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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 6v

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: 0.85.

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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. Adeoque 112. 323 = 123. 312) Et 70or = vop. 3 1
  2. Habemus ergo 32 = 112. 113: 313 323 =123. 113.313 300r e 10opr 319 n (223 = 123. 112:21
  3. unde 100p = 2009. 713: 3. Adeoque 300r = 2009. 213. 313: 113, 13
  4. Sed dubito tamen an ob aequationem 15 commode facereliceat uZ. 1 3 22. 223=9
  5. ita enim ex ea fiet po= 2009. 213: 113, Ergo fieret 212 = 213, nisi forte in calculo pecca
  6. vis postrema Hypothesis a dat suam consequentiam ex aequa5, ibi enim ts fiat
  7. 112. 123-212. 223=0 fit etiam I13. (0p = 213. 2009. Sed videamus arares
  8. an non aliquid subsit incommodi. 21 32 32) fiet X2. 223 = u2 113. 113. 123. 313. 313
  9. seu 212. 223. 313. 313 - 112. 123.813 113,: 313. 313, ubi si loco 22Bsubstituamus valorem
  10. 123. H2: 212 fiet H2 H2 12 123 313, 313 H2 13, 113. 113: 313. 313, seu fiet
  11. (112 +23: 317. 318) (313. 313 113H3, ubi tamen mhil ta commodi vaded
  12. Si in aeq. D (facta ex divisione aequationis ) matuissemus facere 112. 123. 113. 113= 22
  13. 212. 223. 313. 313, prodiret alius valor ipsius 223, nempe 112. 123, 13. 113,: 212. 313. 31, et
  14. foret 100p = 2004. 113. 213: 313.313 et 300r = 2009. 213.313 Qua periade est
  15. ac si locoaequationis 15 ad hibuissemus ag. 16 et ibi fxissemus 212. 23 = 3 12. 323.
  16. id est explicando 312, et 323C, si fecissemns 212. 223= U2. 113.13. 113:313.313, seu H. 1e. 113 3
  17. Oallem Alterutram ergo Hypothesin sequilicet, nec refert, quam eligamus.
  18. Matussem aliquam lecemjustitiae observantem; sed talis non datur disi impossibilis
  19. quae faceet quae faceret 113. 113 + 313. 313 = 0 sed eo sine necessitate recurrere non
  20. ut jam est factum.
  21. pladet; etsi calculum daret, sed imaginarias adhibentem.
  22. Hypothesui, quod 223 = 123. 112,1. itaque habemas ut jam dictum:
  23. 323 = 123. 113: 313 (adeoque 323:123 = 312: 112) et 300r = 100p. 313: 113
  24. Deinde ob 223=123. 112: 212, fit 100p = 2009. 213: 113 adeoque 300r = 2009. 213 313: 113. 113.
  25. Hinc porro quia per 13 est Z = 112. 100p -212. 2009,:, 213. 223 -113. 123, ideo explicando p et
  26. 2(2) = 112. 113. 313.
  27. 223, fiet Z = 112. 2009 (213: 113) -212. 201,:, 213.123 (1121212)-113. 123, adeoque erit
  28. y- 1009, H2 112.212. 213 - 113. 212.212,:3131y 213= 12. 113. 123. 213 -112 113, 113. 123
  29. seu Z = 1009 (212 :, 112. 113, 113), 112. 213 -113. 212, :, 213-113. Sed jam ode video mait actum
  30. tam ad 4. alioqui
  31. debent Ze, a , ZG y, y, Z habere rationem derum est conmpat
  32. nulla est difficultas in extractione
  33. neque enim
  34. damus au recat facere ut e conrssat
  35. +. 313. 31: 31.
  36. 2. 12.
  37. 13. 713=30= 127
  38. Mquit quoipu e rabetur
  39. adeoque 323: 123 = 312 : 112) st 300r = 100p. 313: 113
  40. 2113. 100p:, 212. 223 112. 123. seu per a9. 8
  41. 12. 223 - 112. 123 G = 113. 313. 313. 100p.-, 112. 113. 113,. 123 f 112. 313.313. 123 =112. 923. 313.313. adeoque fiet
  42. 112. 113:313 et 323= 123. 113.313
  43. 212225. 11. 143 fiet Z= 112. 100 p + 212. 2009,: 113. 123 et
  44. =12. 13 + 315 3 3tidem y = 313. 313. 100p : 112. 113, 123 Ex 49 17 V = 213, 2009 -123. 100p, : 112. 113
  45. 223 subistituendo valorem ex aeq. Q fil v = 112. 42 ++13. 42 112 13. 2009 = 113, 100p, : 112. 113. seu fiet
  46. V = 612. 113. 113. 123 + 112. 313.313. 123) 20092123 1313,313,212. 100p, : 112. 113. 313. 313. 212
  47. 13. 113+ 313, 313
  48. H3. 11Z + 112. 124
  49. Hideamque an contrahendi causa liceat assumere 313. 31 = 12. 123, fieret 212. 223
  50. pt y = 100p : 113 et V = (113. 113 4 112. 123)2009-123, 212. 100p: 112. 113. 212
  51. sed exsectemus potius duu ad postrema perveniamus, ie arbitrarias consumamus ante tempus.
  52. actenus fatis fecimus aequationibus ductis ex irrationalibus. Aequemus jam rationales quan
  53. + (123 - 3237) yZ + 100 pb- 206 Y -ab +ad = 0 et explicando 312, 323,
  54. Et primum aequandovalores ex aequ 10 et 2
  55. fiet H12. 12. (313.313- 113 13) C vy + 313. 313 (11HB-31. 313)VZ 4 12Z I (313. 213 - 13 13)yZ + (113113- 313313)00 dopB
  56. et divisa aeg. per 113. 113- 313. 313
  57. palores ipsius
  58. us astez h
  59. fiet L 112. 112Vy313. 313YZ + 123. 123yZ(313. 313: 113. 113)100. 10opp 313. 313al = 0. ubi opott
  60. 125, 212,
  61. ==313. 313 (ab - ad) sit ab - ad = 3K 113. 113- 313, 3B
  62. postiemo eodem modo ex aegque 10 et 12, eo
  63. video autem nos indigere sex arariis. Et sane supersunt ad huc 112, 113,
  64. pos ati renique binae si exalices p per. g +.. 4, quas sufecturas non quidem certum; sperari tamen
  65. Porte sufficiunt aequationes quinque, nam in utraque aequatione tollo destinentur pp, et gq super
  66. restat sequ. in qua q, superest, quae divellatur
  67. nos lucrari posse si in aequubi est
  68. et tentem
  69. v, y, Z explitare per p et 0
  70. Eut duae aeqgus. ubi p et q, harum ope tollatur lHamem aliaud
  71. in duas, ita evanescet q, et per g habestur p. videtur
  72. +. p +. . p + faciamus pp Kp + HK = . 9.
  73. dextram partam hajus aoquationis etiam reddere extraribilem in indeter minatis
  74. enque faciendo in altara aequation ope duarum hypothesium habebimus aequationes
  75. ergo Cietse bil (410. 111-
  76. aro alterius valore Ao2gqup+to+:00
  77. vod saciandum : C11C. H 99 +: Q1o H0aa + = 21. Ho aq - u p 49 + 40 aa + . H0. 11 a9 -
  78. 209 +2+ 10. A1ag 110. tiona
  79. 420. 3004
  80. 1. 11aq + 10. Iaa,
  81. ttrarenda ergo est radix extioor
  82. extracida tulanda extraum. ex fiet rabium extraratur ex 10.109g
  83. egi tote us gerte qo eoster a saumuequete n perpose
  84. Pito2, 410. 410 =
  85. 109+ =na
  86. = H2. H2L4
  87. pretiot oit et Eat ursus modibunt si pro 4 ad ponas 5.
  88. parabuntus vplore, duo priores
  89. tinetur una
  90. id
  91. 22173: 12 13 = quae aequatio dat valorem ipsius 223. Cui addamus priora, nempet et scriben
  92. Remedium erit si faciamus
  93. = 212. 223: 112. 123 (e
  94. 113. (13. 1l 113) Lta
  95. (112 - 3
  96. qu q2K)
  97. u
  98. qu
  99. seu 112. 123. 113, 113 = 212. 223, 313. 313, ut ante) Ita enim patet cbi fore 313. 3cr = 2B. 2009
  100. ex quo successu patet nos recte calculum instituisse
  101. Retineamus ergo aequa
  102. Rem
  103. 0 Itaque ex aequ.
  104. o
  105. 1= 13. 100P
  106. 12. 11Z. 1
  107. gI3. 112.1237
  108. Espo y = 13. 812. 31 3. 0
  109. 10 104 no aquona
  110. as i puliu sunt
  111. ousaro. tropp LE1120qtopa
  112. qu adoqu fina duas.
  113. 10. 10299= 12010a9 = 120. 700aa

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 6v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0012?run=74