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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 138r

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. 137v); this page is its right half.

The machine reads it as

  1. ea 1B.)
  2. y 10 spem + uxtn +XFp yy Z 16XA Iom 4, 10. A LXtm Xtn Y, 10 12 Sxra, arp 1. 11 12 Extmetn
  3. L=30
  4. 31
  5. Et. 1e p
  6. aequationes comparatitia decem, cum arbitrariae adsint c2
  7. o +Nyta astbre a + bo, 10 nitrc
  8. C
  9. 11. 13(41)
  10. ∞, 10r erio b = 20+21+22 10m + en + 12p + a = 2om +rin + up. 10.1 = 20. 21 101 2022
  11. sineslvamue Ex aeg. 11, 10, 97 habebitur 20, 21, 22 tollentur, ne 22 11. 12: 21= (ex 10) 10. 12:20
  12. ergo 11. 20 = 10. 21, seu 21 11. 20: 10 = (per 9) 10. 11: 20. Ergo fet 10 = 20 idemque firet
  13. in caeteris, quod est absundum et glan ae qu. 7 et 8. videam, an hoc sufficiat, ita enim
  14. In caeleris quad est aljurdum.
  15. sed videtur res successuro pro casu triplicis aequilitalis
  16. pi nempe y + a, y+ b, ytc, debearit aequari quadratis vo Z p respective
  17. 9+aLvop ytb et y tC = p
  18. Nempe sit y- 10 exem e, t x+n + V
  19. a
  20. nempe
  21. Nempe sit g= ta ot ri 1oram + tXin
  22. a
  23. y = 10 SXIm. XIn + 11 S ptm. Xtp + 1 Sx +n. XIp + 13X + 14
  24. 4
  25. v= 20 + xim + 21 Sxtn + 22 Extp
  26. (5
  27. Z=, 30 Ynem + 31 YX+n + 32 YX+ p
  28. = 40 sram + 41 Exin + 4u extp
  29. 20.20 F 20.20 m
  30. 21. 211.
  31. 22.2.
  32. Vr= 120. 21 Tumgnm + 2. 20. 2 tumxop t 2 de Sumnip. Et esdem modo se habet Z et 1
  33. Hinc 2. 20. 21= 10 2. 20. 22 =11 2. 11. 22 =12. Et par est
  34. 10d
  35. Et quia pari puie se habent 30, 31, 32. vel 40, 41, 42. ad 10, 11, 12. Hinc
  36. 15)
  37. (14)
  38. fiet 20. 21 = 30. 310 f(2 40. 41 et 20. 22 = 30. 32 = 40 42 et
  39. 12
  40. 21. 22 = 31. 32= 41. 42. Porro ex 49. 12, 14, 16, eoque et ex 13, 15,17,
  41. (17
  42. (16)
  43. (20)
  44. 21
  45. fit 20.20 =30 30 = 40. 40, et 21.21 = _ 31. 31=41. 41.
  46. 19
  47. ((Na 20. 2 = 35 31 Ergo 31 = Nam ex 16 fit 32 = 21, 22: 31. (Ex 14) f = 202
  48. Ergo 21. 30 = 20. 31. seu 31 = 21. 30: 20 (sed ex 12) = 20. 21: 30 Ergo 32
  49. Ergo 30.30 = 20. 20, idemque in caeteris; cum par sit ratio
  50. 22
  51. Hiac possumus facere v = 20 X+m + 21 X+n - Z2 IX+ p
  52. Z= 20 (xIm -Z1 YXIn + 22SXFp, et pL2otmtm
  53. Hinc ut resol ita satis factum est aequationibus 12, 13, 14, 15, 1b, 17. supersunt
  54. 25)
  55. equationes pro jam patis faciemus et aegqe 9, 10, 11. Est ergo exhii est = 12:, 22t=
  56. ex 10) 11:, 2.20 Ergo (ex 24 et 25) fil 11. 21 = 12. 20. seu
  57. seu 212 12. 20 : 1
  58. 2
  59. unde fit 20. 20
  60. Ergo 21 = 2bc: b = a: 20,
  61. t
  62. sit d= 20 trim + 2 Sn tE S ta+byu=vo e+ syus = LZ. Ex 5 et 6 explicatis rascuntur
  63. Ergo 20. 20 = ab:c
  64. (ex 9) 2. 10. 20; unde fit 10 12 = 2. H. _ seu
  65. 210 et2 2. 10. 11 : 12 et 21 et pari jure
  66. 30)
  67. 21. 21 = l2. 10. 12.12 et 22 = 2. 11. 12: 10
  68. 20
  69. X +c
  70. Y v = a + Te sX + M. X LH.
  71. 21. 21 n
  72. 22. 22
  73. 20 d =a 20. 22 = b 21. 52 =c
  74. 22 = C: 21 = b: 20. Ergo 21b.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 138r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0275?run=74