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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 28r

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: 0.83.

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. 27v); this page is its right half.

The machine reads it as

  1. ∞ OD in OQ in D4 = 00D) P
  2. sit ax = CD et ax + ab = O et _x +ac = DC
  3. finte On = C2 - ab = 52 - ac et B = _ a (b - 5) ab + OD: 0 = ac + C),: 1 sit abD + BV -acCteoF
  4. faciamuse C = 1P + Na, a :, 30V + 31a et D = 2.V + Va, a:, ZoV + 31 a
  5. fill - 10. 100V + 2 10. 1aV + 1. 1aa, 20V+ 2a, a = +W. v. 20, V + 2. 18. 1. 20aaBP + 11.11. 20a B + 1(11. 21 a
  6. =+30 pV 4, 10 2 av 21. 2 aa, 1oV AIa, a = - po 2020 - 2.
  7. on - 2.11. 20. 2 3∞ - 11. 21. 21a7
  8. = 30. 30 vrt 2.30. 3lav + 31. 31 aa, 20v + 21a, - aa b = - 20. 30. 70 aB - 2. 20. g a. 31 aa vv = 20. 31. 31 a
  9. 21. 20. 20 aavV - 2. 27. 3031 ar
  10. ut destruatur V, fit 30. 30 = - l0. 20 (10 -20): (10-20) Ergo 30. 30 = 10. 20 et parifua 3HH. 21
  11. et pari jure ut destruatur V, fiet 31. 31 = = 11. 21, Ope prioris tollatur _19ope posterioris tollatur . 11
  12. pyt 16 2 - 30. 10: 20 in aequationibus praedituris, ut sint coefficient ipsius v, et ipsius V, aequales nihilo. Et in duobus
  13. istis coefficientibus _ etiam est asenomia, ut scilicet unusfiat ex altero per mulando 10, 20, 30, cum 1, 21, 31
  14. itaque habita unius prostatio destructione, facili habetur et alterius destructio
  15. 2. 30. 30. 1L. 20 . 307 2 + 2. 30130. 31. 31. 20 11. 20. 20 _-2. 2051 + 1130. 30- 2 20 3031 14191
  16. seu +2. H. H. 2020. 50.30 + 30.31. 3] 2 20 20. 30. 30. 31. 3 t 11. 1. 201 + 2. 11. 20. 3831-1 1. 2020303. + . 1. 20. 7 X p
  17. peli ando 10 et Ul.fito - 4 2. 130. 30. 21 31. 20 + 38. 21 + 2. 3010. 20. 21 + 31. 31. 20. 20 2, 30. 4 - 3 1. 113070 - 2. 20 3031 - 1. 2130, 20
  18. Iir Verulicando
  19. 10 et 21 fiet
  20. seuo 2) 28. 30. 31 + 307 21 21 4 (2s. 35. 20. 25 + 25t. 31. 31 - 2. 20. 21. 38.31C 20. 20. 3050. 71 31) 2. 28. 1 30. 3(=20 26. 21 21302
  21. 12 (202 1 36) - 2. 31 (20.30, 20 496) + 30.30 (20 +30) = 0 et divisis omnibus per 20. 20 + 30. 30
  22. ep destmendo,
  23. Et prorsis eadem prodibit aequatio ex v destruendo
  24. 21 sed hoc non licet, nam ita fiet D quantitas constans. Quin et si conjungamus
  25. 31.20 = 30 = 0. seu 31: 21 = 30. 20
  26. nc huic aequationi binas priores 30.30 = - 10. 20 et 31. 31 = - 11. 21. fint 31. 31: 30. 30 = 11 21: 10. 20
  27. sed 21: 20 = 31: 30 Ergo fiet 31. 31: 30. 30 = 11: 10, 31: 20 et fiit 31: 30 = 11: 10, 1el 31: 11 = 30: 10. Ergo
  28. etiam C desineret esse constans. Haec ergo via non procedit.
  29. Ergo pro explicandis (3 ut 9 assumamius literas binas: C = DaV+ 2+ 12a
  30. v + B0Z + 56a
  31. fiec + ()3D = + l0. 1ovV + 20. 2572 + 2. 10. 20vZ F 2. 19. 12 ba + 2. 25. 12 Z a +12. 1 aa, 300+40Z + 3+a 3f a
  32. Fiet (- 99) = 4301oVMt 40. 407 Z+ 3. 30 40v2 + 2. 303qua + 2. 90 347a + 34. 34aa, 10V + 40 Z +12a, - a
  33. O= +acO = + 50 50 vn + 60. 63 77, + 2. 50. 60pZ + 2. 50. 56Va +2. 00. 56 Za + 55. 56aa, 18v +203fna, + aac
  34. l- abD = 4 50. 5ov P. + 60. 6077 + 3. 50. 60VZ + 2.5056va + 2.6056 Za + 56. 56aa, 30 + 402 +3 4a, = aab
  35. Hic tentemus tollere Z, Z3, VZ2, aZ2,
  36. +20. 20. 4∞a = 40. 40. 20
  37. d346. 40.
  38. O2 1210. 20. 40 a
  39. + 60. 60. 20c - 60. 60. 40b-0
  40. 265 50. 10
  41. D. = 30v+407+3+ a
  42. a 500 +60Z+56 a
  43. A2. 30. 40. 20) +250.60. 205
  44. Unie 40. 40 - 20. 20C
  45. etE 260=20 laib
  46. 60= 40_c o 10- 20l(.
  47. 20. . 1660 (roc 40b)
  48. - 60. 60.3076 = p 20. 39 (20- 2.40) .10. 40 (40 -2. 20) a
  49. - 10. 40. 127 +50.60. 12 7c
  50. - 2. 40. 34. 20. +2.60.56. 205
  51. -2.50. (D. 40) 7 60. 60 (10c - 30b) 4 3. 50. 60 (20c - 40b)d
  52. = 60. 60. 34 7b 29 L20. 34 a β2- 2. 40) 460. 60 (12C- 346)
  53. =3. b0. 5h. 40d + 12. 40 a (2. 20 40) 2. b0. 5b (20C- 406)
  54. Ex his tribiis aequationibus prestitis, haberi videtur valo. ipsius Z rationaliter per v
  55. +20. 20. 34a
  56. in aequationibus prima et ultima, absunt 10 et 30, quae possunt reservari mediae
  57. Z 11. 20. 42 toa
  58. 9o. C 20 toa I prima et secunda absunt 12, 34, s quae possunt reservari ultimae
  59. Aqui sut (60
  60. sed in nihil ab est secundae et tertiae, adeoque prima nullas proprias habet.
  61. 20. 40. 40a +60. 60. 2c media fit 30 = 10. 40 (40- 2.20) + 2. 50. 60 (40b = 20c) = 10. 60. 60C,:, 20. 204 - 2. 20.40 a - 60. 60 b
  62. dicidinosset in
  63. 60. fol, 20 10a =
  64. Sidil f. ret =C
  65. X ultima fit 34 = 12. a (40 - 2. 20) + 2. b0. 56 (40b - 20c) = 12. 60. 60C3:, 20. 30a - 2 0 +o a - 60. 60 b
  66. nhis pro b0 substituatur valor ex aequ. 1. qui est 60.60 = 20. 40 a (20 -40):, 40b - 20c
  67. 20. 40 20a 460 sid indeo trevis procedi quaerendo solas 50 50 ex media, 5b ex ultima, 60 ex prima equatione
  68. doibe = + fit ergo ex media 50 = 20. 30 (20- 2. 40) a + 10. 40 (2. 20 - 40) a + 60. 60. (0c 20b), : , 2. 60 (40b = 20c)
  69. Aru saibe - 14
  70. si firiol 20- qu, a m oc adbd et ex ultima 56 = 20. 34 (20- 2. 4) a + 12.40 (2. 20 -40)a + 60. 60 (12c. 346)3 :, 2.60 (40b = 20c)
  71. oc fatei quia ergo tot literae sp superfluunt, videamus an liceat sevare in numeralonbus
  72. sit roa + 3= qota + b) prima audem et 60. 60 = 20. 40 (20 -40)a :, 40b = 20c
  73. 2020, (a +C:, a + b) ipsorum C et D solas 10 et 40, et destruere 20, 12, 30,. 34, fiet
  74. e40 = 241 + c): (a + b
  75. et 2C. 40 = 4 60.50
  76. (sed ita C fieret
  77. et 60 fiet etiam d
  78. 50 = 10. 40. 40a + 60.60. 10C, :, 2. 40. 60b et 5b= pd ita fit et 56 =0
  79. itaque ante omnia conservare demius 20 et 40, ita stabil 60: nonplicet simul rejicere 10, 12, 30. 34, sed
  80. videmur posse tuto rejicere 10 et 34, fiet 50 = 20. 30 (20- 2. 494 - 3060. 60b,:, 2.60 (40b 20c)
  81. t inisii sit es ti, et 56 = 12. 40 (2. 20.40) at 12. 60. 60C, :, 260 (20b - 20c) et 60.60 = 20. 40 (20- 40)a:, ob. 20
  82. ita tpplicaro bosit 50 = 20. 30 (29 -2. 40) (40b - 20c) , t 12.29 4u ( quiae - 30. 20. 40 (20-40) Ab, : , 2 qu (tob- 201) 60
  83. 1 11
  84. seu 50 = (20. 20. 304065 () 20. 30. 90. 40 (b (= 20. 25. 30. 40 ab t 20. 30. 40. 4 cab) + 20 30 (20 r2. 40) fC, : 2. u( goba
  85. et 56 = 12. 40 (2. 20 - 40) (Geb - 20c) _a + 12. 20.90 (20 -40) ,: 2 qu (40b- 20c)604 seu
  86. SH = 12. 40 (2. 20- 40) 40F -12. 40 (2 20. 20 12. 40. 4020 a fF 12 20. 40. 20d C 1. 2040. 40 4D;, 2qu (gob- 201) 604
  87. fit ergo 50 = 2 30 20 (2.40 -20) aC = 40. 40 ab, 262 2 qu (40b - 205) 2 1 (20. 40, 20- 40, a :, 40b - 26c)
  88. et 56 = 12 +0 ( 20. 42) (1ob. 2oc t 2 (20 (2. 20 - 40) ab - 20. 204c, 12. 40: 2 qu (90b - 20c) 1 (20. 40, 20- 40, a:, 40b - 20c)
  89. dea: si esset 60=(0, fieret ex 1, 204 20=40
  90. ati adtuo unb acehonao o peletaee disi o oa t
  91. u te tius pari tndo dun lict lactre ab 40 ito pec lalea s d 250 simal uee lace totu
  92. 3A; vot 12 et 30 4
  93. o rondorai u
  94. H1 = 26b H. b) lbc -20 C guat)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 28r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0055?run=74