Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 33v

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: 0.74.

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. 34r); this page is its left half.

The machine reads it as

  1. Quaericur (dx LXx -bb, Xx- CC) fiat X- E + compendio-
  2. fiet Xx - bb = aa AA - bb n n, : M et XX - cC = aa N - cc n M,: e
  3. ex ambo Et explicando numerat: es fiet aa b=
  4. aa AA - bb n n =
  5. +sstx anotu
  6. =bB - bb pY
  7. et aadA -cc pn = +sftv
  8. et productum
  9. +2afc0 AV =(compendio) ast + tv
  10. 2bb Atv
  11. +2afco stn = compendio) a 3 + 2) Av
  12. 2 ccrt stv
  13. Ergo xx - bb, XX- cc = aa 5B+ 4 27 t~ + 2a5Y stV,: n ubi nominator est extrohibils
  14. ea aacgttort a ecocoto + a coa
  15. +aa
  16. a c = a et Btaacsts - bb P
  17. aeu =agtr taacoco -cc
  18. au se Z = an egttant aco
  19. dHo aui eroto -gafbboro
  20. ascc Wyytr
  21. +gaafscocotv
  22. ote
  23. arr mesio. aeff itet
  24. =4afcc corp 1V
  25. 2aece tr 2 AtV
  26. am = aet a9 +4aaH = aas - aabb + aaff - aacc + 4aaff - aats. aud)
  27. a tag = 2f - dd aecc + agbb = fsec -bbec + Hbb -6c bb = f dd D 2lbec
  28. +2afsis f _ co 2 tV
  29. +4afCD + +bbc b
  30. = 2c bb + c4) co 1 1 s 1
  31. et erit aaeg = 2bbcc = aadd et baaff - add = 6bbcc n sedt et 6bocc- A dd = 6bbc - be dd
  32. as+ff. af s1 = 2bbec = bedd et ff do t libe 2
  33. ta tandem pro be ponendo a, fiet et bb ponend
  34. aaeutlvr +bauzaate t
  35. quadd lv c
  36. =aadd cocob rar
  37. t renum sst estri
  38. unsee a
  39. aneg - f lbb1c a sdd
  40. en = aecc - agbb + 4bb6 = - ss cc + bbec - ffbb + ecbb +4bbcc = 6bbec - ff dd
  41. Erxpotardum aaegllvB + bua ts) tvcoco + acd +
  42. +6bbcc 1tvYY
  43. otu
  44. servabunt Legem jusitiae inter se
  45. 1t bocc et aF = bbcc
  46. pra 10) st ~) raa tV
  47. dadi qua Bt V) modieiru qu. (. 3. . v
  48. los , - LL240
  49. +2AYZ
  50. +ae Z + aY B
  51. ant ae HZ + a AtZ +ap VoZ
  52. raa -dd compendio ap
  53. bracideam lua, 8a. +94 Mropendio a ita
  54. (6a + dd
  55. co) raadd
  56. + 2a4Z YtV 1a222 - 4aco p. q aa 5 (1 2 aa dd
  57. aa _ itam srrationalibus fit aa ANZ = apt v +2aa (coco + Y) + co +
  58. sit at aZ = h, co+ V, fiet test n = ptv + Ea (Coc0 + p Y) 4 p Co . _ uut = plv F aZZ H ) c
  59. seu ah= a V + aazZ- dd co. Et coincrdentiando partes rationales, fit
  60. ANA tZ +abnn v7Z raepB + am toZZ-20g(0 2 + a Z - 4 co Zax cocopiP
  61. Trapco rapzc0
  62. ubi Z co et fint ahi M- 4ap tv taaquZe - dd coZ + dd coco.
  63. colp Ze0 cocd Et q ga DA LZ +aa M VZ, ap HWB + amtbZZ 2a gtBZ( + 2q toco arutquun Z tap 7 Xo c0
  64. quaenequatio multiplicetur per d et tollatur dd col et prodibit
  65. aa St VEZ tad nn Z = 2 to F am d tv2Z F, addgevah m - 8dd gtvaptv - 2 dd gtv a + ZZ + d1 4
  66. sed fortate hac explicatione
  67. +Haaddizalum _ Guaddz Zapto - aa ddz 2 42
  68. ap achh Apin Fapi6 aapptuo + ap a 2 apah n aptr ap p2
  69. inaq2. fiat L = 10Z + 1a v = 2∞Z + 2ta, c0 = 30Z + 31a 1P = (2. h) Z - co =- (30 Z = 31a
  70. ap- Z co (a : h) Z= co corp = (a: h) ZCo -coeo = R.h) 30ZZ + (a: h) 31aZ
  71. X = 30. 30Z7 - 2. 30 31 az - 31. 31aa
  72. ce a41 55I aha M = 4 ah. 40. 50ZZ+ ah 40. 51a Z t atr. 41. 51 a a = 4 4a p: 10. 2027 + 4 a p 10. 1az. + 4 a p.1. aa
  73. +00,00aaZZ 4ap. 11. 20 a7
  74. =dd (: 1) 00, 2 hZ _ - a. h) dd0o. Vaz tet 3ddna
  75. A = 40Z+41 a n = 502+E
  76. quid si omiiso 2 rem reducamus ad solas co et V. Nempe
  77. +3d. 3631 aZ + 31. 9 au d0
  78. aequ. 1. ex rrationilibus ert aptv + 2a a (Coco P()- aqco= aa An
  79. et 0o oot = nOC + 101 P + 108a et 00V = 210co + 20,1p + 200 a A- Z10c+ 300a = 450 1400a
  80. 00 V
  81. veo t 1o t1FWa 00. 00V = ot 2c5 + 212p + 20a
  82. natore 00. 00 raacoto + 00. 00 2da 1p Y1 = 00. 00 aqo
  83. 30. t eo) aui oi to
  84. 400. 400
  85. 06i00 dn = 310. 47 Ba cito BB 21. eB. A. P = 110. 201 aa cor est
  86. cust egratio ex utionulbus Uvo Y a ntv Coco ip) B adddtB col+C + 4)- agddcon W r as
  87. uuta smaplexo a let lolies toa
  88. tam pliau in aeet +oo
  89. pere lam ceipateilitm t, quam er e
  90. e uteooissu im
  91. ongaitu audda randon e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 33v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0066?run=74