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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 90v

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: 0.76.

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. 91r); this page is its left half.

The machine reads it as

  1. sit dy + m 1. + nydus + pyy dx + rdx Z0. fiat
  2. (2d0) y = tv. unde habebimns ex aequ. 1 habebimue
  3. Btro) tdo + Oat V + n Et vav +ntdt vD + rdx L0
  4. +MaxF.
  5. a pet dx.
  6. multiplicetur aeq. 3 per h: t fiet
  7. (4to)
  8. hdo + ht: BV thnt vdo +hnat vo + r dx = 0
  9. +mhaz..
  10. +hPta
  11. 2
  12. Habet igitur aequatio A tres partes unam.. do +.. V, alteram
  13. .vdo +.. vo, teritr tertiam absolutam ab v. Ex his
  14. tertia est per se quadraturabilis; duae priores videndae summabiles
  15. per arbitrarias h et E, nempe ut d+. fiat summabilis
  16. oportet esse hat: t) + mhax = dh et fiet fat. t + max = sah.h
  17. Rursus ut. dv +. vv sit summabilis, fiet hndt+ hptax= dhnt
  18. seu (2n haC + 2pdx h+ = nt dh+ (nhdt) + ht du
  19. e
  20. nhuc ta d(t) C
  21. n (hat - tdh) = (dn - 2pdx) ht
  22. et fiet
  23. dc - dh = dn = 2p dx
  24. t
  25. seu A = at = 2
  26. h
  27. pax
  28. n
  29. du
  30. n
  31. apdx
  32. n
  33. an
  34. 2
  35. e
  36. sed supra dh- at = mdx. Ergo indx =
  37. Unde patet nem hac via non posse haberi absolate
  38. +
  39. sed posita hac relatione inter M, 1n, P.
  40. Videndum ergo an non res melius obtineatur ponendo
  41. 1 +v + V.
  42. incipdamus he absnitio, et servenus
  43. sit
  44. u Tamysdx tanu dy + pyydxt aat dx =0
  45. legem homogeneorum
  46. sit y= +(. a) + Y fiet dus = tav: a) + dt (p: a + dr. Hinc
  47. e
  48. fobs
  49. (Ato) aatdo taavdt +var+ mtraxtanrax
  50. + n +D+ (dv: a) + et dvBa) + ntv dy + ret do + ravdb, anrar) =0
  51. dx H(vD: aa) + 2p X V: a) + pdx YY + aadX
  52. multi plicari intelligatur haec aequatio perade inde insti-
  53. a
  54. adrunt
  55. tuantur aegnationes qua paulo ante.
  56. et pro dv +.. V, fiet aut patnr a
  57. aa +nr) hav + (aah(at: C) + Mhax + nalnnhar+2h a) cx) V
  58. et debet esse aadB + prdh + h dnr) = aa Hat t) + mtax + nhar + 2p rh: a) aX
  59. pro 2vdv +.. vo, siet (LnHh: a) + Ln: C)h) 2vdo +(h: a) dt + p: aa)hdx) vV
  60. nta atia) tr.C) relt itE)) = netri. as at F pst. au) tax
  61. ergo fiit (7 mo) Lut: ad a Isutd e: (+: a) +(r: C)) atan + ndt)
  62. l
  63. seu dh: h aa t aa(dt: F) + mdx + ndr + 2pr: 4) aX, : aatnr

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 90v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0180?run=74