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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 11r

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: 0.72.

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The machine reads it as

  1. res Numeritales ut summa duorum quorumtibet, et diffecenti
  2. datu
  3. Tres Numeri quaeruntur tales, ut summa et differentia dorum quorumlibet sit quadratus
  4. sint Numeri A, B, C, sit A+ B = Sf A+ C = gg B+C = hh A- B = l A- C = um B- C = nn
  5. Sit 2A = ff +l = gg+ mm 2B = fF - I = hitr. + An 2 = gg - mm = hh -nn
  6. a
  7. paetera A = ss -B = g9= C, sit B = C + - g9 = hh -C, fit 2C = hh + gg - s = gg - mm, fit f5 - hh tm
  8. qua valo substituto in valore ipsius 2A duplici, fit hb t gg = ht + IL et ex 2B omplicifit mm = U+ nn Ita
  9. siet hh = (1) = g9- U hh = (2) = ff - mn un = (3) = n -l Et has tres aequationes solvere
  10. sel paestare oportet; fiat h = 4 = g- l, p: 4. Ergo ex aequ. 1. fiet g- l sp: 49 = 5= gHl. Pursus sit l f m, r25
  11. Rursus sit h= 6 = f -m, r: 5, fiet et ex aeq. 2 fiet f - m r. S = fOm 2= f+m Et ex aq4. 16 fil guli pos- fan, 15
  12. +- l, p: 9 = 8 = f - m, r: s Tandem ex 4 sit fiat n =, M - l, . rest ex aeq. 3 fiet m -l, H. v = 10 = m +L
  13. Ex aeq. 5 fit 9pp = 1 = 994+ (44 seu g il = 11 = PP +44, ; pp- 44. E eodem modo ex r9. ) sit f: m = 12 = 1+ SB, :, rY S
  14. Et ex aeq. 10 fit m. l = + W, , L m: l = 13 = et FBH, : H = vV. jam in aeq. 8, explicemus L per g ope aq. 11
  15. et m per 5ope aeq. 12, et fet P g = p - 49g - f L, f - rra ss f, seu 3 = _ _ (r. 5), vr +Se 1Y + 1s e
  16. seu d = 14 = Y4. pet qu
  17. rrass.
  18. pP +94
  19. pp- 44
  20. Ep: 4), pp tB - pp +99) rrs
  21. Ergo fiet d =15 = PP +49 fL- WV, 1Y - 51 = r9. pp+ 4q seu tt. ∞V, rr - 55
  22. pa ertss
  23. ep - 9q H+WV rY+ AS
  24. p4 rr+ss
  25. pp -49 = h pus pp pq F bt 49 a bih + 1, 19. si + 4 quadrito
  26. pp - 99, H+ vi
  27. Rursus rr = ss = Htvo h es seu rr - U+ vo YA (4 + B+ 2 vV hh s.
  28. ee
  29. H- on e
  30. ec
  31. sine divulsionefiet.
  32. xp YY+
  33. LpP, tt+ vD
  34. Itvi
  35. H e
  36. H - yV, pq
  37. Y5 = 55
  38. A+ v Ettrr, aee
  39. +tth BA 1
  40. ++Vraxv, ree
  41. posset haec aequatio develli in duas r = 5
  42. be posterius to ob oq. 52
  43. sunt duo quadrati
  44. sati aequandi qto si b abesset multipligatio per Haun, et H v
  45. esset confecta se nam appia
  46. p
  47. Aaxrg aX y exxgus exsuponentia quadratum
  48. (99 pp lt + vv) = (H. vv, p9) (55 rY) : r5
  49. Hin P Y qu (4 - pB) qu Crem ss, qu qu s tlave
  50. aurss
  51. live
  52. qua
  53. epu
  54. 2r5 At+vo
  55. Ad a esser H- vv -
  56. es; 2re t, fint rY+
  57. Finganus fidt NS() H E s I- 00, (, Y(1) S - rd
  58. olatur Unitas atrobique
  59. = (16 = 25 r
  60. pd
  61. +F+ vF 2HDP, 4el,
  62. C
  63. et 1q= p (nec spo
  64. Debet esse quC 94 - pp, tF + Wv) + 4 ppgq. qu Hl. vr quadralus
  65. dut due aequantisto
  66. AppGI
  67. RG
  68. un
  69. c Jagamas
  70. dua Heve (a-
  71. fiat r4s = (B:))S, si si Lt. W, 1+5, Y 5, Y.
  72. al
  73. a
  74. BV, pa
  75. +Se
  76. sit r- 5g: p. 9 = ((3 (1) 9: 5 se 45 = 55 = x9 - 99. (3. 1))
  77. +2
  78. r+s s tlvo r+5 - 1V.C
  79. IY H- vV, rtC
  80. u (H. vo)
  81. i ppaqu, Uv p4
  82. = x
  83. seu (pg= 9q) (B: γ) +5s, : 5 = (H- vo)ps,:, (p LH + p VVL 9Ht + quo (EptD + poe
  84. seu (p - 9) q (3. ) + 5s, :s = (tt - vV) p5: 2pov + q(H+ vV). Fiat F
  85. Fiunt tandem - 99 (3:Y) +55, is = 0
  86. seu 5 = +9(B: ) et superest (Pa (33. y) = (1t - vr) p B (9B: V): 2p vo + g (H + b0)
  87. Finut tandem et s, in certie rationibus ad B
  88. seu 2pro (+ __ (9+G, + quV = + () (+t9 - vvg, sit P = 4 sed hoc nolim
  89. Aliter videtur procedi posse in ultima aequatione licita , fiat 2p∞V + quo -0
  90. fial p. 9 = (β3. V)5 Redeamus ad aeq. 16, fiat 9= (B. V), 1+5, et 5 = (: n) ptqu et fiet
  91. ergo fit S = R. () p + ( (1) (B. 1) Y + (A: p) (3.1) 5 Ego shabetur per p et Y
  92. et rq = V: a) ps siet r = βCp +4) = a5,: a = p5(: a
  93. Lt - vV, r2S =
  94. V. C
  95. pa: p
  96. HC+ve, f9
  97. et q etiam per P et
  98. seu V β pat β99 - a5 = Yp5 dibidatur haec aequatio in duas β9-)5 et β9 = a5
  99. si esset r+s = (B. a) r +5(p +9
  100. fit V = a, ita modo ) ponatur a, res per se procedit sine divulsione, si scilicet rq = pS
  101. nam aeqqualio βp9 + (399 pS(F aqS dividi petest per (4- a5, et prodit P + 9, sed hoc
  102. postemius puto non posse fieriato ergo prius et ex aq. 1b fit Et- vo rS B = 1
  103. a
  104. posito ergo X5 β9. a, sint r = (β3p+B9 - B9: a
  105. ser r= βP: a. et sa et siet A re,
  106. U+V
  107. A+ vV p-9
  108. ex -B4, seu H- vo ad egges suesiva so)
  109. +vn
  110. 0
  111. ins usue ko snna ol dat siml ob

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 11r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0021?run=73