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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 290r

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: 0.75.

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The machine reads it as

  1. Y4 CZ cbt en
  2. Vs e
  3. PCoV
  4. (7
  5. erit _
  6. d5
  7. +5d92 + 10d97 + 10d9 2 + 5d9+ Z + g
  8. d. + 4d9 1649. + 4dg. +94.
  9. la toB.
  10. 3d9
  11. 26d3
  12. 2d9
  13. 36d
  14. 3dg2
  15. 6bd9
  16. b243
  17. Eudqe
  18. 364
  19. 4bd 4bg
  20. 5
  21. (2)
  22. 662d
  23. iob
  24. n
  25. 1648. ab331.
  26. 93
  27. 66d9
  28. 3649 3b 9
  29. 3b92
  30. b6d9
  31. 342
  32. 6629
  33. 36
  34. 26289
  35. 412 4b39
  36. 10b
  37. (7)
  38. 64d
  39. 5 b
  40. lg
  41. 649
  42. (6)
  43. Jam id agitur ut tollantur terminus secundus, simul et quartus
  44. delis arbitrariis, d. g. b. ponatur dgH E b. et dividendo
  45. columnam secundam suppositam 0 per b. fi tollentur
  46. simul 9 et b. ex col. 2 et haberi poterit absolute valor ipsius
  47. d. itsque sumendo pro cognita,. Et ta poterit haberi d
  48. pro cognita, jam ex columna quarta posita . fiet aq
  49. et explicando d9 in ea per eb, et dididendo per b. fiet aequalio:
  50. in ea b per d9 fie: eoanescet b. et g. etiam
  51. 10 elgs + 4eb9 16pbbe t 993 +59 b9s eb in alteri quod luntile
  52. 10d 9 + 4 d93
  53. Quoniam tamen explicatio ista semper
  54. in potestate est itaque faciendo 3)b9 d +rb dnD
  55. ive Bp - 399. tunc in columna quarta evanescet d, extra d 9
  56. adeoque in columna quarta non extabit nisi du seu non nisi e
  57. nempe ponendo b et 9. cognitas aut arbitrarias ibique assurget
  58. e ad quadratumo et ope aequationis quadraticae invenietur, e
  59. et ita e haberi poterit pro cognita et ita sola d restabit
  60. M +n men b+C- et nny bcpY
  61. restit ME+ n + b5+ C5 1.
  62. n. 6n F
  63. +n 2 14 Y seu renca Y4b3 B9
  64. in glteca aequatione priore ex columua ida, quod explicando experiemur: et aS + bBC
  65. Columna pa dabit: SC d + +ped + 1+ +ged + 2 +2rC + 5d -sr + 4sd +st 10)
  66. columna dabit: 10 et 294 + 4 e 34 AEp C 37 (+9) +69 e 2 + 99
  67. (13r 2 - 34) +bre 2 - 139 (+ re - 2192 4) + 5 a99 r 4 5 - 279, + + 2 27 q S
  68. usim
  69. Posteriore ergo aequatione inveniemus ipsam c e. absolute. Et ita c. erit cognitas adeoque ejus valore in prioreo
  70. aequatione inserto, non nisi una ibi restabit imognita d, ascendens ad quartum Faut (si datae sindesolidae terminus
  71. secindus sublatus sit ad tertium gradum seu si pto) ad tertium gradum.
  72. Habemus ergo methodim generalem
  73. cujus ope ex qualibet aequatione surdesolida tolli possunt termini incognitae adipares dimensiones ascendentis
  74. porro valorem ipsius e, compendii causa ita
  75. sit jum X +9X +sX + t, vel X + quo X +f B F Scribemus:
  76. Xemn ME + Gm n + 10 Mn + 10 m n = 5mn + n
  77. eu X (+5mum + 5 Cum HN +CC2M + S mN + n
  78. s
  79. sive cciccardi
  80. -simn X
  81. S
  82. +mn ... . + ma..
  83. -imn..
  84. .
  85. - mn..
  86. =vma im3
  87. ergo X 5ma X - sm E X + m
  88. + 5mn X - 5m n X
  89. +umn
  90. + smn m
  91. seu yn A3
  92. Emusus XB
  93. comn in
  94. Vidoamus quid fiat si aequationem Cubicam meliplicemus per X - 3mnX = vipo. ponendo scilicet X - m - n po.
  95. multiplicemus per X +m X
  96. +on
  97. b.
  98. +m produetur cusus aequatio cultca, qua si seu vantitas ee. quae ipsi X - smnX a 5mini Xam
  99. addi potesta eodem omnia omnes aliae aeq vationes inferiore multiplicari
  100. e prodicta eidem addi Possunt, summa erit aequatio , cujus radix ∞ + in
  101. et quae habebit omnes termiras completos, et plurimas arbitrarias, cm et in qua
  102. nulli m + n vel m + n vel m + n vel m +n, non reperiantur 8
  103. m +n non extet nisi in ultimo termino, ac proinde solvi poterit aequatio data per
  104. aegratio as eudem gradus, ut Xam ex pr X + da X + Bm extractionem radicum Eepuanum in cubo. X . dun X po produtamus, nim alio undo
  105. ai
  106. X
  107. Birin
  108. t
  109. e
  110. omur
  111. 0. Cun
  112. sit X d 3 + 89
  113. + b
  114. v d272 + 4 492 16d9 2 44d5 3. g
  115. co
  116. +
  117. 2
  118. d75 4d393 edz Z 1dg19
  119. d+75 + 4d2977 +6d92314d9 21981z
  120. +d B. +4d 9b 16d96. 409 b. 19
  121. v2 4Z +3d92 + 3d 7 + 92
  122. V rpco quo + YO + sux +
  123. a373 4349 7 1dg 23 + g n
  124. co) Z + 2b7 + b
  125. +2bd 6bd9. +6bd9. +269)
  126. b42. 3bag +3b8. +b9
  127. v
  128. 0
  129. 42Z2 +2dgZ +g
  130. 1Z3 +3b Z + 5bZ + b2
  131. 1173 2d9 93
  132. 3bd 6bd9. 3692
  133. 3b4 6bg. 3692
  134. b2dr. 263,, 69
  135. +g
  136. C174 + 4633 a66Z + abZ +b
  137. abd. 4b94
  138. 66d. 6bgL
  139. 4V. 4697
  140. 5 bd. bg
  141. - 10
  142. 33
  143. 2
  144. = smn r 3mna m
  145. in 21 ma am.
  146. + 10 nCma m
  147. in
  148. Ergo X 71
  149. m
  150. v nn 3m
  151. N + pN2+ qXFY A +sX +t H
  152. +Dm
  153. 82
  154. + m
  155. =Pman
  156. n
  157. 30. uomn.
  158. + d
  159. fict: X3 te
  160. u 1.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 290r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0579?run=74