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Leibniz-Handschriften zur Mathematik LH 35, 9, 2, fol. 66v

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: 0.79.

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. 67r); this page is its left half.

The machine reads it as

  1. sias 3M agatur normulis 3MY inax, ilentque tangens 3A 3M3 et
  2. vocetur AxeX et C. AY Y
  3. eX- qua Si vyc X Lx
  4. ec Y (M
  5. et 2a = M
  6. y et M Md, +
  7. ax axxyissem
  8. qui a MX= LXX = yy
  9. et Lgn
  10. r-:queiga AA dx Am Xdx = Zydy. seu dx: ily:: dX: X. Y: ysa
  11. x - 2 4= syu qu Ergo YR
  12. yiia a
  13. n MX iFee seu = a - 2 x jam trangula
  14. crga ax=ha. a fBM Y A, et 9A q F sunt similia, et datur ruto 3MY a YR
  15. Erro YAL q
  16. erus e, et eademomin
  17. interdum, veru per radion
  18. ati (per X et y, nunc efficiendum est ut detur per Y.seu
  19. radium F seu Y, et ei conjagata 33M, et ei conjinaata
  20. F3M seu g- r. seu ejus loco
  21. eCrseu
  22. et F3M = 4- p
  23. v.dea P
  24. de
  25. P g r - qr seu 2r -9 Est autam AF = q. e: 2. (_ p- F N
  26. Ergo FY = X - 4 - C. 2 Ergo X jF Ergo XX - q ex + 9 C: 4 +yy
  27. 2r -p = Er-2749
  28. 49- pp = 41 99-144
  29. similiter quia AC = g+C: 2. fier et OY = _ 4+e: 2 - X.
  30. +arg - 49 = 2sig. rpfret XX - 4+CX + g+c: 4
  31. r. Ope harum duarum
  32. aequationum tollatur X et y. et quidem quadrata a se in
  33. XX = 9+e X + gFC: 4 A yy = XX) + q. ex - q e: 4 ( yy) -(Vr-1+ Ep ppfinet 2a = q+e quod
  34. vicem subtrahendo fiet:
  35. Seu = 2Cx + 4gC = qp. se X+ P = M seu X: C- p :: 9.
  36. ut ep: e sit E = C - p. fint AY ad OE ut A (2 ad duplicatam OF. quod
  37. vel X. G. 2 ut
  38. est theorema per elegans. quia igitur X = q pc q. 2e q e-p
  39. et aq:re ep - aq2 4 eC c= 2Cp + pP = yy. seu fifit
  40. ag: 2) - aqp: 2C(- a9.4 + a9p: 207 agpp: 4eC = yy
  41. quia aq = bb. fiet bbl4 bb 14 1- pp: ce = yy. seu
  42. aq. 4 _
  43. e ess
  44. y: b.2 : ec - pp: C seu y = ec- pp b: 2C cujus calculi
  45. comprobationem habemus, nam in casu quo 3M incidit in E
  46. FR = eg- eV: 29
  47. Aeqeg.Ce
  48. seu quo y = b: 2 fit sec- pp = et seu p = 0 siu differen
  49. R et 9 et 3M A et CB et F0
  50. cia radiorum ex loco eductorum evanescit
  51. jam quaeramus 3esse R
  52. +9-agx sobrigrationem laterum triangali
  53. AFR ee:
  54. que quanqe
  55. quispe similis ipsi 4m2d4M
  56. Characteristico Et quia FY= XG ∞12 et YB = =a - = X. ideo fer.
  57. FR : C ate- q.2 19 8 X. seu a9+ Cg. 99. 29+ 4- aX
  58. jam aqu4qe fiet
  59. o 1qu qu
  60. jam x = L9. ergo ubi ut inveniamus rectam FQ cogitemus esse 3MY in FR = FQ in ZM R
  61. dige rax
  62. 6B= eetqqeaque ergo queramque 3M. R h sest a2 + aa: gX- aa. qu XX + E-
  63. seue
  64. cuta quod verum
  65. Hinc et FR = C9- CC:
  66. tee: 4 X. et in iau
  67. quo FR = C.2. fiet
  68. es eqq eeq + ex
  69. V, ax- a: XX + = aa - aa : gX + a a : 9q XX,
  70. rursus B. a: q XX + aa : qq XX = a0qXX. 1- a: q et 1 - 4: 9 = vC: c
  71. et fiet ruisus - a: q2 F 44 : 9q XX = aCC: Y XX. Ergo fiet
  72. Ec. qu. yy seu 3MR = aa F bb: ggeC- pp =
  73. Rursus 3M ui ACXy Y Cq. y. 29924- ee TRCCX al divis per b. 29 YHG p dat FQ = ,C. 49- e9+ =Cx: bqu.
  74. proba: nin FQ = ∞: 2 seu FC fit p ~ 0 et X = q. 2 st y = b: 2, et fiis subse tatis sit C: 2 = 1. 2 9y - C+ +e9. 64 59q grodieru
  75. verte
  76. quas (aq su 3M_ = C. 9y Saa: 4 + CC:99 1X Ex
  77. nonegteX eiq. seu 3M. R: Saa: 4 + e
  78. jam a - nasq X et a a. g = A. 7 a: g. q a = a eCX : 49
  79. ergo X q.2, a verum 2M R =
  80. rursu FR ~C: f9Gin
  81. in aqq
  82. G. 4. q p.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 9, 2, fol. 66v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068126:0132?run=73