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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 240r

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. 239v); this page is its right half.

The machine reads it as

  1. (7) sunto duae ratices 56 + ac, et 1 ac, eud prior b + ac
  2. Notu quadrando aequalionem 27 fier 3. b + ac
  3. necesse est ergo
  4. brsrae
  5. posteror, b- 4c
  6. D Utobrae
  7. b +bitrac + ac v sed inde aequatio identica sinedubio
  8. b + Sbtac
  9. BFS6 ac V, X ad. Eigo b +b- ac p - b - s6 ac. quod est atsendum
  10. erorem calculo latere. Videndum: Sb + ac p b + ac. Ergo (bfac, ibac a
  11. deprehens est
  12. sive 1 B 2b + , sive 3 - 2by + b b 4 ac, suc tp + ac 4) b, sive y p (4) (6. ac +b
  13. Erit ergo b Fac rH rac 4b, et N ac
  14. +b () A ac
  15. +b Et in posterore aequatione dubrum
  16. f6 ac +b
  17. restare potest, quomodo Explicari
  18. debear, signem y signum _(+ Nisi velimus utrumque eigi
  19. valorem utiobique ext adhiberi posse, unum exprimen quantitatem- sbnac, atterum + Sbrac.
  20. ut veritas eorum clarius appareat simamus quadratum exate extrahibile, ut 4 + 5
  21. 4+5 r
  22. + 5.
  23. 2(+)ar5
  24. Quare non licet facere 4 1 +5
  25. Nam
  26. sive Unde patet debere fieri 2+
  27. sansi
  28. Sed
  29. erit radix
  30. 2 + PA
  31. 2+5t
  32. nquaeramus radicem - S+te sed tunc fet, - 2 - 5
  33. E- Sa+FI
  34. - 5
  35. 2+3l3
  36. 2 = - s4+
  37. sed hoc non procdit siot
  38. potias
  39. fier 19-5 3- Unde rursus patet debere
  40. ccc
  41. si sit radix extrahenda ex, 9- 5
  42. unde patet ffien debere
  43. mule
  44. Jungendo aej. 27 et 28, fiet:
  45. (+197 + 2
  46. F esse 1 sive
  47. =E seu 3 = es solsum, daret eniu Y9 5 4. cum sit 2. nec procedit
  48. +S9. 5 + 3
  49. X e
  50. (B
  51. unde fit 3 = 1 seu 2. Quotum rationem a prisi indagerre, aliter
  52. +2 + 3
  53. cur scilicet(4) non liceat explicare per cum tamen id calculus
  54. fere videatur, altioris est indaginis et videorem a nemine pro merito tactam. luum tamen con-
  55. quam per numeros rgcs
  56. meralilet
  57. fiderandum est, etiam sic extrahi psse radicem:
  58. Sb f ac pi (1) b + ac Unde (b (4. 2bac e
  59. (V+ ac et C (+) 260 4 ac aq + , et F7 (+) 2by p ac et y +D iby +b, a
  60. eb y +(F b, vel + +y +b si St +ac. Quam ambiguitatem ita eruntiabimus:
  61. ponamus + aco, et (4) β2, erit (+) p 2pB, et erit:
  62. =(F) idem quod c β aco, B, aut + Jam aut aco, p B ponamus A, fier.
  63. (3 +) y + (+, 2) b, seu radie ex 1+, N, + sive +, +2, F. Unde frec
  64. (A, +) y + (+, 1) b 5b + ac. sivi _ y (A, +) S6 ac - b
  65. Unde gam:
  66. Nb + ac Y ((+) b
  67. S Casjuc (C ) b
  68. ut exploremus, fier: Nb (aco) ac
  69. - b (4, 1, ) V ac
  70. -b (aco, 2, () N6 (aco) ac,
  71. sive ( sive
  72. quorum veritatem mutriplicando
  73. (Yb (aco, e) b S (4c0) ac et toleendo fractionem:
  74. ab (aco, v e sir (au) ac
  75. b. s V Caca)ac L(ao, 1(P ) 5 Cacosac, ) (aco, Yp ) 62 (Ye 2 1) ac se li poi sipt n
  76. et ordinando: b + ( (aco )b, S. b. (4c0) C p, (aco, β, ) 6 (y(2, -) ac (Y () 62
  77. Et quadrando utrolique (coa, +) () b ac
  78. 1, 24t (ca, 1) , 1 (26) (ac) ac (1 +. ( e04) 11,
  79. 1 -2 ( c04) + 1 B b (ac0) ac (x + 2 () + 1, 0 b+, + 2 (XC0) b ac + aC V
  80. cum non vacet ita dligentius discutere
  81. prcquis Zi
  82. In quo vereor ne error calculi latea, quicquid sit
  83. non dubitandum est e sucadere debere hoc examen remultiplicationis, interim, ut a
  84. suprioa: b + (aa) ac Y4 (( ) 6
  85. fier: S4 + H (B1) +5
  86. et Pp F
  87. + ac
  88. = b (ac, Y(3, +) S6 + (ac0) ac
  89. ad numeros applicemus ponendo ( C sive +
  90. -225
  91. Jam ponendo BH F pier VB - unde 2
  92. -2 (YC) 14 +5 et ponendo B Vp a fier Y (2 4, unde -2 + p. 2 +5 p,+ 3.
  93. - 2+3
  94. Notabilehr
  95. ut autea 73
  96. n. 3+ 5 = +2. semper Moi
  97. similier ponendo acop. fier: Sg. +3 + 3 - 1 p2 et puoundo PB.. fier: - 3 +
  98. et sacedit, sintaotua puo saro subtiluas .d.-Sa re intantus anter midesre. 2 aluo este cun talu avicem coumarta

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 240r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0479?run=74