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Leibniz-Handschriften zur Mathematik LH 35, 5, 3, fol. 10v

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: 0.81.

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. 9r); this page is its left half.

The machine reads it as

  1. ut cartesi literas relineamus esto AG = B AF= FE = c FC = c+ Z. A(M) =y A
  2. Ponatur jam C. in (C), ent C( = c + 27+ Z + C + 2cy +y. FP= erytM
  3. sam FPCCM = P +
  4. CF
  5. CG2
  6. 2X
  7. ce
  8. Ergo FDCMM-AGP CM jam FP + GP = a.
  9. Ct
  10. CG
  11. Ilem CF = FM + CM et CG = EM + a - 2a TM + FM
  12. Ergo fuic Fp
  13. CF2
  14. =
  15. Gua
  16. E CG
  17. FP2+
  18. .Ergo
  19. FM + CM
  20. a2
  21. FM + CM
  22. PN
  23. a + 2a FM + FM + CM
  24. Ergo a - 2aFP + = a + 2a FM + , iderque
  25. F p2
  26. v
  27. F et ponendo a L 2FP = Y, fiet - FP = Y =a, et FP = a - Y es Fp~ a - 2 ap+ V
  28. eodem modo a + 2FM = 5. fiet FM = 5- a et FM = 5- 25a + a
  29. ideoque invertendo superiorem rationem habetimus.
  30. a
  31. = 5 - 25a + a + YCM, inde L 7a + Y = 5 - 2a + 4 + CM
  32. a - 2ar + r2
  33. Ar
  34. AS
  35. sive a + Y - 5 = 8 - C = 0. lude fie: melius
  36. esse non imponere nomina lineis, et calculum per lineas potius per quam per literas
  37. trusigere, donec ad extremum appareat quae commodius elidantur. Jam
  38. ponamus CM = y. fiet: a5 + r5 - 5Y - a Y - y V = 0. autes capendentem Y
  39. sumla ergo recta Y velut ognita, su niveotigemus Jam si lineam FP velut
  40. cognitam sumamus, et pro arbitrio assumtum, a proinde punctum Y, eadem
  41. erit aequatio cujus duae radices, vel L set y dupliciter assumi possunt.
  42. eadem proveniente aequatione, modo eadem maneat Y, et a. Sed si ex
  43. in nostro casu eas radices cogitandum est esse aequales et (C.M =
  44. ipsi ((C)) (M). Ac quaerenda proinde aequatio ejusdem forma, in
  45. qua tres sint indeterminatae, dua sint incognitae, ciuarum quaelibet
  46. significationum aequalium: cm ad simplicem methdum tangentium.
  47. aequatio duas habens radices, aequales non nisi unius sit incognitae.
  48. forma rostrae est -r Y - r5. + r5
  49. +a
  50. =aer
  51. y - e, D = Y - 2Cy + e
  52. C
  53. s- 9 5 - 5ps 5 29545 , fict equatio y
  54. vel ducamus in se invicem y - e s- 4 fiet 15 - yf - es + ef. Sed deest
  55. im
  56. arbitraria quae in hoc productum multipli–
  57. V et 5. deo quaeratur quantitas
  58. cata fin facat.. S 5. iaque tot quoou vitatium
  59. deprua i
  60. literarum diversarum, ut si superiori aequationi data compareturi aequalio obtineatur
  61. Utite focet Bartholmiana de constitutuns et dimitibus aequationum ad eas usu prodacta
  62. quae sint anaruoq et plariut Incognitaerum qut tat ali esitea forno cnhetrentur

Cite

Leibniz-Handschriften zur Mathematik LH 35, 5, 3, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068021:0020?run=73