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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 288r

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: 0.82.

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. 287v); this page is its right half.

The machine reads it as

  1. (1)
  2. Xa +G YX,: ya t yx = = dy: dx
  3. sit ∞ y+ a = e 105 + 1t + 12B + 13Z
  4. V Xta S+EIt + uV+ Z
  5. et y = 405+41 ++qr v + 43Z
  6. C
  7. ( et X 305 +31 + + 32v + 33Z
  8. Et ex 305+ 31t +32V +33Z. 105+ 1IF +I2V F13Z: 405+41+ +42v + 43Z, 20st 21F + eI V+ 23Z
  9. -90. -4). =9 43 et 4e15 fit a = - 120s + 21 F + 22V + 23Z
  10. 30P, 31. -32. = 33
  11. quae dub ao quosduos valores ipsius a ex ay. d et 9 aequando fit 4 40 5 H1 F + EV F 13Z (0
  12. 134
  13. 13. 432: 433
  14. 40.
  15. sunt aequationes 1, 374, 5, et literae X, y, s, t, v, Z. quarum talli debent
  16. quarum restare hebent duae, ergo tolli debent 4. jam per ag. 8. et 9 et
  17. inveniantur set t; fiet es, et dissimulatis affectis per v et Z,
  18. et ut compendio procedamus H 40 scribatur 140, et 1 Et scribatur 141 et 120.
  19. sit +10-40 = 140 et +11-41 = 141 et +20-30 2230 et +21 - 31 = 231
  20. 16
  21. h
  22. fi multiplicando eq. 17 per 230 et aeq. 18 per 140, et Ab illa subtrahendo hanc, tolletur s, et fiet
  23. et 20 +
  24. 32 0 - 330
  25. + 141. 230 tZ ( 2300 +230a et 1140. 231 5 = C23F, 2310 +231 a
  26. = 190. 231.
  27. -1407 - 1400
  28. -141, 230
  29. = 141D = 141 a
  30. et 231= 141 in nomta nm multiplicatore ipsa tolleretur
  31. e
  32. quidem a controbique sedt in multiplicatore communi feret . 141. 140 - 140. 1452
  33. (u) CY
  34. ubi facitemus 230 = 140
  35. et proinde tollerentur + et 1s nec earum posset inveniri valor per n et
  36. es s qu; 10 ubi positis aeg. 2, et 22 evanescunt , et F.
  37. et fieret G Z= v + quoniam 10- 4020- 30, fiet 40 = 10-20+30, et pursi
  38. fieret autem = D, quod et patet
  39. Quia per 22, 12 14, fit 41 = 11- 21+31. Ergo ex 10, 26, 27, fit Z - v. 12- 22+ 32- 42: 13. B13343
  40. ita in aeq. 7. poterimus tollere X Z e q. similiter ex aeq. 17. fiet per 1n, 14, 2
  41. per 21, 22, 11, 12, 1314, 26, 27 fit porro 140 = 20-30 per 21, 13. Et 141 = 21 - 31 per 2214
  42. quibus valoribus substitatis in aq. 17. fit. 20-305+ 21 -31 F= (+a, quod idem
  43. seu
  44. ardisus prodiret ex aeq. 18. seu fiet s - 21 3t t + CoC XC lbE v. (2242: 12293
  45. fiet 22 5= 1730a - 2t simulitae qu. 28 conpenduse sentemus sic
  46. ergo subeta Eli jam sed scibititatis his valoribus y et S inventis per 32 et 33, substatutis
  47. in aeq. 7. redibit a ob valorem ipsius S. Cit idqe locis quatuor
  48. Tentemus ergo
  49. ita explicare _t et V, ut tolli possit a itaque suciamus + et sea et vahtda
  50. +64) 51a, et v h + 52 a. et substituendo hos valores in aeg. 32 et 33, fiet
  51. fiet 38
  52. - 231 + 2351 a et ex aeq. 33 fit 2= = h. 12342: 12743 = 12342. 52a: 12343
  53. 30=
  54. 230O +
  55. 130
  56. perz
  57. quibus valoribus ipsarum 5, F, et V substitntis in aq. 7, videamus quonodo
  58. ex aeq. 3. (5
  59. 6 250
  60. in quotua locis solli possit a ope arbitrarinenu ponere porro valores v etZue substtnendo
  61. _ prisem cmultiplicatorem monerutoris debet esse o=. 3 in aequatibu valore ipsius O fiet
  62. -12h - 12 52. a CAp + 13, 1274212 +135 12442. 52a. jam ponamus + 42E 73
  63. 142. Y42.
  64. 3
  65. irio
  66. (39
  67. 2. 5 -60
  68. 4212343. 230 230 27
  69. fiet 5= 61 h - 231 C + 60 a, et 12342: 1234342 70 et
  70. 1343
  71. 34513
  72. fiet Z C -70h - 52. 70 a. Hi valores Yv, 7 5, t, ex aq. B, 3543, 41, 34 debent substi
  73. 4 135 12342
  74. bui in aeg.7 et tolli a, quatuor logis exi pempe explicando arbitiarias ita
  75. et 412
  76. sed praevideri d, nullum sic dari exptum quia
  77. res eodem redit ac si o partio in aeqq. 3, 4,5b usi fuissemus liters asiem
  78. ut restent soluius h, e
  79. les generaliter co redit, data aequatione qua sint a, X, y du: dx invenire
  80. R, et e, Generitissime de sine a.
  81. Aest generaliter eo redit, sit aequ. dus t= dy:dx = X. y. a. et alia aequatio sit
  82. aliquim alias duas in qua sit X v, a
  83. e pryposita quaeruntur du ∞ dyodo _X 6Za et y-
  84. H
  85. X = ∞oa et y v. a. Ex 4 fiet dx: dque = Zoa (quod significat relatiorem Z a dari exrelatone Z. a)
  86. H
  87. et ex 4 fuet dy: do= p. a. Ex. b divisa per 5 fit dydZ: dxax= a: 20a. seu sperq
  88. A∞: dz et valore ipsarum A et y substitato ex aeq. 3 et 4
  89. H
  90. substitutis in aeq. 8. fiet: alZa a. Ea. v. a 0a: v a = dv: dZue. ubi 28
  91. fit Za Xy. a : v. a
  92. -
  93. (10)
  94. notandum si sit quacunque quaentetus :e dbe O: b = D.a seu si
  95. ratio
  96. ipsiu Dad a, seu dari D O: b per D: a seu fore 6L) D: a. Ergo pro quantitas y: a habetur per
  97. polam Z. a, adeoue s habetur per Z a, be similiter hy X et, dailq, et dg. dv. Ergo pro

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 288r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0571?run=74