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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 10r

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: 0.78.

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. 11v); this page is its right half.

The machine reads it as

  1. s
  2. Gl, X 6m, X +N aequandum quadrato sit X = N. = N 7, fiet
  3. 5et 7 e ( 7 7 = hh. et 51Z = h+ Z s, h- 2 il. pe Chinentotales
  4. Scilas ittg sicuplices estil se Z c Esto N = Ap h + IpI; 7 = Lh - 2 H, seet.
  5. h = 51 - Ip Vl, ip = pY (p + YI) . fiet 5V: 2 = pCp+ H) + Pst. sed hoc non licet
  6. si B sit isustans. Si vero sit p varians poterit fieri 5N = pt 2Yl, et 2=4: p
  7. se _ Fa ert X quadratus et Et similitor agendum esset adhuc bis, fieretque N = Y + 2sm, C et Z = 5: p
  8. et deniue N = t + 2In V et 7 = v:t. qui valores ut concilientur, s. et
  9. q: p =) s: Y et v: t = s: Y
  10. quibus quatuor aequationibus praestitis, haberetur
  11. desideratum
  12. Dividatur aeq. 2 por aqu. 1 fiet pp + 2pel = rY + 2rIm fiat p = Z pV = r+ 2Fm, et p+ 2fl,: WY
  13. (4
  14. et p+ 2Hl, qe trum, s et f + ia, v = Ya2m, 5
  15. fiet p = Y + 2sm, : N et (Y + 2Im : WV) + 2M s: W = Y seu Y + 2Ym + 2W H = WWY ac antsue
  16. similiter devidatur equ. 4 per aeq. 3, fiet +++ 2F in = rYY m, fiat t ∞ = r + 2tm at+ 2: = r
  17. r - 2im = 2W M, :, WoW -1
  18. fiet + = Y + Dm; 1 et + = r - 7 I, et r + 2Im = rv ip = 2 In et r = 2. (m + 2W Ma,: Y -1
  19. Ergo tandem (3Am + (2W0HL,:, wo - 1 = m H In = v V - 1. Maltipli
  20. Multiplicando. per crucemfiet, 1+1 - 1, Im + 2oA. D +1, bo - 1, im + 24 In
  21. fiat val gie sin +2 WV= Vm =2 WoHL Wontm t roC VM =+m) -2 In
  22. 2W Hl = seu 1 i 4- ut sM
  23. =2
  24. Y
  25. et (up = WWo) An + 244 it
  26. =2 p 1oW In + 2V In
  27. sen ( +10, P W0) Im +eo (H et - Wo In) + in- W0 1G -0
  28. si esset n = ofieret 44-, = coW -1, Im,:, im + 2Wo
  29. seu
  30. Wip = ow im im IL: 2tm +2Wi
  31. fieret
  32. 4: P
  33. si esset 10 = _ p. g et 48 et um + 2H,:, 21m + 2Wos
  34. fieret _sm l: ndm + cs = Y: ∞ et VGim 1GAt = 2Ysm + V 811
  35. a quatio Dividi colest siC in uas ut sit cs s 2 . Im et 29 sl = 24Y gL sint es 2 et 1 = + 1
  36. fiet W0 = + F2 4 -1 - o p Wo =
  37. sit WW -1 = pV- 1. fit Wio W _ g= WV, unde fac rerum
  38. 1 = - W et 2 m + 21 sl = 2m - 2W NR, sed ita fieret M = In quod non
  39. licet s fiat 102 y 1P - 1 = ( W0W = e tiet loco-H F + 8
  40. DV L (Ptoto = + 1) et
  41. W YH (W00 -1) - 1oWo + = EH
  42. 12 4 17etim + 1o H) = roco 2, Am+ Y tn si eset n-o fieret
  43. +211 1, im +w H ap V iin (Lm) + 2Y 2o H- cost = 2evotm () Im
  44. W (Ymt. W Am + pao MC Im) - 20 sl = 10ro Im + wwY su CmIn
  45. quod si sit n = l fint i (toto tm: sen+ W sL) sint 1 sed totm +r W
  46. im F WVIL
  47. si esset cotm + Hl san twol, safieret Htam = W0, seu 20 = F et 1
  48. et fieret fint coro n tw Hl= B= W0, Woim + st
  49. Wwl tim
  50. si Wm + M = W0 s + Im fiarat A(- Im = W, Hl - dm, et Ww = l et ( = su
  51. Yb + W Il
  52. et ft sed ila fieret et V t= = - 1. sad ita in aeq. ), cun contra s invi
  53. cemtolli debent f =1 et 10co - 1, ut fiat Im + Wil = sm, quo casu fie, et
  54. W = contra prius invettum sad per o multiplia D, (id est a V = 1, et W1 - 1)
  55. multiplandus est uterque numerator respective quivis per
  56. sede sa pa Ex his patit non habere exitur, nisi e et W0 sint constntes.
  57. nihilo aequalem, ut ounia evanescant
  58. Ergo etiam Y est constans. une et p et E sunt constantes Ergo ratio 5: est constans
  59. AC
  60. contra intentum Ergo non licet sacere s = ph + 2 psl at
  61. et similiter adhuc bis

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0019?run=74