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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 341r

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: 0.85.

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. 340v); this page is its right half.

The machine reads it as

  1. ppoliia trausici posse
  2. Hoc loci tamen videntur omnia minus
  3. 1. stit (t
  4. (31.2. 20 A2 21
  5. 4
  6. Ar Ex aeg. 3. fit 180. 34d = 20. 1a+30 (3) 2t. 1r1, +ba
  7. 2. 10. 30,50
  8. faciamus
  9. 110. 2. 1 -72. 20
  10. 50, 10. 3( - 11, 30 690= 50, 10. 31 - 11. 30
  11. han
  12. equ. 5. fil. 10. 340 = 10. 21 + 11 20 + 20. 31+ 21.38
  13. 2. 50. 10. 31 + 11. 30 40. 30ba
  14. benique ex
  15. Unde ex aq. 9 fit 1031. 2031 + 11. 2030. 31 10. 1. 21. 30 + 10. 21. 30. 31C vel 20l1)1030,. 11F31
  16. Ex 10 et 8. fil 20. 104 30. 10.31Y1130 10.30. 21. 10+ 30 + 10. 30. 20. 11431 fit 20
  17. ,. 16. 36 100
  18. 10470. 10. 31+ 11. 30 - 10. 30. 114 31
  19. Ex 10 et 9 fit 21. 11431. 10. 31+1130 = 11. 31. 20. IF31 + 11.31. 21 Fo1 50 fit 21 C) 11.31- M F2
  20. possemus jam jungere egq, 13 et 15. qui ambos leges homdeoplotorum observant, 11131. 10. 3) + 130 - 11. 31. 102
  21. ed praestat
  22. tamen alteratiam harum Conjungere cum aeg. 11, nam eo ipso quia sic proditiae quatio
  23. quae si non observat leges homoe oploton, necesse est quaedam in ea evanescere, ut ad homveopu
  24. F homoeoploton redigatur; cum, quae hc proditura est, sam tum sit simplicior
  25. quam quae ex 14 13 et 15 orietur, 2an ex 1 et 13
  26. 10+30, 11+31, 1031 +430 = 10. 30. 1143, = 11. 31. 10F30
  27. fiet
  28. sit 10+ 50. I+ 31 1931 +130 = 10. 30. II431 + 11. 31. 10 + 50 quoe aefontio est honocoptotos
  29. quod si fiugeremus 1 10430 = 11 + 31 ifieret 10. 31 + 11. 30 = 10. 30 + 1. 3) e ex 1 per1s. fere 3
  30. jam quaeramus 140. 340 ex b et 7. fiet 140346 = 2. Y18.31 282] - 10. 14 21. 2 - 3034 30 20 + 11. 30. 20. 21
  31. 50. 10. 31 = 11. 30 et fiet
  32. ubi numeratorem explicemus, et primum pro 21 ponamus 20. 11. 31: 10.30 ex aequ. id
  33. 10. 3(. 20. 21 = 10. 11. 21.21 - 30. 31. 20. 20 + 11. 30. 20. 21 = 20. 2
  34. 10, 30, 11 31, . 31 + 20. 1 = 10 31. m B. M1. M. 31. L. 10. 30. 3. 3o = . 10. 11. 31.31. 10.3∞ - 1. 15 + 10. 30. 3031. 1111 - 10.30
  35. 10. 10. 30. 30
  36. Ergo ex numeratore epharento fit 20. 20. 26. 3, 1. 3130. 30, 10.30- 11. 1 L
  37. 10. 10. 30. 3
  38. aliter 10. Z0 H31 -30. 30 + 30. 30, 1. 1- 10 50
  39. aieoque fit 1010 = 10
  40. 31. 20 H1. 1.28 31, 16. 11 26. 31 = 30 30, - 2. 40. 3, 110 30 1 M, 1131 3030
  41. A13. 3B3, 10. 30 - 11 a
  42. 10. 31 = 11.3 antequam
  43. a contrahi adhuc amplius calculus in aeg. 21 possit,
  44. eam quadremus, p lollamus inde prius et it et 31 quorum valores quaecenus ope ce 9g. 17. et 18.
  45. ex ag. 17. fit _ 31 = 10+ 30 - 11 quo valore substituto in req. 18 fit 10. 10(410.30 -10. 11 H(11. 39 = (0. 3d + 11. 16 13 . 1 1
  46. Contequam Uet vero apparea
  47. seu 10.10 + 11. 11 - 2. 10.11 = 0 seu 10 -11 = 0 seu 01 1 = 10
  48. E Et similiter 31= 30 ita in aeqqu. 6 et 7. evaneselrent 140 et 340, nec invenitentur
  49. sed arbilrae sed semi arbitrarcae manerent, facto tantum ex ipsis dato; et
  50. lunde fiet 10. 1t0 - 1) = 11. 10 - 11
  51. ex aequ. 6. 1t fier (explicata 21) fieret 10.30 - 111. = 0 et 11. 31 - 30. 30 =0, ande ob 22 et 23
  52. feret 30= 10 _ utrobiqus, quod placet, quod ita non prodit nimia determinatio
  53. sed video jam in quo peccaperim, omsomisi perliceti ba, sunt. ex XX + ba
  54. tende falsae aequ 1. 14, 15. itaque rem resumamus
  55. 20, 10+30. 11. 31 = 10. 30. 21. 31+31 + 10. 30b9 et fit
  56. 10. 30. . 11+ 31. Et ex 8 et 10 fol 20. 160430. 10. 31 +11 50 = 1033, 10021 + 103. 142, 2
  57. 1 sd ergo nunc in aeg. 4 suppleo
  58. sed quia in C3 et n rursus labet 140.340 et fit 21= 20, 10+ 30. 10. 31F11. 50 = 10. 3a. 1+31 3: 10. 20, 10430- Quos duos valores ptru 21 exegg. 11. et 13.
  59. ompe ex
  60. ideo haec aequalio aeque equemue inter se, et fiet: it. 3e 10r 10. 11. 30. 31. 1ot 30 20 - 10. 10. 30. 3c. 101 30 ba = 10 10. 11 31. 10. 3( 1130. 2
  61. 1on3o 31.1 0 130 f. 1010,103B, 1131 - o+ 30. 113) 1 t 38 .
  62. - 10. 10.3030. 11+31 29, et fit 20 (8, 10110. 30. 30 1at30 ba
  63. 10.11. 30.31. jer30 +. 10. f6. 3630. 1143, = 16.36. 104 30. 1143,. 10314430 10 vel 9 vel 10
  64. Ego per 13 et 1sfit 2(1) 16. 3b ba 00. 31+11. 30 - 10. 30. 112)
  65. 31. 20 = 11. 21=10.21 ∞ 30.20
  66. tollendo 140, 340 ex
  67. fiet 140= + 340. Ergo opus est adhuc duab,s literis habemus autem arbitraries ad huc residuas:
  68. Superest tantum una investigenda aequatio
  69. ope a99. 6 et 7. s videamus an non licept facere
  70. sed ita jam prodit ncommodum, quod non praevideram, et cujus remedium in hoc
  71. calculo non apparet, quod nempe ex a (ut aq. 1 reperta est, ita similiter
  72. 10, 11, 30, 31
  73. ficilt 21 = 11. 31. 70 ∞ 10+ 30 = 10. 30 ca : 60. 36. 11+31 unde sequitur absurdum, fore a
  74. Nec video quomodo hoc evitars queat, si Xx + ac et Xx+ ac
  75. ponantur illud = 0∞ 5, hoc 59G Ergo, non licet facere ut O et e similiter se
  76. ba = ca seu b =c
  77. habeant cum inde hoc loco oimodum aequalitas sequatur, secusfuisset, si sit ecrammpo adrata
  78. Motandus hic usus considerationis similim. sed factis ergo C et
  79. valore dissimilibus, perit fructus divulionis, ut x tac et xxaac separatim aequentur
  80. cateu alicui

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 341r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0677?run=74