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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 173r

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. 172v); this page is its right half.

The machine reads it as

  1. Aequundo duos valores ipsius M ex qiput et nc. fiet
  2. (inIFM. 13. (416. 315) U m no (483 = 405) nnG id. 3o5 qqui). + aumg Cosit a ) fbrac)
  3. O= 112. 310 Mo 31a to5. 2o. 1 9) +2. 1s ui gn (gu gos, q2 (0) MM. + 3. 112. 30) 10, (91 a 5oz - 40) 310) l
  4. Habemus ergo duas aequationes 8 et 121 ambas secunctum C et n sed quia una harum duarum
  5. potest quidem inveniri pervulteram, sed non amba inter se, ideo debent coincedentiar hae
  6. duae aequationes, ut vel prane plane sint identica, vel saltem ha eaedem, vel saltem
  7. habeant communem ladicem, quod sufficit. Compendi causa sint duae aequatio
  8. 610 l + 603un + 613ln + 600 aa = 0 et poll + go3nn L7 13ln 4 700 aa =
  9. Tollarmus literasB N ergo et d invirem fiet. brall 610. 703l(+ 603. 103 un +613.703 In + 600 o3da
  10. 603 2603
  11. 603. 710l607. 703 nns 603, 113 In =- b03. 700aa
  12. (613 - 4. 610. 60 ) l = 4 600. 603 au - 613
  13. 2. 603.
  14. 703 nn + 703. 713 ln + Z 713 = 4713Il = 710. 703ll - 700. 73aa
  15. fiet 703R + h 713L = N(4 713 - 710. 703) IL = 700. 703ac
  16. (713 - 4. 710703) Il = 4. 700.703aa = 713l
  17. 703 f613 - 4. 610. 605) l = 4. 600. 603aa = 613. 703l ( 603 1513, - 4. 710.703) lL= 4. 700. 703 au -603.713
  18. sed ut n habeatur per l rationaliter nec tamen ratio n ad l fiat data; oportet
  19. 2)
  20. g . 13F 4. 110. 763 = 0 et n L 703a . daae, b2d 60. vet ilatit lntie
  21. Et superent.
  22. Et superent 703t Z. 703 a Y- 600. 603 = 613703l ∞ 2. 653 a V- 700. 703 - 6og 7 13l
  23. unde duae aequationes 703, 600. 603 = -603 700. 703 seu 1703. 600 = 603.700)
  24. vel 608.703 =
  25. et 1613. 703=603. 713 Ex. et Z est 612215) 610. 63
  26. et fieret. S (2 403
  27. 705
  28. et ex + est
  29. 2 710. 703
  30. 610, 603.703=710703. 603, unde vel 603. 203 = 0 vel. 620. 703 = 111
  31. Si 60370) =D non admitsitur fiet 603
  32. Ex aeq. 1 et 2
  33. 613 - 600 si 603 703 non aotur
  34. 613 4. 610. 607810.615
  35. 7132 = 4. 710. 703
  36. 710.713
  37. 610 - 603 - 713 - 600
  38. 610 = 710
  39. 000 700
  40. et denique 613 = 4. br0. 63
  41. itaque revera duae aequationes 9 et 12, quoties et n extant tantum
  42. in gradu secondo sine l et n si primi gradus, debent coincidere inter de
  43. efficiamus primum aequationem 613 =4.610.603 quod in aeque Dabit
  44. 613 = 2 1610603. et fiet L(410 -310). (403-303) = + . I4 (310. 303 + 410. 403) + s (410 303+ 310. 40)
  45. en rgritio nene
  46. seu +418. 403 = 410. 303 = +, 3102303 + 418, 405 + 2. 310.303. 410. 403 pro eiui 5i 1
  47. 410. 303 +403. 310 =0 seu 4W = 31
  48. 418. 3035 +310. 403 + 2. 310. 303. 410. 403
  49. 41403 + (2, 410 303) +(4). 310. 303. 410. 403 =0 5e u 410-- 30
  50. 3102. 3032
  51. si = sib, , fiet
  52. et nx 82d
  53. aro 387l. 400 5 205) un +. = (316. 105 0. Aor. ) In 4 2 (30 303 o. 405) (ab tac)
  54. 2. 703
  55. Hi duo valores ipsius n, ut aequentur, fiet
  56. 4. 10403..
  57. +2. 123. 310, 40. (310 4032 410303 ln
  58. et fiet - B sn = sial = = ((15- f10 Co1) U -1 600. 603 aa
  59. seu n n-
  60. seu n
  61. +2. 72 n (3B0. 303. uo. 4o3) (abtac)
  62. R e 603 nn, + 603. 613l1 + =613 l = 4 61 = 610. 603l = 600. 605 au
  63. invenionius literam n
  64. 700
  65. Sin + sit a fiet
  66. 4032. 310
  67. 4032310
  68. 403 30)
  69. p. 110. 403 + 3 10. 303 =0 ff + g9 + f = 9 fit sf +59 + +99-
  70. (2) 410. 403 =+ (4), 310. 303. 410. 403 = 0sin 410403- - 310. 503, gg - 99 2ddd
  71. seu u
  72. 3. 3032
  73. 3102. 303
  74. tantius et fit f+g:
  75. priore. modo fit 410 303, :, 403. 31o =
  76. postenore fit 41o 403:, 310. 303 = consenti seu f. 9=
  77. seu f:g = f3
  78. = - 403:303 fiet 403 - - 110, 303: 31
  79. prre do quo (BOZ pusterore 410 (4) 303. cum jam pri aequatio L()(
  80. adeoque cum sit = 31oval + 303 san, fiet D = 410 +al - 410(303: 310) an. seu fiet
  81. 283 123(410 -318) FL. V2. 310. 410 10. 13 40. 203) sisumamus qeo. reo
  82. orenes io at rodaa, in que atit at cocoerrod
  83. si fecissemns 610 =0
  84. et 603= 0+ adeoque et
  85. 710=0 et 703= 0
  86. et 6131600 = 713:700
  87. habuissemus n = - 600a
  88. Sed hoc non licet
  89. Nam sive faciamus
  90. n = .. l sive n =. 1 : l
  91. foret In rationalis
  92. contra intentum.
  93. ebbe to
  94. d
  95. et 6137 = 4. 610. 603
  96. vel 7137 = 4, 750. 703

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 173r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0345?run=74