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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 23r

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: 0.79.

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. 93v); this page is its right half.

The machine reads it as

  1. Ad dimensionem c curva Ellipseos aut Hyperbolae requiritur qud
  2. sumum omrium y= Saa +bXx
  3. aa + CXX
  4. qudtoscalitur a geadraturms rutionales
  5. seu y= Saa + bXX, aa + CXY. Quae revocabitur ad quadraturas rationales, si possit
  6. C
  7. aa + Cx
  8. ebeclecet
  9. Quadra e
  10. extahiradix ex Caa +bXX, aa + CXX seu ex a + baaXX + bc X
  11. 2) compendi causa baa + caa vocetur e et bc vocetur h, ergo a + eX X + 1 4B caa
  12. a
  13. a
  14. quadrato
  15. compendii causa (() sit B+ c = e, et bc- h, fiet co + ecob+ h v quadrato itaque debert
  16. Y et co inveniri in integuis quo ad indeterminatas. sit v = 10 + il n + 12n F 13 n + an e
  17. et C0 = 20 + 21n + 22 n + 23n + 24 nt et et DC~
  18. quibus Valoribus substilutis in aeq. 6 debet inde fieri aequatio identica. Sed sffecerit rem
  19. antabimus intio in brevissime hypothesi, ponendo v = 10+ un et c = 20 + 2n et
  20. 9= 30 + 3in +32 n firt c0 = 20 + 4. 20.21 n + 6. 20: 21 n + 4. 202P n + 21 +
  21. 10 + 2 10.1LN + IIN exaeq. a R, COB = e1010 +2C 10120 A +e. H. 20
  22. 20 + 2. 20. 21 n + 21 n
  23. 19320 + 2. 10 11. 20n + 11. 20 n
  24. +2. 10. 20 21R + 4. 10 1 2031n + 2. 15 2021N
  25. + 10. 2 n. + 2. 10 1 25 n + 1i ai H
  26. 10. 2021 B 410. 11. 20.
  27. 10t. 25 p2 10. 1125 X
  28. hv = k10 + Ah 183 H1n + 6h 10. W N + 4h 1D. 1pn3 + h W1 n
  29. 1(B)
  30. O2 = 30 + 2. 30. 31n + 230. 32 n
  31. +31. _ n + 2.31. 32n + 32. n 7
  32. sit ergo 30 = (202+ e. 10. 20 + h. 10 et 32 = 121 + c. 112. 21 + h. 1, 4
  33. t
  34. et 31 = 16. 20. 21 + 6h. 10.112 + e. 11. 20 + 42. 10. 11. 20. 21 4 6, 10. 21
  35. suprsunt duae aequationes. 2. 30. 31 = 4. 20: 21 + 4 h. 103. 11 + 2C. 10. 11. 28 + 2C. 10. 20. 27 + a h. 10. 11
  36. et 2. 31. 32 =
  37. 2. 31. 32 = 4, 20. 21+ 4h. 10. 113 + 28. 111. 30. 2] + 28. 10. 11. 2p 4 4 h. 10. 113
  38. 2
  39. et fit 6_ 20+ C. 10 W0 +h1 in 6. 20. 2 +6he1. 1 + C. 1. W0 4 4 p. 19. 1. 20. 21 F e 10. 2
  40. et fit +20 + 2. 10. 10 in 6. 20 2p + P. 1 2 + 40. 1011 20. 2 = (21, 2. 10d P. 1. 1. 4
  41. 2.
  42. +h. 10
  43. 6h 18. 15 C. 10: 25
  44. Item sinilter + 21 + e. M. 2, in . lo. A 1.
  45. (20)
  46. J2H 10. 1(3 P. 10. 11. 2)
  47. Quae duae aequutines 19 et 2o solae restant praestandae. fit C- fLgA - NN: B.
  48. t h. 11
  49. fit LLB= NNA et quia aliquiod arbitrarii superest, faciamus C = 0 fiet L = b et M-0
  50. ot L= 0 fit 1. 21 = 11. 2h. 10 + C. 10. 20 4 21. 2. 20 + C. 10.20. seu
  51. (23
  52. 11. 21 = - 20. 228 + 2. 18: 10. 2h. 10 + P. 20
  53. et ex N ~0 fit 1P: a 1I: 213. 2h. 10, + 11. 21 e. 20 + 11: 21 C. 10 + 2. 20 =0
  54. ita in aeq. 23 substituendo valorem ex aeq. 22. fiet:
  55. 28,2. h 10. . b. 2. 2 4 C 1) +26C. 20. (2) 2. 2 + C. 10. 10. 2h. 10 + 2. 20 4 20. P. 10. 220
  56. 2h1c. 28. (] 220+ C18+ C. 20, 20.10 (21228+2.10. 2h. 102+ P. 25. + C 10. 20 10 220 L C10 ) 1. 5. XC 0 pJ. 2 10 (. uv
  57. Rarsi in aeq. 21. seu ob C = 0, fit C 6h. 10: 11: 21 + 4 C. 10. 20 CII. 31 + 6. 200, ubi lollendo 11. 21
  58. ()
  59. e. 10
  60. in aq. 25. per aeg. 22. habebitur rurtus aq. inter 10 et 20. Sed video cum aeq. 24 sufficial ad
  61. e. 2
  62. ere
  63. invenendam 10:20, si iterum reperiretur C. 10: 20 per aeq. 26. prodituram vitorem, inter
  64. eat relationemm inter datas quod non licet. Itaque jam vide, non licere ad hibere
  65. eqvationem 21, adeoque 1 nec L et M sed simpliciter insistendum esse aequationbi, 19. 20
  66. evera enim res redit ad duas incognitas 11: 2 et 10: 20 sit li. 21 = , et 10. 20 =
  67. set A- 269 1+ h p + C p et C = 28 2i, 6h p4 + C99 +. pp + de P1N6, et L = 20. 1, 2 + Bt ex qt ep
  68. ce
  69. et M = 20. 2B, 2YP9+ CG tefq
  70. seu brniloque A = 20 20 D B= 21E C = 20. 21. F L = 20. Q M = 20. 213R
  71. a 1+ h 9t + eq
  72. et et cpag 19 (20. 29) DF = (28. 2 2 et (21 20( F = (20. 21 R
  73. derge
  74. epE
  75. (2
  76. 1+ eq +h4t, in 6 + 4 epqt Cqq + pp +6pp 9q = L2, 2 + exq. + C q + 2h past
  77. ab qu. 27. subtrahas aeg. 28, fiet c9. (29) divisibilis per p-9 adeoque licet facere (2) p26
  78. 27. slis equalu 1+ ex + hpt, in 6+6epp +6p ( 2+ + 2hp quae aequatu est
  79. e +ahpt, adeoque fit (3) + 3C pp + 3 p = + EC p 2h pt
  80. quae est plana
  81. t = e pP = . sed jam video non licere in gredi hanc viam, nec facere
  82. instantum, unde et xe foret stans contra hypothesin
  83. et 2 essolvre alio modo ordinario nempe per ag. 27 habetur q4, cujus ope
  84. d hhabebit ratiorem
  85. vatio ad solam p quae verect ne satis alte assurgat. Hoc soluem
  86. velitur cgil t ar. 27. et 20 palte Por q este rad es esisde aequalibus

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 23r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0045?run=73