Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 116v

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: 0.86.

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. 117r); this page is its left half.

The machine reads it as

  1. Verum brevior haec operatio: sit data Xb + yC + X. yh
  2. quaesita
  3. X e + y f + X. 9
  4. Assumatur, aequatio: X L. + ym + X. yB aequ. 0. cujus diffecoentialis ent
  5. liqu
  6. Cujus differentialis erit: dl ax + dmdus + dn dx + (du) dy. aequ.0. seu fiet
  7. x (4 dm +(dn). aequetur hic valor valori aequationis, et multiplicatus
  8. B aequ
  9. dus
  10. a1 +) du
  11. terminis er fractionum per crucem, fiet:
  12. X b d 1, 4 yc dm (+ xe dm + yc dl + X b du tyc du + Xghant refentes sela
  13. X b +1) + Xedm + Xb du + Xe(dn) aequ. 0.
  14. yC dl. + yf du + yc dn + yf (dn)
  15. xgh dl + X ygam X. yh dn + X. yB (d 1)
  16. I qua aequatione sta omnes termini, qui componunt xb dl habent solam literam X
  17. non vero literam, y. Et omnes termini qui componunt yf dm habent solam
  18. literam y non vero literam X. Reliquae quantitates omnes aequationis 5
  19. componuntur ex terminis habentibus tam y quam X. rebi tamen ad huc
  20. Superest aliquid annotantum X. yn poni potest aequ. Xy X p + xy Y 9+ XG2n Cujus differentalisent, D egu a sospitdus hyt ry B1 Exry gi ex) dscx A rus dgudus ex Bstx tudidus
  21. annotandum aliquid Circa reliquas aequationis 5quantitates
  22. Ergo d X. yn seu dn d x + (da)dus erit aequ. y xp dx F X xpdy + y y gdx + Xypot, tyXy dindr +x. y
  23. 60
  24. seu du aqu y xp + yy9. et (d n) aequ. X x p + Xyq
  25. et similiter potest X. y in poni aequ. X XIp + Xyy2q + X9 X. y3n
  26. Xy
  27. et eodem modo X. 93n _ aqu xy X3P +Xy y39 + Xy F y 4n
  28. ubi tamen aliquando si aequatio 2 sit finita, finienda erit ipsorum Xyn
  29. progressio. Hinc fiet
  30. X. yn aequ Xy XP +xy99 +XXyy XEp + Xa ry y29 + X Xy X3p + Xy y39. 8C
  31. memorum
  32. Ubi tamen fieri potest; ut aliquo terminus, ut Xxgypq sit aequ. 0.
  33. c107
  34. Htuc jam d X. yn, seu dn dx + (dn) cu erit aequ.
  35. =aequ. Xy. dp dx + X. Xp dy +GXp ax + Xy. d9 dy + X. y9 dy F y. y9 dx
  36. g
  37. Xrgy dip dx + pd + EX VyxpB L Xxgu l Adus + Xxy iq
  38. 2Xky Lepas
  39. Xy dep dx +2X y. Xip y + 2X1 XEp dx Xy. d29dy + 2X y. yequy +2xy y2qdx
  40. XY d3p Ax +3Xy. X3pdy + 2X. XBpdx) Xy. d 39 dy +3X y. y39dy +3xJ. y79 dx
  41. et
  42. nunc quidem nondum necessaria est haec distinctior explicatio exta sed sufficit aeqat
  43. Xy agdy + X. y9 dy + y. 79 ax
  44. et fiet an aequ xy dp t yxp+ din
  45. aqu d xy Xy 2n
  46. et (d n) aequ X et fiet du aequ. y. yg + y. xp + xy dp + dEn
  47. d2n r 22)
  48. qui duo valores ex aequationibus 12 et 13. substitui debent inaequatione S
  49. foret aequ. I X. 923)
  50. (du) aequ. X. Xp + X. y9 + Xy dq + (d 2n)
  51. aequatio 6ta, et erit d X. yn es seu dn ax + (du) dus erit aequ: xio dBiry +ysodgiry + xaodgrry
  52. ) X y dp dx + X. X p dy + y. xpax + dEn ax + (d n) du
  53. ea
  54. Sed quoniam ex omnibus his terminis duo tantum excerpi possunt, X. XP aus et yyq
  55. ubi sola est linerax vel sola litera y, sublatis scilicet dy et dx. hinc nostro scopo
  56. C11)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 116v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0234?run=74