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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 382r

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: 0.78.

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. 383v); this page is its right half.

The machine reads it as

  1. X =
  2. X = lam XF = l + dm X = (+ X ellm. X = l + 4 ln + Ellmm
  3. Xx = i + um
  4. X = V + 3Um
  5. = 1 R alma cum = I1+ 2tm + mm
  6. X = i +alem +6Ulmm
  7. X = I5 + 5(a m + 10 l mm
  8. X = I5 + 5 Vm + 15 (emm + 20 l n
  9. X = 17 + 7 lom + 2t mm F 35 l’ nd
  10. = B3 + 3Ulm + 3lmm + m
  11. = V + aBm + 6Ulmm + 4ln + m
  12. = V + 5Im + 1ol hum + ollm + 5 bm 4 m
  13. = l6 + 6( + 15(2on 120 lint slbuislm + m
  14. =I7 + 7 (6m + 21 ( mon +35 ( + 35 (3, 2 llm +D In L m
  15. Regula ad namaros coefficientes. sit T forma n, quaeritur coefficiens, dibuntur exponentes 413,
  16. is erit numerus hnionum, rerum 4+3, seu 4+3, 413-1, 4+ 4 1, :, 1. 2. 3
  17. X = 13 + 3Um jam Um = Im X, fit X3 = 1 + 3lmX seu 13 = X - 5lmx
  18. nta
  19. (om = lm il seo 11 = XX - 2lm fit l’ m =lu XX = aUmm et l = X +- 4Bm -6mm = p - auX a binx + Gllmm
  20. = X
  21. II = XX - 2lm
  22. 13 = X - 3 lmX
  23. it = x- 4 lmxx + allmim
  24. V = X - 5 linX3 + 5UlmmX
  25. m = Im l = lm X - 3lhamx l’um = UmmX
  26. fiet l.= 3 - SImX + rellmmX seu ( = X - 5 lmX + 5 UmmX
  27. 16 = X - 6 lmx +9 lmmXX 4 - 2 l m
  28. Em = lm = lm x - allum xX + 2(3m lum = Umm l = Umm XX - 2 m
  29. 1 = p - 7 lmx + 14Umm X - 7 Pm X
  30. 1 = X6 - o lmX + 24 llm X - 12 (3m = X - 6lm X + gUmmax + 18 l’m3
  31. 18 = X - 8Im + 20 UmmX _ 16PmAX + 2l m
  32. =15ILmmXx + 30 (3M3
  33. lm = lm 15 = lm X3 = Gllmm X B + 5B mX Cmm = Umm l = Umma 23 ( ex
  34. V m = VmX et fit l = x - 7 lm X + GClmmX - 35 (m X = X - 7lm X + 14 lbum - 7 ln X
  35. 12 = X) - 9 lmX + 27 UmmX - 3d(m X + 9lm X
  36. 10 = X - 10 Im p8 + 35 Umm X - 50 ln X + 25 (tn XX - 2 l ’m
  37. Iu = X - 1 lmX) +44 UlmnX - 77CnX + 55 lin X - 11 L iX
  38. ju - X = clmu +sq llmmX = 112 ln X +105 (i X - 36 l ’inxx +. 2 lm
  39. l = X 3 - 13lm X + 65llmmd - 156(n X + 192( . - 91 la X + 13 Cm. X
  40. Et ita porro, columnae sequentes oriuntur additione numerorum
  41. columnae praecedentis, sius prime autem columnae in qua extet lon prosigitum 2)
  42. 2i UmmX +63(2m57
  43. 35 (2m 3X
  44. sit jam aequatio cubica data X + pX _ Y9 = 0 fiet pe lm = -p. 3 et P+ m = - q. et M = - p. 3l) nnich. 3
  45. et 13 - p (. 27(3) e = - q et fiet 1 4+ 9 ( = p. 27 et (3 = 1 = 49 + p) - L. 4
  46. vel X - 3p X = q sit p tm sit X - Uem fiet p = lm et 9 = (+ m3 et m - p: l et M = p. 1
  47. sit aequatio surdesolida X f pX +) PFX X - 5 pX + 5ppX = q
  48. et 13 + p C.(3) = 9 et 16 913 = - pd firt 1 = 2 4 + N(4+ 99 - p3) et m = 29 - s (199 - p3)
  49. _ sit X - SpX + spp X = 9 fint ln = p et ( + n = q ergo (3 + p (. 1) = q seu 10 - 915 = -p seu
  50. (10 - q 13 + 199 = a 49 - p et 13 = = q + Y (499 - p5) et m = L9 - 1( 19 - p
  51. Et generaliter si numerus par n sit impar, posita aequatione
  52. X - npX .= + ( (a - 1. n. 2 - 1), X (u -2. n. 3. n. 4 - n. 4)
  53. (n - 3. n- 4. n - 5. n-6
  54. 1. 2. 3. 4
  55. M. S. n- 6 ) X n - B
  56. n - 4. n - 5. n - 6. n -7. n - 8
  57. 1. 2
  58. n- 6. n - 7. n - 8)
  59. 1. 2. 3
  60. nug0
  61. (n - 5. n - 6. n -7. n - 8. n - 9. 1 -10 n. 7. n . 8. M - 9. M - 10) 6. Ma 12
  62. 1. 2. 3. 4. 5
  63. 1. 2. 3, 4.5. 6
  64. 1. 2.3. 4
  65. etc = 9. suet et sit X = l + m
  66. in
  67. 2
  68. et lm = p et M - C p: L
  69. 1. l. 3. 9. 5
  70. et In + pC. () = q et Jin = q1 = - p
  71. seu jin - q 1 + 49 = 4 99 - p et l = + q + Y (299 - p n)
  72. et l = 2) (29 + Y (3 49 = p : )) et m = 3 (.= q - 1 (+ 99 - pr7)
  73. _ et X = Y(+ 9 + Y C99 - p.)) + YC2 4 - ( 449 - p 2 1)
  74. ( qu i C794 - p 2)
  75. vel p = n (= 4 + Y ( 94 - p:)) +
  76. Hic calculus paribus imparibusque gradus est communis. Et credo etiam ad fractos
  77. si P sit radius et X sit subteus
  78. arcus circuli erit subtensa arius circuli nun qui sit ad priorem, ut n ad 1. Hinc cum p sit major quam 9
  79. et irrationales exponenles poterit applicari.
  80. un qumine unitate erit Y( 44 p) seu et q= 1) quantitas imagina
  81. sit ergo vadiqu 1 ares subtesa arcus saberr erit n cubcensa arcus qui sit ad qum englabtusa qut t ad A erit
  82. a e + fC 1 23)
  83. 31 = 4. 6. 3
  84. Bisa
  85. ot
  86. entus
  87. 3
  88. 5 6
  89. 2 2n L 13
  90. n+3 - 25
  91. ergo
  92. Ergo 9
  93. reu
  94. aTan + gR + h) =
  95. 25n + es=
  96. isras
  97. et proiit
  98. 13:
  99. 25 -1 d f = L
  100. y
  101. 3 = 25 +95
  102. nn +
  103. 182
  104. Ego nuran -2
  105. n+ 1, n- 3.
  106. B. p -, nt rontis - 9
  107. 4 20
  108. 5. 1. 3 - 10
  109. 1. 5. 15.35. 70
  110. 0 2.9. 25. 55
  111. 1. 3.6 10. 15
  112. 2.9. 25
  113. 1. 2. 3
  114. 65 s
  115. 51 44 - 10- 3 -
  116. 4. 32-4,-2 -2
  117. b. 5. 4 - 20 - 4 - B
  118. 123
  119. n
  120. I l.q et
  121. 6. 942, 4. 3 = 1 6 =9
  122. 1. 2.3.C
  123. 6. 54. 3. 2 - 4. 3 2 - 6. 4 -2
  124. 5. 4.32 - 32 - 5. 3-2
  125. 1.2.3
  126. 1. 2. 3, 4.5
  127. 7. 6. 5. 4.3 5. 4. 3 = 21 - 10 = 11

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 382r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0759?run=74