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

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. tres Numeri tales, ut duorum quorum libet summa, et duorum quorum libet differentia
  2. sint quadrati. sint numeri
  3. 10 nx yy + IUxy + itOXX + 102yy
  4. A A+B = ex I AD A = gu B I 200 X + 202y4 2 UXy + 22o XX + 202 yy
  5. Sint nundri A, B
  6. BFC =L
  7. A BaC = nu
  8. +100Ct 1t0X + 102y +II2 Xy + WOXK + 1027y ~.
  9. 1E00 210
  10. 40 Xx 202 1
  11. A= led 4 10 + 11X + 1XX + 13X ∞1 + 15 X + 16 X t erc
  12. 3=
  13. 20 + 21 X + a2XX +23X 124X 125 x 126 X + et
  14. 30 x31X + 32XX F 33X + yX +35 X 136 X + et
  15. ponendo A majorem, B mediam) Cminorem
  16. ponamus X esse 2
  17. U X
  18. ad qontata
  19. 40 + 4IX + 42 XX + 43X X 145 X 146 XE p et pp = 40 + 2. 40. _IX + 2. 40
  20. 50 + 51 X
  21. 60 + 61X
  22. 70+71X
  23. 80 + 8l X
  24. qu+91X
  25. GG = 10+2. 10. 51 X + .-
  26. HH = 60+ 2.60.614 +..
  27. EL = 70∞ 2.70. 71X+.
  28. Mm =H, 2. 40. 81XF..
  29. NN = 9d +2. qu. 91 X +..
  30. 12p2 = 2. 40. 42+ 1. 41. 41. 13423 = 2. 40.41 +2. 41.42 14129 = 7. 10. 13t2. 11. 43+ 1. F2. 12
  31. Htinc ob s aequationes AB A+B = YF_ AYBagu BrC-ht, fiet
  32. s
  33. 10, 10+20 = 4040 00, 11 +21 = 2. 40. 41
  34. vel compendio 18, 10+ 20 = Bo 11t 2 = id1 12+ 22 = 14C 13+ 23 = 13 14+24 - 13+ C4
  35. 130 =40. 131 = 1. 70. H
  36. 4
  37. 132 L 2. 40. 424
  38. 10+30 = 140
  39. 140 50. 50. 14 - 2501) 4 +30, 2, (50
  40. (4d = 2. 5c. st + 1. 51 51 10 -20 = 230
  41. et il porro
  42. 10-30 2 240
  43. 11+3I = 141 (2+32 = 192
  44. 21131 = 151
  45. 19- 2 =271
  46. H 31 = 24
  47. 21-31= 251
  48. 22132 = 152
  49. 12122 = 2)2
  50. 12 32 = 292
  51. 22. 32 2351
  52. 13133 =143 141st = H4 = 4
  53. 23133 = 153
  54. B23 = 273
  55. 13 33 =243
  56. 24134 = 154
  57. 14 24 = 234
  58. 14 34 = 244
  59. 2333=253. 2434-254
  60. FF
  61. 20-30 = 250
  62. ita tollendo ope 6 aequationum literas 10, 2000, vel 11, 21,31; vel 12, 22, 32. vel 13, 23, 13 vel 14,4, 34, et
  63. Habebimus pet qualibet aequatione tres aequationes, quobus mantonatu in quibus solae erunt 40, at, ek ; c. A, etc bobiera
  64. latione
  65. Aliter sollantur prius ete A, B, C, et supererunt tres aequationes, ram
  66. A + B + A- B = 2A = 2A - f5+l = 49+nm 2B = hh + nn (f - II 2C = g9 -mm = hh - un
  67. lssitrum fil nm= I1+ nn
  68. Rursus ex aequ
  69. sibatum fit lin ZU =94 (5)
  70. A sit h - n = A 9- m, B: 9 Et Aet g+m( q - m = h +. H, (g - m p: 9 -
  71. fit ff -g9 = mm -l, se sit m -1= f-g, Br: 5. Unde ex pracedente fiet
  72. Cum ope aequ. 4 et 5
  73. f+9 (f -g = m+ l, f- g, r. 5. Restat E aeq. 2.
  74. possimus habere valores ipsarum 4 et m, quae non exstant in aeeq. 2. supererugt
  75. Ex 4 et5 fiet , m hq nq Epogus + est i m= pq op Dpha + nq, :p
  76. aequs est M Ex aeq. 4 est 9 = hq Lnq + mp, : p. Ex 5est g = lip + p mq..
  77. quos duos valores aequando fit h99 - ngu tmpus = app + Rpp = mpg, seu M = h(p. 99) An (Bp+99): epq
  78. valor ipsius mD substituatur in aq. 8, fiet g = (2f94-(ngq + lipp (tiquen pp + nqq: 2p4 vel valor ipsius inque substi-
  79. tuatur inag. g. fiet g= (2) pp + Em pp C hpD + hqu ApP ngq: 2pq qui duo valores ipsius u conse nttunt
  80. eadem modo quaerantur m et g ex agq. 6 et 7, per f et l
  81. Y et 5. Ex duobus valorbus ipsius g habetims et ipsius m, poterimus tollere h, et _, et L per S et l, quos
  82. et fit g = h (pp +99) + n Epp - 44),: 2pq
  83. valores substituendo in aeq. 2, habebimas ff. H, oper P, 9, Y, s, ubi id agitur, ut valoem aliquem simplicem obtineamus
  84. itaque hic solutio non usque adeo in potestate est
  85. Brevius videntur rem conficere hae tres aequationes gg-hh+l min-llann ff - hh+ min
  86. seu ubi g semet et u semet h, l, m, bis. hh = gg- H nn mm- II nn sa hh= in f- mm
  87. Hinc ex aeq. 1 et 4 fit 9-l, p: q gH. Ex 3 et 5 sit f- m, r: 5 = f+m Ex 2 ut 6 sit m- 1, +. v = m + l
  88. h= X g B, 9- l, p: 9. = f = m, Y:5 R = m m - l, t: v
  89. Ex ag. 7 datur g: l, ex aeq. 8 datur fem, ex. aeq. 9 datur m: l
  90. Ex eq . (q. 5 explicatis m per f, et 1 percg per g, datur 8 f g: f. sed ita g: f datur bis; adeoque
  91. +: V, quae an tractabilis dubito. videanns
  92. () p+q:p-q. Ex 8 fit f: m + 5, :, r-5 Ex c9n sit m: 1 = t1V,: t. v
  93. Ergo res redit ad ag9. 5, 7, 8, 9
  94. Ex 5 per 10 a u, fit g - p. 99, p = f - 5 7 seu (91+d(A ( tgrq (F Wy + fist snsre
  95. tandem prodit aequatio, in qua p: 4
  96. fit 20
  97. 4
  98. r+S
  99. ptq
  100. 13
  101. peu g.5
  102. sed g. f adhuc semel inveniri potest,
  103. ergo fil. 9= ete
  104. 124
  105. 25
  106. tiv ris
  107. 4
  108. Y, p+4y: B, rS
  109. tm e m =
  110. =
  111. Y+5, 5
  112. = X, 14. Et firt t- v, r- 5 Y quae aequatib est solubilis
  113. 1
  114. P
  115. r15
  116. p- 4. t +V
  117. mo puto ese errre
  118. calcuili
  119. si nullus
  120. rationaliter
  121. Hic sola litra e ab adest semet
  122. A= H e -B = gg - C
  123. B = C + A gg = hh = c
  124. sit 2C = gg -s +hk
  125. et dt
  126. pet 55=
  127. pono etiam 40, 4, 42, ek; Goyst, 52, et, 60,61, 62 et
  128. 70,11172, etc. 30,S, etc, 9019192, eM esse
  129. pa
  130. 72. 41. 42 51. γ1. 43,.
  131. est
  132. GG
  133. est eror in calculo pulctro
  134. habetur quaesitum
  135. verte

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 11v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0022?run=73