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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 5v

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.

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. 4r); this page is its left half.

The machine reads it as

  1. Y+2Y - 423r-9
  2. r- 2r +g = q- V - p
  3. X44 5, c. 3
  4. eg. 7.
  5. fi et 6= 10. 15. 7 - 27.
  6. 1+ 10. H1. e ex
  7. aeq. 10 fit .. 6=
  8. 12. 131.7. 7, : 12. 13-1
  9. ee pp) - 4qrr = (eCpP) - 2 CpV + v. fiet ep- vvr. ggrr: 2V
  10. seu ep = v: 2 + ggrr: 2D sit Yv par, seu = 2d siet
  11. sit Gr av seu v- gr: 2. seu co qr s+ pe pares
  12. et 2 seu 4co = 4. fiet co=4: 4 sumamus ergo a = 4 fiet
  13. pan
  14. (0 =1. et v = 2 t et fiet ggrr: 2V = 44 , 6rr. 2. 2 = 4r2
  15. et fiet ep sit e =1 et fet p = 1 + Fr ar? Ergo cepp- ggrr
  16. 1+8r + 16r - _16Y = - 8r + 16Y cujus radix erta - 1
  17. Opp- rr et respp - ggrr
  18. et see- pp exprimenda in numeris.
  19. et 9q ee
  20. quod fiet si
  21. horum factores sint quadrati se aut quadrati ad idem
  22. latus applicati p+r = 42
  23. e+ p = 6. 7. C- p = 6. 7.
  24. ex + qu = 4. 5 ep - qr = 4. G
  25. etq q+e = 89. et q - e = 8f. 9. Ergo 9 = 8.9 +5. 9: 2
  26. si contenti simus aequatioibus
  27. usque ad 10
  28. et ex
  29. f
  30. et C = 8.9 - 829,: () et e = 6.7 +63752) et p = 6.7 = 6. 7,: (39)
  31. et p = 2. 3 + 2239: () et
  32. (1)
  33. n= 2. 3 - 22. 3: (2). Ergo fiet
  34. ob e fiet 8.9. 9- 8(.2 =
  35. 6. 7. 7+6(.2), et ob p fit 6. 5. p b:
  36. 2. 3. 7+2(2) e et ep fiet 627 1- 62 (4)
  37. 2
  38. fil 6. 7, 7- 6(. P2
  39. quos duos valores aequando et 9r = 8. 9, 2.3. 9+B. 7- 2, dui paulo ante eunt ex = 45. 57 4. )
  40. connescnt 7, et fit
  41. 10, 11 1. 12. 13.-1=
  42. et gr = 4. 5. 5-4: (2) ergo rursus habemus: 627. 7 - 6 (2)4. 5. 514
  43. 5
  44. et 8. 9. 2.3. 9+8. 3-2 = (2) 4. 5. 5.4 tantum ergo efficiendo
  45. (6
  46. si jam aequationem sunt aequationes 1, 2, 3,4. proaeq. 1. fit 8 = 10.6, et 9= H,7, fiet
  47. 12. 13, - 1. 1. 410.11
  48. divellamus in duas,
  49. 10. 72 =1 L0, et
  50. 12. 1 = 0. fa
  51. 10 V: 11
  52. et 12= ri
  53. pondtur cpu e
  54. ponatur 10 = o et
  55. 12-e2. fll
  56. 20
  57. Are
  58. 20. 11 = 12 13-1 =
  59. = 22. 1-. 1+20. 11
  60. sit 26. 11 +1 =
  61. 19. CB 52.k-
  62. et
  63. ex aeq. 1. 10. 11. 1B11.7 - 10.6 =7+6 rursus ex (2) (it 2 = 12. 6. et 5- 13.)
  64. ()
  65. 1928. 11 - 1, 127. 13 - 1 =
  66. se
  67. (2s
  68. 12
  69. fiet. 12. 13. 13.7 - 12.6 = 7 -6 ob aeq. 3 fit 4 = 14, 62, et 5= 15.2
  70. 12
  71. fiet. Ob aeq. 3 sit (es 4( 14 6os. 7 6 et 5 sit 15, 6. 7. 46,
  72. e
  73. et fec en aqa fiet: sit 4 14.6 et 5 = 15. p. siet
  74. -62 (2). 14. 15. 146+ 15. 72
  75. i
  76. postremo ob 0g. E. fili
  77. 14)
  78. 10. 6. 11. 7. 12. b. 13.7. 10.6+ 11. 7. 13.7-12.6=(2) 14, 62,. 15. . 15,-146
  79. Superest ergo tantum ut aequationes
  80. 13 14 in numeris grantur
  81. sed maxime aeq. 1 (3. ubi fiet _6
  82. 1 4157: 1H)14
  83. debet esse v 14. 15= v. 1+ (2)14. 15 sit 14 = 164 2b et 15- 22
  84. siet , 16. 17 16(2) 17. 22 - 16. 22 - 21, 17 = 21 (2)17. 22 - 21 28119
  85. ete
  86. = V + () 57. 16+(2) 16. (21 1 et + 22. 162+22(2) 16. 21427. 21
  87. 2 v+ 2) st 4. 21 posito jam B=
  88. fit e 22 () 24 sed non debet esse v= i difficultas autem
  89. et f fiat, 21. 22
  90. est priori similis, sem aeq. 15. ipsi aequationi 17. sit re eamus ergo
  91. ad aeq pp vel 16 In aeg. 16 faciamus V = 1+ 16. fiet
  92. (1-14. 15 1 1 (1) 16 4 (4) 1B (1 + (2) N. 15 + (2) 16+ 167, 1 + (2) 14. 15
  93. sit si sit 14. ise 17 14(g. 19.1 sit 1+ (4 15 17. 14. K
  94. fieteec cujus aequationis ope hibetur 15. si jam hunc valore
  95. p(2)42 15 = h. 15 Sit L Sit f1 1bq
  96. sit (2)16 + 16= 17. 15 tollitur tera 16 ex ag. 18. et simul via
  97. assumtum sit
  98. in ea dividi possunt per 15 et fit 14. 15= (2) 14. + + (2) 1 1. 17.
  99. e
  100. quae aequatio dat f15 sed solverta adhaque aeg. 19. id est devet
  101. 17. 15 + t aquadi quadralo = (4∞ 14. (2) IY. 18 + 1718,
  102. hec in duas, seu ponatur
  103. et fit 15 = (2). _ 18 + 17. 18 (2) 16 + 16 =d seu 16 = -2. sed hot non ot H
  104. v
  105. Dividatur aequati
  106. in Numeris
  107. ~22. 13 + 1, _ +20. 11

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 5v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0010?run=74