Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 20v

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: 0.84.

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. 21r); this page is its left half.

The machine reads it as

  1. ZF2 =, 5.
  2. 218
  3. Videamus an BOD. Vaa, seu Od. Y aa vel OD +a sit diisibilis peroc
  4. sit C = 12F 11t + 1227 + 10a D = 21t, + 224 + 20 a sirt OD, ad - 11. 21 h + 12. 322 2 + n. 22t2 + 11. 2out +12 20al + 10. 20aa
  5. O+ D seu 1H + 124 + 10a ducatur in 21F + 324 130 et fiet
  6. Extrmini hq ah2, L fi Y fit - _ 10. 20 a + 00 00d
  7. 12+22
  8. coinc
  9. 10+ 20
  10. + 10. 2 ab +10. 22 a 4 +00. 00 aB
  11. dentianda
  12. uhser B et . +. a gih 4 X l doaha a 3oa 4 + Lonua
  13. 2 31 Eo3l. 10320.
  14. Ex termino s sit 1. 22 + 12. 24 = 11 4 11. 12 22 + 12 427 1 21 mul iplictur hoc aepuatio per W C ut2C. 1+ 22 seu per MA2 F 1. eF12 21 (4 2t
  15. Siet 11. H. 22. 22 + 1212. 21 21 + 2. 11.12. 21 22 = (11. 11. 12. 22 + 21. 21. 12. 22) + 2. 11, 2(. 12. 22 (F 12. 12. 11. 21 + 22. 22. H1 2D+2. 12. 22. u. 2)
  16. (11. 22. 11. 12 + 12.21. 11. 12
  17. et fit 11. 11.21. 22 + 12. 12. 21. 21 - 2. 11. 12. 2122 =0 seu _. 22 -12. 2120 seu 11. 12 = 21. 22 et fit 31 -32
  18. Extermino Z puodit idem hoc solodisutmine, quod pro 1, 21 tonitur 1, 22, ut fiet g 2 t 1. 6. rar 2. 13 2. . 2 Z (1B A tront oproa, 00no d 10. 22 - 21. 20 = (12 + 22) 00 AB. a) Ergo per 2 et 3 aequantur
  19. 11. 22. 21. 22 + 12. 21. 21. 22
  20. Ex termino t fit 11. 20 +10. 2 = 10+ 20. 1 21 + N 1 9 2 10 10 a + 00 0B. fiet 1. 1 25. 25 119 28. 1. 5- 2 10 51. 1 1 sto 1. 4 oatt M. 4r0 p) 00r a0 B
  21. Ex aeq. 3 (tellendo 22 per a q. 1.) fit 1. H. 3 (2) 20 20 + 10 10 12(2)7 12] - 2. 10. H (12)20. 12. 21 = (10. (127 11 H + 10. 11 (2) 21H 13O M 1 + V. 20 2 ip1) e0 0d
  22. 11. H. Hrg fiet H H. + qu (∞ 2 q (10. 21 1. 20) - (10 +10. ~ t 1, 20 + 2021) 00 00 - 11 (10 1t + 10. 2t +n. 20 + 20 21) 00. 00 b
  23. Ergo fit y = 12 Ergo 22= 21 superest ergo 5q. 7. per quam datur relatio inter 10, 11, 20, 2)
  24. quod si ergo βCD +) aa dividi potest per O + D, poterit tota aequalio si dividi per O + D, et restat
  25. aequata in qua pro c et D substituendo vatores per tu et 27, habetur lantum aequalio
  26. simplex inter tr, et 4 seu n qua ut +.. 4 +. = 0 quod est desideratum,
  27. Nempe aq. N Divisa per O+ D dat (1 4aa) (+ 3) + (i 4an ) (3 + D +b +C) + 3 (31k + 344 + 30a) =0
  28. ubi pro (, D, 31, 32,30, β assumendo valores inventos fit haberetur.. +. 4 +. = 0.
  29. Nota quia q adhuc arbitraria est putassem hic tbum eju potuisse adhibit adhiberi utiliter, faciendo
  30. on aeg. 7 faciendo 00. 00d: a =
  31. qu (10. 21 - 2C. 20): (10. 11 + 10. 21 + 11. 20 + 2021)
  32. porro in B: a labet. 9, et invento. D: a seu B: Y potest inveniri 49
  33. porro in d
  34. sed video eo iorso quod I _ 12 = t 22421 redigi t et 2 ad unam litera
  35. seu non dari nisi in E t+2. ergo in ultima aequatione non forent duae literae
  36. itaque proinde res erit qc si suntiserans ( = 116+ 10a et D = 216+20 a
  37. et fuisset D = 1 2168 (6D +) aa = 14 2564 + 14. 20 a6 + 1020 aaq
  38. (et O+D = (11 +2) 8 + (10t20) a, qu
  39. quod ducendum in 318 + 30a dabil
  40. ex 68
  41. fit 31 = 11. 21
  42. 30 = h0. 20 a + 00. 00d
  43. 10420, 1+ 2 = 1011X10. 21 4 1120+ 20. 21
  44. 0 +20
  45. + 10. 21 a5 + 00. 00 40
  46. (ur2I) 36B+ urri oab + (ot 20) g0aa
  47. 20+ 2. 11. 21 40 20 + 41t . 00 ert
  48. aed
  49. 200. 00d
  50. Crprc31ab
  51. 200100H
  52. (010.11. 20620. 20. 1 21+ 2. 1010. 11. 21)
  53. qu 1 (102 1. 20) B:, 1. H + 2t. 2.
  54. 10. 21 -1. 20 = 00. 008 = 00. v0 unde habetur 99
  55. Hinc ex aq. s ( dividendo per O+ D, fiet (1- 4 aa) (O+3 + brC) + 3β8 + 30βa = 0
  56. 1L + 21
  57. et pro D +) ponendo valorem fit (1- eaa) ((1 + 21) 6 + otro)a +b+C) + 31 ( + 30Ba- ubi ut evanescat 6,
  58. fiet (neque enim determinata reddi debet) fiet (1 - 2aa) (11+21) + 32(3 =0 + 11. 21 (3 = 0
  59. et (1= +aa) (0a +roa + 00b + 0oc) + 30B =
  60. 1+21
  61. in quibus duabus aequationibus substituendo no inventes valoris 30, 31, 4. adeoque B, Y
  62. hab pote prodibunt duae aequationes nova, prastandae ope arbitrariarum 10, 20, 11, 21 nisi quid
  63. Ex duabus aequs novissimis sit B. ( ag) = β: (4an - 1) = qu (11 + 21) C_ B (104 20) a + 00btC), 1020
  64. subsit, quod impediat solutionem. Ex da
  65. 11. 21
  66. 10.20a + 00. 00
  67. seu 00. 00b = ((10+ 29 a + 00 (b+C), 10. 20. 11. 2,) = 10. 20. qu (1t 2) a 44) 1o. 2 qu (10. 21- 1. 20)
  68. qu C1 + 21))
  69. Habemus aequationes duas ad huc, huic conjungendas
  70. B seu L seu
  71. bc - aa (bbi cet ibe) () 10. 21 - 11. 20)
  72. = qu (00, 11421
  73. Hujus aequationis ope habetur (qu. (1+ 21))
  74. hatetur H. 2 21: 11
  75. qu (11+21) seu
  76. 1. 21
  77. 2 - 92 (5) qu (11+ 21)
  78. 4 -1
  79. I1. 21
  80. fiet
  81. d: a = V: B
  82. (3. Z = (10+20) a + 00 1b+c), 10. 20,:, 10. 20a F 00. 00D Ex c9. 2 fit 21. 21 + 2 f4. 2) + 11 = 0
  83. seu 21. 21 + (2 + 8), 2 + (4 + 4 P + BB ) 11. 11 = 28 (D + 48 + EB (1)) 1. 11.
  84. seu 21 + (2+ B) 11 = 1s (4Bd + BB) se 21 A) +(+CA + BC) = 2 A _ B
  85. ruitus ex 1 fit 10.3 = 20, . 1+ 2 = 00 1B: a) et 10. 2 - 20 = 00 18 + 21 0o et fit 21 2 00 ( a) + 20
  86. 10 - o (B: a)
  87. quCa r2) : 1. 21 =) B: seu 1 + 2 21. 21 + 2. 21. 1 + 11 1 (B. L) 11 21.
  88. 4 = a 4aq - 1 - A da bc - aa (bbtcet 2bc) = 1) a. et fiet
  89. 10. 31 - 1. 20, :, 11+ 212 00 fB: a)
  90. fet
  91. inde ex ab fit 1N0. 2121Y, 1. 112 20C2. 10 202) A(0. 1. 1. 20 10 o 1 X 1 20. 2 v. 10 21 21
  92. unde tandem
  93. seu Exerpino

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 20v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0040?run=74