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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 164r

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: 0.77.

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. 165v); this page is its right half.

The machine reads it as

  1. 120. 300 - 10. 400
  2. per comrpendium +21.30 - 11. quo vocitur . Ergo ex aeg. 1. fint 402 = 21. 302 Lap - ga, , la p - , 302 - ag
  3. quo vabore subsituto in aq. 3, fiet (20. 52 - 10 302
  4. Seu 302 =
  5. (21 - ∞1. 21) 302
  6. 2i Tap d 1 :, 20 - 10. 21
  7. as ap= re
  8. et 402 = 2 af B21. 19 ag
  9. (1) 11a f - 10 a9
  10. vel ert erit 302 =
  11. 11. 20 - 10.21, Vap
  12. 1402 5) 21 af- 20 ag
  13. U. 20 = 10.21, fap
  14. 21 at (- 1021 ag - 2 20a9 (+ 16. 21 29
  15. H1. 11 ia p)
  16. 20 = 10. 21
  17. quod satis harmonicum est
  18. Expedivimus ergo penitus aequationes 1 et 3
  19. (3) 20. g - 21. F 310.
  20. Ex aep. 2. fiet 20. 31g - 1. 40g = 21. 310f - 11. n0 f, aque ad eo 410 =
  21. 109 - 11f
  22. Hos valous abstihomus in valoribus 3B) = 140L. ibi 2oc3 o 10. 41 ((20. 2og - 2. as
  23. iti 20. 310 - 10. 410 = (i0. 203) e f 1120 ( 10. 20g 10 ls - 1 (10 i - 1. 20) 5
  24. 109 - uf
  25. et 21 302 - 11. 4ot = (21. 1 ag 2tvag - 1. 2tas) tu honque
  26. u
  27. Ergo. tandem siat
  28. 1.20 10. 21, Fap
  29. 1 20 1021
  30. .s16. C qu ( 10g -us) a ap n) +60 quadr (10. 21- n10) ffa
  31. 30+ (4) uf - 109
  32. 10.217 es
  33. 510. quadr (109. 115) (2tap - m)
  34. +601. quabr (102- y 20) ff a (5) aol
  35. 510. 69B. quadr (10.21 - 11. 20)
  36. ubi f significat 20.300 - 10 400, et 9 significat 21. 300 - 11. 400.
  37. Ita Et ha quiaque aequationes nihil aliud habent quod explicatione egeat
  38. iveninus, ergo 302, 402, 410, 301, 401
  39. et manent arbitrariae 310, 300, 400, 510, 601, 10, 11, 20, 2), secundum ommoditatem Explicande.
  40. dei Exhis ergo habetur Vujq quaeritur jam sydx est autam ix = 5io Zdv- vd Z.
  41. et de = - d B . (DV - 4.08) + 5a5 - 10d8 = d D (DP - 405) + (3d 3 - 20 d9) (M - 4C ∞)
  42. DD- 40Q faciamus atq sint dae = d B = -D NaZ: _20 et ( = - d3 Vaz + adt: 20 sat
  43. 26 (B) - 409)
  44. 20+ (∞D- 404
  45. vel do = . Atia Z F a tati dh, . 4 a eh. Et dx - si. Z 2a tdD + az latu ih + 6 ot - a bt
  46. D, 10. 601 a - p. 510aD + 1. 510a tatu = (2. 10. 601aZ - 11 510aD) (3. 20601a7. 21. 30 aD) f 11. 11a (2 2o ber az. 21 110 21) (a
  47. = 21. 510 a (2. 10. bol az - 1. 51Da))
  48. 2. 2061 a7= 21. ( aD +21510atat 11. 510. 21. sionaatue
  49. Du (220,60147- 21. 51041) = 21. 21. uaaatus
  50. I. hiac eih
  51. a a 86∞s1a. aQ. 2310a + a0 1. 3ua) Natr
  52. r unoa + 475) A488 - 21 2. 310 3e aG
  53. 22448 +72521510 gitati
  54. a ri +u. sio Balo ( 24 1. 10 + 46) 21. sio al +(5 (2 1s1o + Z6) - 21 sto (at 4 unv az ) fa 17
  55. a _Zh, F6 - 21. 21. 510. Mvaq
  56. Uubi sufficit Amissa parte rationali considerari iriationalem est autem ad = sid t dB +EDdz) catur it 8 = 510 (aqdG- raz 1 2)
  57. = 2. 10.601 0 az- 11. 5104D 8 = 2. 20. 601 aZ- 21. 510a)
  58. Dest 2di padus et est tertius
  59. desimanus B 20B = -+ tiz 20a0 = - + altue - dd aouti tadh = 40 av = 2d05 + ad h, ah. jam a C. 60) da - 2 40 va2
  60. et fint 40. 68 x = 40 ao - 4 0v 2, vndi sit + 2d Aa s) + a chz sat +. 2 atit 2 aqu satr a2 - 40 801 da
  61. seu 406et 1-
  62. 25 +63 sah et Y = 8 + 11. Sib sat. 40 Ddr. y- 4 +us1o at + (1. 5i02 + s) tat
  63. S= + 21.510 sati
  64. 22, B + 2t. scolat
  65. (2Y +asiob ) = 2. 510 (11. 5187 Sgat (B (1. s1o 2 47 253) - n. h0 (25 + 11. 510 8 al ) ) tat
  66. h22. 84 - 212510 at
  67. 7((l. 310B - 2sco 2) S - 11. 21siS 27) atue H (uS -214) 503 + (5 4 - 11. 21. 510 ab) 5) sat
  68. h2Z, 82 - 21 510 ati
  69. = rotah, fint 4( eo t77 ax 31 + 3o lat, 41 + 4olatu 5.50 saqe
  70. 51. 51 = 50 50at
  71. A 405du = 30 + 3 latu
  72. Iq 10
  73. R 18+ V + C0
  74. 3, 4 30 e1 +40, S1 25C = 31. 41. 3IL 31. . 504 31. 40. 51 + 31. 40 50 (n 31. 41. 51, - 31. 91.50
  75. a simoboreu
  76. 4b. 10. da 436. fl. 31
  77. S1B1 -. ∞ 30a 1a 50
  78. n
  79. ureoI Huvas
  80. 40 51. 5.
  81. 3 Q ugo us
  82. - 1141. 510 8al d2
  83. , 6=2t quat G

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 164r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0327?run=74