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Leibniz-Handschriften zur Mathematik LH 35, 3 A 30, fol. 4r

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: 0.76.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. Invenire tres numeros ita ut duorum quorumaibet summa, et diffe
  2. rentia sit quadratus.
  3. 2
  4. (4
  5. (5)
  6. 1
  7. sumeri a. b. c. Conditiones a+ b ( a - b p m a +Cpu a-c F pr b1c. 1. 5
  8. a(tB) +a CB) F) l’ + M Ergo a FI lL m. a( d + aCD ,, n + p, Erx aF n+ P. Quos duos ipsius
  9. 1
  10. a valores aequando erit 1 + m p, n +p. Eodem modo b +c + b - C B q +Y. Ergo bps e r
  11. a- b + b +c p7 m + st ergo a +c m +q. et idem aequ. n. per 3. Ergo n Fi m + g.
  12. (14
  13. a+c + b - C ( n +Y. Ergo a +b, n +X. Ergo per 1. ae erit P f + 1
  14. si in aequ. 9. pro
  15. 1 substituas ejus valorem aequ. 14 fiet (∞+1 + m ( + p. seu pm +r. Utamur
  16. ergo his tribus aequationibus 12. 19. 15. Quippe simplicissimis
  17. Et primum in aqu. 14. V_ n + N.
  18. faciumus (F r+ e. fiet: C (Varre + e p n LB seu rei n -e et 10) n 4C Eodem a mod
  19. 2c
  20. resolvamus aequationem s ponendo Gp n. f fiet (D) A n AX- 2nf 4 p. seu nfi m+ f. et m-flG
  21. se d utile erit facere frhe. et mti hgc: erit n, h. g + tc
  22. rhe
  23. C2)
  24. vilche the. ex
  25. es vitix-4e. Nunc
  26. seu r
  27. ergo solam quae restat aequabionem , 5 absolvamus explicando n et r in ipsa habebimus:
  28. p lge + a v he - 8vhe 4 16e
  29. 4
  30. 2
  31. scribatur: 6 P p, 649 si + V ht - 8VH
  32. =XV s
  33. + 4 X
  34. 110
  35. seu 64P 5 64tig + v+ h2 - 8Vh + 16.
  36. + A16
  37. + XVH - 4X quae aequatio dissolvatur in duas:
  38. 64 P1 8. es 6 8pG Yt - 4 + x
  39. 59125 XV - XVCX, 9X -∞, 10. sive
  40. nat
  41. fiet 64gco X - Vc X + 4 - x f16 s? scribatur ruisus: siet inde no
  42. 648 co X - 4G x 4 - GX YCo X + 4 + 4GX G
  43. 35
  44. 645c6 48 X,70 seu X p64918- 48 3
  45. 6
  46. epe
  47. (32t onis
  48. Vel et aliter 6co X - Y Co X + VX + 4 - x - 4 X. 7. aequivalet aequationi 31
  49. seu X645co +
  50. seu 16
  51. 144
  52. et
  53. fiet: 649 c5 + P + 6. 645co 4 + 4 p 16v c0
  54. (36)
  55. vog
  56. Quos duos valores inter aequando
  57. Ponamus vsesse cognitam
  58. quantitatem, q. scilicet pro arbitrio sumta, et faciamus geo 1 γ:sid: eo
  59. tut turbamur quod _ g. +1 et fiet: 649c0 +1 +6491c0 4 +44 169 + 39 + 168
  60. 649 se 2 + 69 c0 4 p+ 40 f 1692 510 + 1610
  61. dividatur haec aequatio induas ap +64g 54 et 4 Ponatur 97
  62. +o g fiet: i 164 i, ac2A 16 64+ dco
  63. 9H.
  64. Y+ 649 44 + H B (g c -64 9 1o + 16o seu Bf 165t-149 +rc d 5-
  65. scribatur 1 +649c0 41 C A 4AY N + ansutu
  66. seu
  67. + or
  68. et fui:
  69. sit (3Co et fic
  70. Blo B∞ +649to +(3 + 4 at 1692 ct-g + .C coV
  71. ficit birg Eo β ( 1694-649+ 16. et B + ap opper se p
  72. 64q
  73. ergo int oveut non et
  74. 1+ 4bc0 et
  75. oaedis e et aB F o
  76. aliter Fo 169t - 6 g + 16 et 644 + AB. rusus absurdium
  77. 64g co + (3 +64 g c0 4 β + a (Co p 169t co + est g eo + 16co
  78. 2co 1 169 0+ 329 co + 16Co
  79. aco
  80. se 5+6 p ihos (329 + f. seu _ d( 1 49 - 4
  81. et β + 649c5 4B + aB C 5 co p. seu 1 +649 co 4 + 4βco - s βa p7 0.
  82. 249
  83. BF
  84. 1
  85. 77 e
  86. et rusus ext 4 fiet: veok p 2 + gX. seu
  87. (39
  88. divellatur in duaf. 649 co - vceX + X po. et 4 - - 1x 0
  89. 50)
  90. et et 649 k - X rH + 4X - X 57 0.
  91. Faciamus hp, cox. fiet. 64 siveltopt 10d
  92. Div ellatur in duas
  93. 61
  94. 110
  95. con
  96. C
  97. 19S 482co p, S 4 64 d g co . sit S5, Bco
  98. fret: 49 co- 4 pi cot - 1b f + 16 ( du + 64 nga
  99. 269+16
  100. ged - et rursus = 1691 4+ 16464 9 c6. seu (1 649 5
  101. 2 4c g o1 16
  102. 6 4 (nco4+ n co + 16
  103. 50Y 2+ 156
  104. 4e
  105. 256
  106. +
  107. 89r+90
  108. 5 -29 + 110
  109. 297-9-1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 30, fol. 4r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068243:0007?run=74