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Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, 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: 0.72.

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. 10r); this page is its left half.

The machine reads it as

  1. Dres Numeros reperire, quorum summa quadratus, et summa quadratorum
  2. () Qua dratum L.
  3. (2) quad. II.
  4. (3) quad. 1IL
  5. (4) summa Ltorum: 2 - - -
  6. (5) summa Ctorum . . - -
  7. (6) Pone
  8. D Equlx 4. 5. 6.
  9. (9t sone
  10. (Fab X H
  11. N 2XC
  12. Quadrato. quadratus.
  13. x- xequla 2a sive 3
  14. yr 94
  15. =2
  16. X2 + 2 1C d
  17. ayr 94
  18. I ZG. senquadrato quadcatus a Z
  19. Cn (1) 5(+ 2Z erit CnS Z
  20. axhC
  21. BX p6
  22. Jam ZaC X
  23. +2X C
  24. ponendo aC B e
  25. destinitur ois X,
  26. utc restat niso X
  27. vel b. sumitex
  28. x - X 2. , a l.f 15 XZ + X 2. n 210
  29. sive destructis destruendis:
  30. +4 + 1.f lf 1Z
  31. M d
  32. IX
  33. at
  34. 0.
  35. L, et ZH If2X
  36. (t) S (4) X4 + 17 X + (X
  37. fk
  38. -----
  39. ..-
  40. dut _ b, 145 p.sd X1 s2 F 125 d (F 7d 125x
  41. +XxF......
  42. WX
  43. (H
  44. 0
  45. d
  46. d. +d n d
  47. Sed facilius se o supenoris paginae methoro exitus habebitur
  48. () 2abX - 2ac X + a b 2abc ac vt (X) 4IX9C+6X C+ Xe
  49. unde incipe a nund num. 6.
  50. sive ab ta bc + aC y X + 2 abX t ( a b a b +2 abC
  51. 2ac
  52. sii ab adc p Fy4 = pbXCL ab C
  53. + 2ac 1
  54. fiet ( X 28 2acX + 2X X raC H3
  55. = + se . id est quaerasuo nuncrus balie, ut si a dimidio quadiato anferas
  56. unidatem residuum sit numerus ipse,
  57. 55 at 4 l) =l Quod est absurdum, ergu talis numerus est in possi
  58. tilis, etiam crrationalis si semper est imaginarius. sit enim s l21
  59. o
  60. 1S
  61. sive Xb + a bc + a y = X + ab X + rabc
  62. + Zac
  63. sive ab + aC + Vt- x 2ab X abC
  64. 12ac.
  65. Pouc ab + aC (8) ap7d A n () a 33587 ato a PA
  66. erit b b ....... . . . ..... ............ . - a
  67. Et ay25 n () a B d 8A E F )aSN, + a 307
  68. +4X ep 2 ab X + 2aCX, + (1C0) 2a259 v v + _ B
  69. ca
  70. pd, 444
  71. et 2∞+ + (477 + 2Xd ( 2 145 d + d+ (2
  72. X +413 fa
  73. 2ab p
  74. seu dep b riive- Hac
  75. Ergo 2a b2
  76. 2
  77. orgo
  78. I y2 - X + 2aCX + (8) a βYS dn X (Y) a βdBEX (0) a614 X act
  79. 2
  80. 232549 aar. BR GX + a
  81. per Ne = BXCaC + 2aC + 2X eaC (24c +2 ac (6X C) = 4X C3 + e+
  82. 130
  83. aC C. ac 1. gc
  84. Y Sed matum in
  85. videamus an 2X e 2 - 8 Xeac + 2a + 2ea cY destrni possint ideo pone cp X + t, fiet:
  86. 2X eReas X 8 Xca b + 2a
  87. pone ar B X. fiet + LXC- BnX + XN NC f Ergo X Be. Unde posuendo C⊓) .
  88. En e fiet X p, 6 on).
  89. Et o rasedit LMXC +C, fiet XH Z. Ergo C
  90. 12- 6+ be ecnpo
  91. 365nB
  92. no
  93. Auc on n fC 11. lu 4e 145. 3 et 1t 5 e - hcet 1t. a 4 B E
  94. Ln 52+
  95. fea et + Quer t) spse. Sx te, 1 fict et c = 2579e- 35 ∞t e = set + r e 1qute svte
  96. 50
  97. Ex
  98. 75 videnmus an licent pontre 1 - 3579 - 35t + 9. V 770, si = 35l = 1 50 en 5 - 5l + L3 ⊓+
  99. (8) Num L.
  100. (9) ... II.
  101. (1..... 11I.
  102. (11) Summa Numerorum:
  103. 12) Ponatur
  104. 3) x
  105. (2 sonc
  106. () fier. per b. 7.
  107. (9) sione
  108. (2

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 11v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0022?run=74