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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 125v

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: 0.75.

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. 126r); this page is its left half.

The machine reads it as

  1. 5 1431+ 14 aequandqus quadrato, fiat quadratum a latere S_- l rl.
  2. ans qu set equatio: (5). (145 1F1, ( 25 1+ 25 r1 ( 19- 2B r +, 2 a
  3. Hiec aequatio Reformata: 12 l 5 p 2r l5. 2lr = 10
  4. fiats Unde erit 5 Cr - 2Vr. diide
  5. tone sp Y P fiet rpV Ir - 212 1217- 2r
  6. 121 ir sive
  7. x2 lr 2P
  8. F
  9. 12l - 2Y
  10. o Intelligatur p e n +2nt + 12 et Yr 4+ H, fiet:
  11. Ponatur tnt a ul ( tG
  12. fiet hp
  13. si r ur, est quadratus
  14. n + 2nt
  15. et altera aequant erit. quargul 14
  16. 2b quqimtntntqureha
  17. =2k
  18. +12 l n 4 + 2nlq + l9 4
  19. ----
  20. multiplicetur per 12C= 2rl, ∞. F hn + ahul +ht C29
  21. erit adhuc quadratus, id est + n + 2ut + 12, 2qV
  22. r= 2 lY, multiplicetur per
  23. I2l- 2rl, fiet:
  24. 12tr - 24Br- 27 l + 417
  25. sive 16lr - 24Br - Erl
  26. Multis aequetur quadrato
  27. a alr + fl
  28. fiet (Il 17
  29. 1(16 (r) - 24 137- 21
  30. ponamus ar + + f2l fit
  31. fC
  32. 12- 2r5 2Br +Y
  33. pone rasf Irt -2 1t fir WM
  34. snrato q
  35. 2 = 12 + 152
  36. na lp
  37. fit siqua
  38. tn artiul + h1 C +2
  39. v B q+h - 212
  40. R + 2nl +F, ∞- 12lh +1h
  41. +lk - 2 1
  42. Quaerenda jam esset talis explicatio ipsii
  43. h. vel n. vel g. vel duorum vel
  44. omnium ut numerus cognitus 214 vel
  45. ab uno vel ab utroque latere, si distributus utrinque est, ev anescere
  46. Certaque ars ac methodus ei rei, quippe omnium utilissimae praescribi deberet
  47. 12l+ 2qth.
  48. v 4u+ 29h +k 2
  49. 121 94h
  50. 28
  51. 4 25
  52. 46 46 240
  53. 4s 96
  54. 1200
  55. Cqtt
  56. Ergo V multiplicatm er ii ()h B Aet - a P videamu an h = H hl + 1e1 L
  57. H (121 21 sio) (121 -8
  58. sit quadratus at 113. non est quadratus, hoc ergo non succedit
  59. 8lar+ rX+24 Tota ars solvendi problema ejusmodi difficilia in eo consictu
  60. methodus aliqua sit repetitis quantum opus est explicationibus f
  61. venore si possibile est ad destructionem, coplicando itrum h, habebinus verbi H
  62. gralia
  63. (07. 29, 411) 8l- 29 g+1(5) confruntur 2st 7 d acd co
  64. 74
  65. possit, quo facto di deprimi poterunt dimensiones utrobique:
  66. BIrs + f l +24Brt2VloB B+ V fet 2t
  67. pone ve fBur. fiet.
  68. Se Y +fr +f
  69. Ergo l4
  70. h + idh
  71. n + ul + ( ∞ 42h, p, C qh - 213
  72. Sper Epohe vel sic n rul +
  73. 2r( + e, rH e
  74. 8l sa
  75. 2al
  76. (I 13 12L. 29. 2h
  77. reductis omnibus ablata fractione
  78. rI. Atr d 2t.
  79. 5r= = si
  80. n.
  81. iI-2r
  82. qp. Flp p 19
  83. l rt qu+2gul + q+ hn + rhul+h, lg+th. S
  84. 5+ co p - 2V cor
  85. 1212- erl
  86. 12l=2rl
  87. A 5
  88. t..
  89. 81-29
  90. g
  91. At fp. Y. fier
  92. ergo HEHgE I 2b
  93. sie r-nr+ i
  94. gth huc siperar
  95. 4ry q+2, fier

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 125v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0252?run=74