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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 85v

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: 0.78.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 86r); this page is its left half.

The machine reads it as

  1. In omni omni aequatione simplice quotcunque indeter minatarum tolli potest terminus ultimus
  2. nam in ea est una ex ipsis, non aliter quam sic 10W+ 1d + , nec refert quot aliae ad sint. F aciumus ergo
  3. W = n + f habebimus dW =d + dp. Et fiet a 10M + ii den + 105 + 11de sit jam in aequatione absolutus 12.
  4. et fiat 108 + 1 de + 12 =0 hatebim subt (quae aequatio est tractabilis) Et sublatus erit terminus absolutus quodsi
  5. pluces adsunt pta literae plares totidemque aequationes literas illas continentes, poterimus unuue lotere
  6. sint ergo jam vinae aequationes ad binaflim carentes absolutis 30X + 31 + 32 d +33d p = 0 et
  7. 40 A + 41 n + 42 d A + 43d n = 0. Faciamus 2 = Y. b et n = P. b erit d = d. 6 + deo l B. et
  8. explicatione follerere
  9. d n = d l + deo GF itaque omnibus existentibus divisilibus per t evanescit 1 et habebimus super numera
  10. 30V + 319 = 32 d 1f + 33d9 =0 et 40 + 414 + +2dy + 43d8 =
  11. 30l1 = - 30my. + 30 nv
  12. 32dco ) 3edco My 32dco nV.
  13. 31C51 - 31 py, + 319 V
  14. 33dc093 3odcs p y, 33dco qV.
  15. 33dG = 33 dp y. + 33 dqu, F 33 pdy + 339 dv
  16. 42do + 43dc 8
  17. +40lp, 240 myt +gonv.
  18. +421B5 vilco Myi + 42dco nV.
  19. o Et + A 7 141 py et 41 qV1
  20. 143dcoG r 3lco py 1 243 dce qu
  21. 112d=+ramus + qdnv + 42m dy + 42 ndo
  22. 43d8 - 3 lpy3 + 439 dv et 43 p dys + 43 9dvs
  23. Hae binae aequationes 7 et 8 multiplicatae illa per e, haec per f addantur in unum
  24. dabitur sin eeaq ut compositum fiat aequatio tractabilis aodatur yductum in differentiam ectum
  25. ductum in differentiam eorum, quae afficiunt v
  26. = d3 m y - d, en v, + d3, pN) + dusnv = ad4 Smy-datuv + damys r da m
  27. - 32d m y, - 32dn v. + 32cdm y + 32 an B
  28. d33p y. - d339 v. + d3 n, td239 u
  29. -33d9V 4 37dv y 4
  30. quam-quanv. + 42Sd my + 43dnD
  31. 143y. 139V. + dispu 1dqetqV
  32. +42y +42d9V
  33. s aresy t
  34. mats per f
  35. Ex his aeqq 7 et 8 multiplicatis auctisque fiet aequatio 9, hanc divellamus in tres
  36. pite und
  37. Ita joend aequationem intres, fiet quaram ana erit
  38. huem dy + 3 en do
  39. 4im sy +grsndo quae aquatio est summibiles et fiet m7
  40. 33lp dy + 33C9 dv (10) 43 ds
  41. demus +d38V = dartny
  42. 2uamys 12ednv
  43. d33p Ry + d33qV
  44. ap Y +32dq V
  45. Armdeus arnder
  46. 13p dfy 439 df V
  47. 32em y + 32 env = 42f my + 42fn v
  48. 33C p y + 33eqV
  49. Reliquae binae aequationes in quas divellenda est aequatio
  50. 32Mde + 3n de V
  51. 33pa C7 +38qdeV
  52. pro destimendo v, fiet 30m + Sadcom +p + 3 3deo prum + 33 dp
  53. reliquis et y et v
  54. hae sunt, pro destinendis
  55. (1) 4o fmt au deosm + q1 F 4ye diospr de sam ris pes +u n ot
  56. usu ex eamdc
  57. -de sm sp B s ( 42 falu 13se 13 pas
  58. (+ 433C + 33 de - 31e) p 7 : (32C - 42f) m + β3C. = 43f.) p
  59. (11 d32C + 32de -) M 4 - 443+
  60. et da = -d42 f - 42 df
  61. pro destruenda V fist
  62. -d33 Cq∞ 2edn- 33edq 339de
  63. n
  64. aendsuqosinu 13 fdq 43 q
  65. 124,: (328 - 42f) n + (33C= 435)9
  66. quo duo valores ipsius deo debent aequari. Ut vero aequatio fiat facilior, faciamus eorum nominatores esse
  67. (4) (+re + 32de
  68. d435- 43df + 4p)
  69. in ratione aliqua V ad a, seu ut sit (32e- 44f) in + (33C- 435) ,: Bre - 425) n + (32 e - 435)q a:
  70. -da25 - 42df +40
  71. et inde fiet n = (16) = ~ m + (33C -435) p = (33C- 435)9. sedae quando numeratores
  72. Sed aequando numeratores valorum etiam multiplicatos pereta fint similiter
  73. 30em 13(4 3e +yide
  74. et fiet n = (18) = m
  75. v(a
  76. d135 - 43df +415
  77. a -d43f - 43 df + 1f
  78. +d3rC +32de
  79. dqs- 42d) + t0
  80. -d4f Baf +4s,
  81. - 1f 42d5 + s)
  82. +d33C + 43de - 31e
  83. Ergo ex 16 et 18 habemus duos valores ipsius n - a M, fiet vel N P = 1 vel - 435 - 47e5 + ail - 320- 425
  84. -1425 = 42if +40f
  85. se prius non licet aliops fol ( per 18) ct m.a = p: q quod noulicet dais = qu.
  86. quia ita V et C erit in ratione anad somet ut at B rideunt ad literam eandem, ilam praestat posterius.
  87. 2m =1 et (ct 1. q - m: n contra intentum
  88. haestit aeg. 19. uibi faciendo
  89. i inh 3ih valie
  90. ponamus P = 1. fiet ex 16 vel 19 n = ~ m, seu
  91. potumus enim vet q redici prodice y et V Y+B lit in C
  92. 33C = 43f C 3.1 92e- 92 t h: a, seu
  93. et ex 19 fiet: +d3 3ea + 23 de a = i 32 PR + 32 de h - 30 et ubi p Psatu sX exaeg. 2
  94. 2+ 42Fdh 32des d3 rek + 32e dh. 7tam ynjungendo cum aeg. 22
  95. darsa -43d5 atusa- d42 fh - 42 df h, + 40fh
  96. rdirca tuiaeaqret nea -rocti E 2 sih A . 21) F38C at
  97. 22. 173fa =43d5 a + darsh +a2sh -41 fa
  98. Cnet ACa Z-0
  99. sit jum 2p 2) my+ nv et g= p9+ qu et a p = am y pdn VF mag+ ndv et 19 3 sq qu. Fiet
  100. 32 du e + 33 lo 8
  101. 3idij = 32 dmy, + 3edn v, + 32 mdy +32ndv
  102. 1te
  103. a a
  104. agin aqu. u a Joh grat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 85v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0168?run=74