Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 14r

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: 0.80.

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. 13v); this page is its right half.

The machine reads it as

  1. dderve d, rse = rdise +dr io
  2. ex 1per2F (31
  3. Erqo d, r= (rdo + drix -) rav + rvaras
  4. se
  5. d, S (= d, Bi2 - 2 v. 2- ) )dv
  6. Sit (sax s rso quaeritur Y, fiet hdx rd+ dr v. seu
  7. hVdx cardo +radr. sit deLdco: a fiet vhdx - Yfco + 2Ba dr
  8. seu _ 2hdxdco :do - rdco = dv, seu Ehdx: deo - =r_ dr: du
  9. 2V0
  10. prer sit hdx: deo = Z et - + = 8, et ex 9 fiet dr: deo Z + 8Y. jam
  11. alibi invenimus in casu aequationis. H. si sit logu sdco, fore r W ( Z. 10: a
  12. Ergo per 12 erit log. WV= - = co + β,: a seu dW: W = (- deo =) ( (per 7.) - = adv: V. Ergo
  13. ex aeg. B fiet _ r = W Shdx: W ia posito B dv: W0 2. : sav. B
  14. Ergo denque fiet ( shaxs W Shax.u Y, pusito sduvin a istr
  15. quod calulo comprobemus nempe differentiando aequ. 18, fiet hdx Iv ( hdx: u) + Thariu d W. i
  16. ergo W S debet esse quantitas constans qua seu d W0 ip =o Quod et verum esse
  17. sie patet d, W so = So dio + Wdv: 25 0. Ergo duv: W = - do: 2v. Res
  18. pro cuculo r aa - xx fiet h = 1 v = aa - xx H. ) Saa -XX dx = W S faa- XX. posito
  19. ergo succedit.
  20. esse du : W = - dv. 20 se nL lg. W = loge - : log. B. E. gu 1 =
  21. Vaa-X
  22. aequatio identica, nan fit Saa x dx = (ax tuaa. itaque et aequ ++
  23. seu generalis est inutilis, na fit d 1: Y. ergo aeque 8 fib identica
  24. Frustra sc. aequadem quadratoriam vvocavimus ad Fangentialem, et hanc rursus ad quadratoriam
  25. redit enim ut video quadratoria prior
  26. interim didicumus solvi posse squ vetida do dx =. hdx- d Y seu de = Z+ Gr
  27. si quia datur dr- _Ax aV Y cum reducatur ad di = Z + gY, posito Z et e dari ex
  28. potermus et fontie X vd. dr = Z + dor seu de vdr +
  29. dr = E + gY datur sit sed quid si rr = Z+ gY sit r = co
  30. fiet 1 dco = Z + 8 teo
  31. C d= Z +9 r= f9 + 8Z fit 8 -L(. r
  32. r= e 1. e sit + = Za 8 seu dip- Z9 p. seu de - Y2- g
  33. quae datur sit dY: 4 = deo fiet de = num. cdZ _ -8
  34. dy: dx = lamys + ngy, :, 9+rg + sgus etc sit yc . ficblus =
  35. Ergo fit- do: nodu = R + m love, s+ rve quu et adevque
  36. O8:))-
  37. v b
  38. v
  39. c
  40. dy: dx = t bx + b + cy + ete + fG = +gG., : l + mG+ etC+ p V= +95.
  41. Sit B y = i fit = dv = bB + C vC et + fV + g, v2 e t2
  42. ndx L0 tmp
  43. possumus, et pro X fucere yze, et sit ax = X ly + ydz et dx i du = Z + yd2 = f D: C)
  44. et du d = et 9 d- 0Z: O =y dz: dy seu dy: d3 = 0y 3 Z. ita necessario
  45. omnes termitai numtraloris habent
  46. Centemus Aliter sit y X = xy fiet du = Xdv + vax , :dx = C: D. fit dv:dx = 0 - dv, : DX. sed
  47. ita quaesim non asinetu ax
  48. ydy= 8tg +m dy- t+mytngu dus =myrngu: gtry. A quaeritur
  49. aequalio salisfaciens: a +bys + cgys + eh etc. et a sit constans vel unitas quod semper
  50. pt intelligi frat da et per reguum per regulum da 9= rbl dar + db. g = 1bm + Ahabetur b
  51. dbY + dc = ibn +2Cm et per regulam nostram habetur C. et de r + deq = 2 cn +3em habetur e
  52. et db et deg= de. Y = 3em seu de = 3en: Y quo inserto in praecedente, fit: der + 3 en g.Y =
  53. 2 enF 3em. seu rrde = 3CnY, :, 3YM - 3 R9 = e Unde et habetur de, quos vatores
  54. Citistituendo in aeq. der = 3en habebitur aequat in datis, quae linutat quae situm. Ergo
  55. restituamus da a, et sit du = l+ my,: gtrus. sit q. a + by + cyy +C G3 et =C
  56. a daq = 1bl. Ergo HH. g Y + db g 1bm + 2Cl. fit db = v t q g bmu seu da = b. 1l: 9
  57. et b. Ulriq + db. 9 = 1b m + 2cl. fit db = - b. ilt. 44 + b. 1m: 9 + c. al: 9. quo valore substitutet in aequave sequenti, fit

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 11, fol. 14r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068056:0027?run=73