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Leibniz-Handschriften zur Mathematik LH 35, 10, 1, fol. 12v

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: 0.80.

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. 13r); this page is its left half.

The machine reads it as

  1. 99- eC = 4lm DV
  2. et pp lx
  3. sit 9+ e = 2v et g - e 2m v
  4. ee -pp = b 4 l m XX et sit et p = 2lx e p = 2mx. und e fiet
  5. qu Iv+mo, c= sit (m = bc. firt et p = 2bx et e - p = 2CX
  6. et fiet q = lV + mP, C = lv - mV = bX + Cx. p = bx = Cx
  7. quod si faciamus l = b, et m = C. fiet X: v:: 1 = m: l + m, seu X = 1 - m v: LF m
  8. sit v = _ ltm. et fiet X =. g l = m et q = g l+m et e = g H - nmm et p - 9 L- m
  9. et 19q- ec. ec-pp 4 lm vX = 4 gg Im UI- mm. Im numeris
  10. 20
  11. est
  12. nam se qqee -qqp - e + cepp= mg 1m U- mm-
  13. 9u -mm. 1 - m = g II -mn, l + m - 2 l- m + l = m
  14. = gt I1 - nm , l +m = 2 lF m. 1- m + l = m
  15. seu
  16. = g4. H1 = mm in L) 1 = m - l = m. jam + l=m = ICF 2tm + mm
  17. =m = U + Um = mm f = 4l.m
  18. jam porro; debet esse (nn)= 169 em - n =(nn - 2ny + yy
  19. est autem n = eea 9 - Y et p = 2X - 9. Ergo r = p F9: 2. Ergo n = 9q - p: 2
  20. 96E
  21. est autem seu n = gln (m (mg, Ut 2l m +mm = U + 2Um - mm Em. a - 2glm
  22. lae
  23. ponum y = g4h. et fiet 169 l me i- nm = glm ghi
  24. P Fgh2
  25. seu emm. II un + hh : tmh. e g = lmh: umm. I- mm + lh
  26. sit 1 = 2. p = 1. h = erit g = 4. 3F: PE A 13. 2 9 - 13 n - 26
  27. 043 4 137 4. erit g- r: B et ( y. 16: B n = 8: 13 et Bet
  28. 64 132 F16 13. 4
  29. erit g= 2: 4. 9 + C.37 seu 9 = 2: 3
  30. y = 4. 4: 37. n = g. 37. L64. 37 - 16, 1b: 37 1. 9 = 64. 37 - 161636, : 37
  31. sit l = 2. m = 1 g - 1. fiet v = 3 et X = 1 et q = 9 e = 3 et p = 1
  32. ergo jam Y = p+9: 2 firt r = 5 et n = 4 et 9g - ee = 72
  33. DF 3
  34. 99- Zec - hh quadratum semaxis trans versi
  35. seriaxem dat senitatus rectum 4 = a jam hin: q est latus rectum
  36. SM + M N = 16 3+1: 15. Ergo GN = 16 s10 : 15. porro FN : MN:: FG: GM. Ergo fit:
  37. Nam 43 4. 3 ∞ 4. 3: 16: 15 :: 4 : r. 5 jamFZ: FN:: GM: G, N.
  38. rursus GH = GN(se 161r0 215) + N e GQ (. F9:: 3: 1:: GM: MN. Ergo Gq = 12: 10) F +
  39. ER C. AFR seu Cn. 4eo seu 5. 4: 9 ser 4 , 3 :. +QR (seu CBe - F 91 est autem FA.
  40. = 3. 4: 9 = 4: 3 et FN = 16: 9 et FZ = 16: 10. Ergo ER = 4. 31 10B) RH (= 5. 10. 3
  41. quia RAE RH: QR :: 5: 4 sed idem aliter OA = C r: 9 = 315: 9 = 5: 3. et OR = 25: 9. unde si anferas
  42. OH = 25: 10 e∞C et fiet OR - OH = 5 .l: 10: 3) 1. fit eergue
  43. fit ergo GH = 12: Yi0 + 4: 3510 +5: 3110 = 452t 45: 3 10 = 15: sio
  44. Est ergo GH seu 1 1s: sio triplum ipsius O H, seu 5. Ho quod etiam ita esse oportebat:
  45. 25. fL.9: 81 -1
  46. 25. 72: 80
  47. Ecidus la
  48. . cujus latis
  49. 15: 110
  50. ergo FQ = 4: 3. 16: 8: 16. S0: 15, = 4: sio jam F9: _H AO OH:: FR: OR:: FG: 6G.4.5
  51. F N= 16: 15. 4: 16: 5 = 4: 3
  52. Ergo BH( = 5. F2: 4) = 5: sio et quo D5 OH: GH:: 5 MN: GH:: 1: 3 f et GH = 15. S10
  53. n: 4
  54. 23d
  55. quidi qui si dividatur si pu 9- ee = 72. sit 49 CC: 4= 18 hit
  56. et 18 divis per 9. seu se latue transversum seu ter
  57. Ld∞. Da. 68:5:: 12:8: 36:f:: 1. 3. Ergo LD = B. 8: 15
  58. 29 = 80000015:5 = 0000024
  59. GM 16 16.5 MNa 16:15. GN = GM + MN
  60. c hn pust = = 12: 5. 295b 1443 25 e nn - pn = 16 - 149 - 1b. 25, 144-
  61. 256:25 - 16 = 16. 16: 25 -1 -616 - 25, 25 = 16. 9. 25
  62. =144. 25 n + m GM = 4 + 16: 5 = 36: 5
  63. d bL2 VIat +q
  64. integrum, seu a. Et fit a = 8
  65. OG5. FG4
  66. 2
  67. et ec -pp = 8 et S9q - ee. ee- pp = 172. 8 - 19. 64 = 3. 8 - 24 -
  68. = 400 - 144, 525 = 256: 25 ergo Inn -mn = 16: 2 - GM
  69. 16.5 + 4 =
  70. =: 16 22 s1: 15 seu 32. Hs Nam GM165. GM = 16. 3: 15 et MN = 16:15. Ergo
  71. AV, 8
  72. es
  73. 8+A - 12
  74. seu co= 7
  75. e+ t
  76. EC 3
  77. 4
  78. 159
  79. 69
  80. 16
  81. 232
  82. 0
  83. 144
  84. 4576
  85. 400
  86. 144
  87. 25b 1b
  88. 16 144
  89. 6
  90. 1
  91. 24
  92. 40+32
  93. 256
  94. 1600
  95. 176
  96. 1824
  97. 5.
  98. FR ~ 3

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 1, fol. 12v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068154:0024?run=74