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LBr. 705 · Overbeck, fol. 86r

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.

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The machine reads it as

  1. Numerus C revendus est in duos quadratas xx+ jus fiat
  2. X = t: Z et g = v: Z, fiet cZZ =a + +loV fiat FL gere v
  3. Fiat L = M + p n = n +Y et fint. EZZ = lmm + Emp alpp +lun + dur+rr. quae divellatur
  4. in duas
  5. 1.
  6. c27= lnn + unr + hur et lrum + amp + lpp- hngtlir
  7. fiat lZ= n et ex hit nn = In + Ur+hr EP ~g. 2 fit Imm + lmp + lpp =- lrr+ hur
  8. fiat alim +p =BY et tn ilx et im+p = -Ir+ hn,: β. itaque pro literit
  9. n, EY habemus tres aequationes simplices 4,6,7 sit n P: n, et
  10. mip. r
  11. ne us ex A habeatur r: n, et fit ex aeq. 3. fist lZ2 U: M et ex aq. 4 fiet
  12. U = In + ur +hr, sit 2l+h = q et suit ex aq 4 siit 1cn +gr. Ret ergo est
  13. reducta ad aeqqu et (m+p = t fu
  14. (1
  15. siet F = 3r: l = - lrthn: B seu BBr= -Ilr + Ihp, seu H = ( 4) - BB U1,: th a
  16. =X per 10) lc - qr, : l. unde eB, aY + qY = c, seu rIhc: ββ- 11 + tg
  17. Rursu ex 8, st H = P: C, fiet CK 14,
  18. 10
  19. B: nn = r, B- U,: Ih, seu r= (h,: (2, (B- II
  20. Ergo ex 15et 16 fit. C, n, BB l = B, BB U+hq seu denique l. h - 17- C(M B, B
  21. seu C = 13, βB- l: (3 (h9) ~ ih +hh sit h AB+ L, _I) et C C, ). l - El + h
  22. LE+h, seu h - 1 = (CMM - (B) ((3 - 1)= 2V,: Be
  23. et CM - (3 B- l, γ: 1469
  24. Et siet, β(5+ = cM n βYY - CM lYY -(3 By + 147Y - 2(5), seu
  25. 3(0) (4yY - 2B - 16 C (n n)),: 15 + 13γY-cn VV
  26. Resumamus cZ3 = IEF + lnn + Elar + Lrr, quaedividatur in duas cZZ = lnn + dur + hur
  27. +hur hnt
  28. et IH = hur-ler fiat n = 1Z: n set _Z = II: er, fiet Cl2. n = 1: + Elr: nen thrl: p
  29. seu C = cl + 2Y +hr, n L (4. Et H = I + trrn = Btr fiet
  30. t = Br: L et prodibil lβ33 n( t er = Ist fint ren = lh: tBB + H = ( - len,: h
  31. 3at = 1B BB( + (5 - ( ne =ILC ( n sint Y - lh B +H = (4- lan(, : 2lt h
  32. _ Z, n, Y, F
  33. Z. h
  34. . Y
  35. +, n,
  36. = an fial lc 2Z-Hut nun +Er+h Unhar
  37. fiet n
  38. = Br. l
  39. IPerr: HI=nr-Ur se Ber = Ihn UY
  40. (cZ2 = lH + lnn + ilaer + ler +hap - hur dividatur in das cZ2= lnn + Eur + hur
  41. et IH + Err = hur seu IH = hur - Irr. sit en: l et ex aeq. 2 fiet
  42. CMmnn: l = lnutrlurthur seu cnn (3n + 2Br + Utr. Ex aq. 3 f
  43. fiat L= βr: l) et exaeq. 3 fiet (BBrr. H= har - ler seu eBY = Ihn - Ur sit n l:n
  44. sit. sed quia sit per aeq. 5 et 6 haberetur bis M: Y, ideo ut hoc impediamus fiat
  45. nmn= Ulf) seu ita habebimus A et Y ex aeqqe 5 et 6. sed tandem valor ipsius n
  46. parsus aequandus esit quadrato divisoper f. et fiet Ex 5pet fC = In+ 2lr + hr. seu
  47. = Y= fC - ln, i, Elt h = (ex 6) Ihn:, B H. sed video careri posse
  48. (10) 3 imo
  49. iptius n set restinatur pro f ponendo Mnn: U, et fiet, C pn = Bn:, El+h = Ihn:, BB- U
  50. et quanescet n, fietque cnn - 13:, il+ h Bh: BB- _U fiat trg B
  51. = (+ l, 9 et CM p - (3:, 219 +hg = (:, β- l quarum aequationum
  52. Resumatur Numerus datus C divellendus est in binos quadratos t: ZZ et rv. ZZ fiat v = n+Y
  53. ope pabebimus β et h
  54. et pro unitate assumatur l. fiet H cZZ IH + lnntlur + Cer seu czqe = Ut+ lin+ dircbralin, hur
  55. quae divellatur in aegg. duas 122 = (2) = lnn + Elnr +hur et IH + Irr - kurseu lH = 3 = hur-lrr
  56. fiat Z= 4F NN: L et ex aeq. 2. fiet cmmnn. HI = lnn + dur+hur seu cmnn s= ln + 2(r + Uhy
  57. Rursus fiat t = +6 = Br: L et exeq. 3 fiet lBBrr: H = hnr -lrr seu eBr = lhn - Ur seu r = 7 - lhH:, B +
  58. Sed ex aeq. 5 fit r= ce - (3:, 2β + Uh
  59. 2th + Bhh = c∞ BB + C M MII - BBB, 1e
  60. V, hh + 2h H = c BB + C pll = 13 (β seu (3, hh + ahita + BB + 2B(h HI)- ce t
  61. 13, qu (h+ 1 3) = (C M MBB +CC llcep + 2(3 (3(h+ ()
  62. =AlurL CZZ = CH + lnn - 2 (nr = lrr
  63. ondum apparet via
  64. H cZZ = lt + vo C c2) MM ccr
  65. CZ7 crr: IE) Et = = (B - crr: 13) H + vo
  66. desideratum
  67. r: WE
  68. C27 = H+ vx + 2to sit + = BZ:l fiet
  69. E+ . GB; q= v + .92.
  70. eet
  71. H+oV
  72. Crr- B sit quadratus seu C= Coco+ B,: rr, sed ita pettur
  73. N cZ3+ Ap: 1). ZV= qu (v.t p :1) Z)
  74. to
  75. A7 1D+ pZ
  76. at
  77. Aequatio

Cite

LBr. 705 · Overbeck, fol. 86r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0171?run=74