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Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 1v

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: 0.81.

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. 2r); this page is its left half.

The machine reads it as

  1. siet ex (x 4lv P 61V. (
  2. 24) intelligatur siteq r.
  3. t7V+ fV + f9
  4. olv- 29. 4 alq f argH pp Aula
  5. (21) Aeq. Reforn. 1g2..
  6. (26) Aequatio simplex H = lq. 2 j at + + 2l9 - 29 - 12
  7. Quasita: V H
  8. Daterminatio ad
  9. evitandos Nihilo-minores
  10. (27) Num L, ab 1 e
  11. ut vlgertaq
  12. 21 4 10l + 49
  13. 1 + + Cv + F eq +CD 1 0
  14. L Hoc obtentum
  15. 2o)tmll. ac H + f ev + fCq + e2B H 0
  16. intra num (32)
  17. tm I1 X atac ) ev - et - relB p0 ind. X (3364)
  18. 1) Ponatur
  19. 11 ++N
  20. erit qp
  21. poreq erit fictque ab e l + Cq
  22. Bnatur G HD erit ab pro. per () sumt ,
  23. . Fiat P p 2. erit X abac p 0 per ()
  24. etit X ab ac por per (2y)
  25. si qua sia prp et X ab ac p
  26. (2) si 20p4 fiet ac pe per (1)
  27. Har sol, erita + atque 29 - 1 pi Q, sive
  28. multiplicundo per +
  29. C150-
  30. 2t4 (10 21p aetq (49)
  31. solvetur, perinde ac si ita sconceptum esset:
  32. Tres invenire quadatos, quorum summa
  33. quadnatus IHa i summa sit quadrabus
  34. et summa quadra quadratorum sit
  35. quadratus, et summa quadrato-quadra-
  36. ab
  37. ac H = 5 - 1-
  38. - ab - ac p - 1 +3
  39. debebat esse X - ab- ac p, tZ
  40. ponamus 413. eri 1.
  41. fier YH 16 - 18 -1.
  42. Ut ergo tres numeri quaesiti frant affirmatio
  43. ponantur aepuri quadratis, et problema
  44. ab (I. 1 f ) + 3( (1)
  45. ac ⊓ 26 - 3 76 -12
  46. X - ab - ac p 169 f1 - 26
  47. sive in integrs tres pumeri erunt:
  48. 64. 56)
  49. 1 - 12+3+13
  50. A13 -3 + 13 HI
  51. 169 - a (+ 10 3)- 12, ((1) (1
  52. APne ert 1. 1++ 14n. FB - 41
  53. (1), noque B e + + + + lq N C)() y+ BL
  54. (3) Ego- bil 4 atev +4 biq. 7751 β. sve epatetovos
  55. fiet:-rh el 4 2hB in rk+ hiC arh b
  56. ive appellando l+ 2V X, fiet rh hh n +rhianti
  57. et HI. aequetur Ato
  58. fiet: hen-htr
  59. Multiplicando omnes per i6 ut in integnis
  60. qui satis faciumd proposito. Nam eorum summa b25
  61. quadratus c imd quadratoqua
  62. summa quatrapn
  63. (Y) 167281. à 409
  64. 23104 X
  65. 194481. et Geadratos
  66. Qucuratus a latere. 21.
  67. seu 25 - 4 seu 25 - 1 re ad fractio
  68. nes restucta, posita 2 6. et e p 1. porst
  69. teen- h 5 he 45ted sd H FAd AS p, Ax +) eAB + B2
  70. ergo prollemasie
  71. solvi ires divanre
  72. ueros tat
  73. Unde A H ha n -her (2+) 8ABF- 4 ( +2EC +C H X. ergd ess 2 , seu vergo EB ib
  74. Bpahre + ten +hEY (+4) 8AD1 + 495 sive βpa XvdoVcos (B el (2 +) ∞AD1270 409. tmmma 625
  75. explica tam V. exprimente, inseratur,
  76. Nam si suo quadrati in se ducantur, actus est quadratu uactato, quad culocua
  77. Qui valor in aequatione numeri (31)= valorem ipsius B. sed posss et XH
  78. et summa quadratorum ab ipss
  79. sumna quadratorum
  80. feris hts h Aex 1 A h+, k 2h AB t Ahs(quadrato quadratus datus. S velics quatrat quara factum ex nuntio
  81. _Tie ducend B in Y(+) ys a β
  82. quad itum a 25. +4
  83. est 194481 . Quod erat
  84. Faciendum. Et quoniam semper potest, obtineri qbatia o quado
  85. Cunque supponatur. 4. limitibus tantum (pro evitandis negrativis) observatis sua
  86. poste; in pelities adtine vis mrereis quamu sinne quones tel famma su duum quarato qua
  87. erutus datus.
  88. 4096 a
  89. ot (41) Factim ex
  90. X. ab. ac H 62G - 16-20, 409
  91. habeantur, dabuntur numeri tres
  92. (39) Factum ex
  93. =2 410 - 12F) 4
  94. acp50 3 e 1
  95. et hr ahar+ Xs
  96. E-. (10)
  97. 1 104 a dpetu s ettu b6
  98. fiet V, - 6 - 18 - 1
  99. 64. 6 152.
  100. ter - Vil ponans Y Aot fiet (3, hrl- Ah
  101. et B Eer tvl V (+) yC
  102. Ducantur in se terminus primus et secundus
  103. Sadtut. tn1.
  104. -2 + 10 - 12
  105. analytile sol et has quoque conditiones adimplere
  106. iq
  107. epsm 2 as. hol 1 tev 9 A C
  108. (33) Nam 1.
  109. fiet b1
  110. Pone 41 =
  111. F 56C50, 3176
  112. 64264 40eb
  113. 1949 2t0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068001:0002?run=73