Y + 5C +6. aequ. 0. accommodam
  63. ergo sr = s aqu. B3 paequ - , Erx dSaqu. E + 3+. kaego pp + dd
  64. seu daequ = 1, + 3
  65. on quia datur r S. aqu ditmer faqu 1.
  66. cd 1 S 22 7.
  67. 1) vabetur ergo constuctio quaesita
  68. atbuc aeqe X
  69. Jaqu aec
  70. 14y)
  71. icc

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 64v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0128?run=74