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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 100r

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: 0.88.

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. 101v); this page is its right half.

The machine reads it as

  1. 30 januar
  2. 1679.
  3. rus ratiious
  4. +d Fx +ad L.1. = bd
  5. +CX
  6. eberitea
  7. X +ax +bsx
  8. +X +CX X X -bd (D
  9. +a
  10. (F) (E) +ca
  11. conser scrediasma ejadem diei, de
  12. A Incognitis tollendis per aequationum exacta
  13. tionem.) praectarum hic compendem
  14. pro aebilianis autilibus vscindendis
  15. X +raX + X + b
  16. +a
  17. un poshibilis
  18. Deseriebus infinitis maniversum. de
  19. 9 potentus
  20. proveniat formula () destmendi sunt termini
  21. possililis +b2 aequ. a + 4aX +6ax + 4aX + X
  22. possib. 8b aego a + gaK etC. Xx
  23. ut
  24. e, utque fil (2). (F) ideoque fieri
  25. debet: + ad +bC qu. 0. et +d + b aequ. 0
  26. Ergo d aequ- b per. 2. quem valorem inserendo
  27. in aequ. l. fit: - ab + bc aequ. 0 sive
  28. fit aae c aequ. a. itaque valoribus
  29. +b
  30. ipsarum C et d per aequ. 3 et 5. in
  31. equ formula D. substitutis fiet
  32. est impossibilis generalis
  33. Hujus scribantur altiores:
  34. trax ae aequ- b
  35. (2) a
  36. re
  37. jucatur formula in formulam (B
  38. itaque aequatio X +raX + a aequ. 0.
  39. secundi gradus.
  40. imposs. b aequ a +2aX + x
  41. adde
  42. intel
  43. redam
  44. invenire F perx.
  45. patet sequentes omnes fore possioites, et solam primam impossibilem
  46. jam in prima collatur, x ope ejusdem in secunda non
  47. nde fi
  48. restabit in prima nisi X et X, in tertia tollatur tum X ope secundae
  49. nova
  50. prodibit alia in qua erunt X. X x Y itaque in ea habebitur valor
  51. ipsius X qui substitutus in locum ipsius X aequationis primae hansforma
  52. ta, prdibit aequatio in qua aberunt X. X aderunt vero X. X. X.
  53. =b aeq. a + 2aX + X
  54. + cbt
  55. ca t AcaX + BCaX+ZCX + C + 2
  56. odb da +6daX +.. dax+. da x+ dex L. dax +.. dx
  57. +eb
  58. ea + Beax +. eax +.. 1a X + .. ea X +. . eax +.. Ca X + eaX + ex
  59. eti
  60. X
  61. e 2C
  62. ubi natet loco arbitrasirum dari arbitrarias
  63. dic. esse
  64. tantumtres, una adhibita C tollendos tamen, desiderari teminos
  65. tres X. X. X. ad obtinendam aequationem simpliceni, et adhibilis
  66. duabus arbitr ariis c.d requii ut tollantur termini aideoque superesse
  67. et dhibitis duabus arbitrarus c. d requiri
  68. Terminos tollendas, 2. suliae
  69. ut tollantur termini 5 et ita superesse tres tollendos. Et adhibitis
  70. d tribus arbihraris c. d. C t tollantur requiri ut tollantur
  71. termini septem scilicet +2. X2. pt. XS. X6. X x. ita supecesse
  72. tres tollendos. Atque ita Supererunt tandem infiniti gollendi
  73. quare ut res suredat nec proinde assequemur ccopum hac methodo
  74. nisi demonstremque, effici posse ut licet progrediamur in infinitum
  75. semper tamen finiti tantum tollendi supersint, adeoque negligi
  76. queant.
  77. Auic malo succurremue quoad ejus fieri potest, simulque
  78. generalissimum exhibebimus modum, qui est talis.
  79. eu
  80. Series infinita proete
  81. X +a rb
  82. L +C +dB (B) E
  83. diies ut
  84. de modo extrahem
  85. adi cen seve
  86. infinitae per alioe
  87. serrem infinita
  88. = ++
  89. 9 l’eu

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 100r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0199?run=74