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Leibniz-Handschriften zur Mathematik LH 35, 6, 26, fol. 14r

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: 0.86.

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. 15v); this page is its right half.

The machine reads it as

  1. be ad R. Jac. Ber Roulliz
  2. aris
  3. Quadraturae orrationalium simplicium
  4. Quaeritur SQVDdx. posito D et e ex esse formulas
  5. gitur
  6. rationales integras quoad X. Quia coportet quantitatem et
  7. ejus summatricem ejusdem esse ambignitatis, et quanbitatis
  8. uno irrationali vinculo constantis, ut VD differentiale
  9. siea hanc ipsam irrationalem multiplicatur; ideo
  10. facio, (qYDax = eZDYD + (2 YDdx. ponendo sormuta
  11. habe
  12. + veluti si D esset 10 1X + 2XX + 3 XtCk
  13. H eamem ambiguitatem praestantis
  14. irrationalitatis. et difcerentiale
  15. et quia
  16. habxiorem quam e quantum oposest etlicet, ut quae sita quadratura
  17. et habenaar absoluta
  18. ed Ergo utrinque differentiando fiet
  19. e reducatur ad simpliciorem ejusdem ambignitatis
  20. eD d + (er1) E d D + 2 dX - Gdx = 0. quare
  21. cum formulae 8 et 2 sint arbitrariae, abeoque potentiae ipsina X, in his formulis
  22. iptos in ipsis habeant arbitrari coefficientes ex
  23. eo determinandos, dum quivis terminus est destruendus;
  24. quo
  25. hinc posito gradum ips Exponentes gradutum ad quos
  26. et, 7) ponendo a, (3, V, d, fore oportet
  27. sC
  28. ut quantum satis arbitrariarum obtineatur, et 2x tamen
  29. assurgunt D, E).
  30. fier
  31. maneat quam licet simplicisima, fore V = β+ 1- a
  32. et constare ex numero fui
  33. in minor expone ipso a posse esse habere terminos
  34. A X, X, X, etc, vel X, X X, XX, X, retc. vel
  35. XX+X X XX, X, X et eodem manente numero ipsorum a = 1
  36. sed primum tamen casum esse simplicissimum, quo posito fiet d -( _- 2
  37. Esto jam in exempo unde reliqua aestimentur,
  38. DuX 1aXX + 1X + 14X
  39. praeterea considero pro formula , composita
  40. A ex maltis terminis X
  41. Sit formula _ _Quantitas & posset quidem esse
  42. los
  43. Formula composita ex multis terminis, velut si esset
  44. sed quia
  45. Q = 20+ 2IX +22XX F23x + et c. sed si nou quodque
  46. ex unusquisque ex his terminis, velat 20X in ductus
  47. qualis X s qu est ordinatae est valor, cujus figura quadraturam uodrati
  48. madmodum
  49. potest gulos tormines data et
  50. si nonermo,
  51. rumquales Xit
  52. dufetermint qualis X, X, ductam Y3
  53. contrahamus, sumus exemplum ponatur exemplum
  54. unde reliqua ostimentur.
  55. crmulatione
  56. ipsis conflata sum mationem haben
  57. ulorum etermingmre fractari
  58. indenta sipta extalibus foruum
  59. etiam
  60. ta
  61. e
  62. 3) = 10 +uX 2x + 19 X L SAX aK
  63. D= 10 +HX H1KX+ C3X +4X K X H H
  64. Y y XX Y Y X I + X data - X X x Y H X X +XB
  65. 8 = 30 uC 1 133 X Sx , 3sN H X X, ∞ , 8 - 9C + 31X +3 1XXt 33 X 13H + HX X X X
  66. 9 onaxt aet _ X X 1X AY X. X q5q. h h, =40 + E, quxx X H X X X X
  67. Fiet a - 4 B- 8 f6
  68. d= 2
  69. fiet a = 4, β = 8, 7 -5
  70. Compendii jam causa assumamus numeros
  71. novos, quales 130, 152, 173, et similes,
  72. qui significant. 3C +0, 10 vel 5C+2, 12 vel 7C + 3, 13
  73. abi gabris e, 253. os de sunt poneri veri
  74. continuossedtamen
  75. Timo et non contiiu sed sempe
  76. +0.
  77. vad _x +CXX

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 26, fol. 14r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068071:0027?run=73