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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 168v

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: 0.84.

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The machine reads it as

  1. 4
  2. Aequatio +h gradus habens duas radices aequales
  3. 100 C + 101 C + 102 C + 103C + 104 = 0
  4. +3. 101 C3 + 2. 102C +1.,103C
  5. nes apliqus sul. 60 pagina
  6. quae et tato isset ha quae et potuisset haberi ex 1.
  7. 2 ex aeg. 2 et 3 fiel +1. 3. 101 101 + 1. 2. 101. 1028 + 1. 1. 101. 103 (4)
  8. 0
  9. mulliplicatione Arit hueliea
  10. eg. 4. mulliplicetur per 190 ee, et ab ea auferatur aeq. 1. mulliplicata per 1. 3401 = 24., 100. 102 siel
  11. - 2. 4.100. 102 - 3.4. 100. 103 -4. 4. 100. 107
  12. 1. Ac + 1. 2. 100. 101. 102 C3 + 1. 1. 100. 101.103 p. t 100 101. 103C
  13. 1. 3, 101, 101. 107
  14. =2. 4, 100, 102 104
  15. -4. 4. 100. 100,104 -44. 100r 100. 104
  16. = 1. 3, 101, 101. 102 = 1. 3 101. 101. 103
  17. Aliter ex aequ. 2 et 3 nova ad e, fieri potest, ullicmos terminos aequando,
  18. 42. 4, 100. 10d 102 F2. 4 190. 102.107
  19. scilicet 4. 4. 101 194 + 4. 104 4. 100 C + 4. 104. 3,1012 + 4. 104. 2. 194 = 0 = YF, 4. 100. 104 e +
  20. +2. Y, 106, 101. 102
  21. -1. 103. 1. 101 = 1, 103.2,102 = 1. 103. 3.103
  22. aequando terminas summos, sit
  23. 10CC+ ue + 12 =0 20ee+ 21 ft 3220 SF. 1. 3, 101. 101. 204, 101. 104
  24. , 11. 20C +12. 20 -, + 19. 228+11. 22-= 2. 4, 100. 102, 3. 4, 101. 104.
  25. - 10. 22 412. 20 =0
  26. = 11. 22 i 1012).
  27. = 12. 21
  28. 20= p10) C + 2. 102C + 3. 103C + 4. 104
  29. 4. 101C =4102C 74103C - 4. 104
  30. = 3. 4. 100. 100.103
  31. = 1. 3, 161, 101. 10)
  32. jungantur aeq. 4 et 5
  33. +12. 20110. 22
  34. 11.20
  35. seu
  36. versae
  37. 4. 100e+ 3. 101 e +2. 102C +, 103 0 multiplicetur per e, et auferitur inde eq et 1. mulliplicola per
  38. fiet
  39. =10. 21.. = 10. 22 = 12. 200 - 12. 25
  40. et
  41. e
  42. +12. (2. 20. 25
  43. +10. 10. 22. 22
  44. )1.3. 101. 101,. 1. 2. 102. 103.
  45. + 2. 4, 100, 102. 1.2, 102. 163-.
  46. 10 = 1gol. 101
  47. -2.10. 12. 2022 6)
  48. + 12. 12. 22. 22)=c
  49. 102 19, 101. 10
  50. = 4. 4, 100, 104. 1. 2. 101, 1021
  51. 4 1. 1. 101. 103. 3. 4, 101, 1021
  52. + 4. 4. 100. 104. 3.4, 100103..
  53. = 2. 4, 1001102
  54. H = , 1.2. 101, 102
  55. 1. 1. 101, 103. 314, 100,103 a
  56. 20 = A. 4. 100104
  57. = 1.1. 10l. 103
  58. 21 = f3. 4. 101. 104
  59. = 1. 2, 102. 103
  60. faci
  61. (5
  62. (5)
  63. -3. 4. 100,103
  64. - 1. 1. 1011103 = -12102 1031
  65. + 1. 3, 101, 10). 2. 4. 102. 10c
  66. 2. 4. 100.102. 2. 4, 102. 100
  67. = 1. 3. 101. 10]. 1. 3, 103. 103
  68. + 2. 4. 100102, 1. 3. 103, 103
  69. = 4.4. 100.194. 1. 1. 101. 103
  70. 4 1. 1. 101, 103 1. 1. 101. 103
  71. +4. c, 100104 4. 4, 100. 104
  72. 1. 1, 101.1634. 4, 100. 10
  73. Et ita tollitur incugnita ex aequatione
  74. habente duas radices aequales.
  75. si in casu aliquo sneciali sit 20 =0 su - 13 20, prurimum contrahetur calculus, et fiet 10. 22 - 10, 11. 21. 22 -0
  76. 22 = +2. 4. 10+. 104
  77. = 1.3, 103 103
  78. Hinc e = - 22 = 40
  79. 1
  80. 10. 11. 21. 22
  81. + 10, 12, 21. 21
  82. 13 = Y 1. 1. 101.103
  83. = 4. 4., 100,104()
  84. + 11. 11. 20.278
  85. = 11. 12. 20. Y
  86. 20 = 12
  87. seu fiet 19. 22 11. 21. seu 4f. 3110l0
  88. Et in pe q. 19 pro 4. 4. 100. 104
  89. poendo 1. 1. 101. 10Z (sb aeg. _2)
  90. fiet 41. 1. 2. 2. 101, 102. 102. 103
  91. ta
  92. 1. 104
  93. O1. 102. 3.
  94. 2. 4. 102. 1044 (,0) (+ .
  95. ∞1. 2, 101, 10]. 1. 3. 103. 102
  96. 2. g., 100. 102. 1. 3. 103. 103
  97. 4 1. 1. 3. 3. 101. 101. 103. 10
  98. 41. 1. 2. 2, 101. 102. (02. 103
  99. ponamus jam 101 = 2. 1050. 5) 16. 18, 5. 32. 52+ 6 gb2 nempe ex ipsa aeq
  100. (4P. 1. 3.3. 105, 101. 103. 103)
  101. in hroc calculo pro ag. 6. sufficit ct q. 10.
  102. ponamus jam 100 = 10. 50.
  103. et 14 1 101 = 2, 1050. 51
  104. et 102
  105. 103 = 2. 30. 51. 52 + 13. 61
  106. 104 = 10. 52.52 +2. 62
  107. Cubi 10, 2) fiet
  108. alia sunt
  109. aequ
  110. ro ladiorens
  111. 4. 16. 50. 51. 52+2)1 X . S. genus
  112. arbitrio assum
  113. seu 61 = 4. 10. 59l. + B1262- 251.57) est sine ffam
  114. quamin Seu 4. 105548. 1262 = 251 32Y 125161
  115. aeqb
  116. 11.5
  117. sed pari jurefit 61 = 4. 20.532 +8. 22. 62-2. 2051. 51
  118. a ipsum quod
  119. obitinere debere
  120. 2. 12. 20.51.52 et divisis abus per 100. 22 - 1812
  121. supposcama
  122. F (2. 35, 52 + 8(2) 62(-2. 10. 5( 52): (12)31
  123. . 12, 2260
  124. seu 61 = 8. 62:51, idque utroque modo atque ita ratculus debet succedere. Sed suppectum
  125. et fit 410. 22. 52 8. 12. 22, 62) - 2. 1022. 51. 52 = 4. 12205248,
  126. fit 4. 52 2517.52. seu 52= 5251. eti 2. Ergo b
  127. quod ita cale 10g12, res, ut saceutu laos ingredtinntur
  128. u
  129. 101. 104
  130. 4. 14. 104
  131. L1. 3. 103.10
  132. p.104e)
  133. = 3.4, 106. 105
  134. 1. 2. 101, 102
  135. F 3,4. 100103
  136. quae aequatio
  137. ci suppositior
  138. quod immenso
  139. 2. 102
  140. 02. 103
  141. id consecnti sumus
  142. dentica
  143. calculo aequati
  144. evoluto, obtin
  145. onis 6
  146. semus
  147. semr ob sinnt 2
  148. 10c
  149. Nempe ubi
  150. ratiolinationi
  151. hypothesis. s
  152. decit
  153. identicam, signu
  154. Unde fecter
  155. quitur a
  156. pro

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 168v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0336?run=74