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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 219v

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.

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. 218r); this page is its left half.

The machine reads it as

  1. Sit uine formula
  2. 70tratpxxtek,
  3. pX + n. + etc. 6. et. volumus no
  4. tollere terminus summum et secupdum fiat X = GC 1902191, a : 80ZF∞1, et fiet
  5. +10, + e 101Z t et
  6. + H. 100. 200 N. 100. 201 do q. t ek
  7. +12108 300. 4
  8. 10. 100 GC l+ 10. P. 1011.7
  9. 11. 100:3. 200
  10. l
  11. 12100200. d 1
  12. 13. 103 0 d4
  13. +M. Crtooal ..
  14. +, 11. 100214.0..
  15. 1. H 72 V.4,
  16. FB3. C3 aa21..
  17. +3.13. 103 200,20)4.
  18. sageni
  19. rCC 200220)
  20. s
  21. +12. B1204 .
  22. +2. 12. 1. 500301 -.
  23. ei odi titor Z
  24. 1. 104. 2. Z 711
  25. 20027+ 2 200. 201Z
  26. ubi primum terminum faciendo aequa
  27. tem crihilo habetur ratio inte–
  28. 100 et 200, seu 100: 200, per
  29. aequationem quae origetur si fommul
  30. proposita esset aequitio
  31. lenm nihilo habetur ratio inter
  32. VoB at, 20), seu 101: 201
  33. 2 200Z + 201 5. _ hic si velleus valtere utrum
  34. terminum fieret 200: 100 = = 19: 11 = 201: 101. sed hor mplicet, nam ita X
  35. ita num ita sip X fieret constans sante Z + (101: 100) = seu Z- 10a: 11 = 0
  36. sed verum quia ita 8 ipsiu 2 priore modo fieret x - a, quod non licet
  37. posteriore vero nullus haberetur. Vator ipsius X, adeoque nec ejus explicatio
  38. tollerse non
  39. aut formulae mutatio Ergo novissime absolutam mutare
  40. non licef
  41. videamus an in aformula secundis gradus ut XdioXxFHX+ 12 liceat
  42. tom tollere simul terminum primam et secundum faciendo ut prius x: 4- 002+
  43. fiet 410. 100 10047Z + 2. 10. 1001017, = 10. 101. 101a Ni c sulalotermino primo, fiet
  44. i. Nu Y1(., 100. 200477+ A Daa 101 aZ +, 11. 101. 20) a i o 18. 100 4 A. 11100. 200 + 12200. 200 = 0
  45. d + gHL (O1. 2004Z ecp in Sin 1010. 100100 aq + 10100 a. 1. 200 + -1. 1. 200. 200
  46. memr _ 12. 29. ∞Z F 2. 12. 200. 201. Z Fe12. 201. 201
  47. X= L 11. 11,200. 200= 12, 200.200
  48. seu 10. 100. 4 = 1. 200 = 200)(4 11. 11 - 12)
  49. 100 (Fum 2) L Pari jere D00 1xa
  50. Neu 2002
  51. nam signa hic sunt opposita irrationalium
  52. ambignitate. attautem recundus, etiam terminus destuatur, siet
  53. adat
  54. seu 201 524aa + . NVa (a Y IL.I = 10. 12) - = 117 : 12)
  55. 10p bu
  56. 10
  57. 12
  58. e frara nL. 1919
  59. 01 = - 2. 10. 100a a I1. 260a
  60. n 2
  61. 2. 12. 206 11. 100 a
  62. seu 20t L
  63. 1. Ha, 4 2. 12(_s( (1- 10. 12) L 11 . 11Z
  64. 2. 10. 121 = 1. 5 . 11 u1.
  65. na en a YC u 10. 12)H 110)
  66. mttr t un
  67. ne
  68. et pla
  69. at e00 (t. AVC LH1iore) L Ht d
  70. duo tergu sumri sunt oltendi non minus brevis est
  71. t
  72. 100 F re
  73. et maris est tum st generalitatem tum s quia ita netomentis calculi
  74. Interim via per radice forimuli cungia
  75. opus nom est praeferenda videtur
  76. ab Esto formulae trium geauum ru
  77. ees xX facta ex AL D,X41, et a fat X- 90Z+ 9B, F 8Z+ 81.,
  78. formula erit productum ex +902. F 91a
  79. t f.81
  80. qu aZ + ha aZ t _ta
  81. 31. et
  82. 41. 81
  83. ubi falieuus 90: 80= - 1: a quotcunque sunt agradus. ptollendo Terio samino seu primo
  84. sed proi gollendo deimino secundo cunique gradus sult duous sator terminum primum esse
  85. desinctum, utique pat secundo destrendo solum opus sit hacunna bicrivne
  86. aZ + 31. 8C,91 a +71-81 = e Sed inde video oriri absurdum nam hinc necessee
  87. vel 90 aZ + 31. 80 0 sed sa oporloret esse 31 = 21, id est forent duae radices aequales
  88. vel onvite et fucchre gla +24. 84 = 0. sed ita fieret Ali 81 = 90: 8 quod etiam non licet
  89. ita jublatio ut duorum summorum terminctum in aeq. quadlatica non procedit. Sed bene
  90. summi saeciendo. 9ea +21.80 =0 et 91 a f31. 81 =0, in tertio gradu pro sublatione
  91. secundi termini primi termini, manentr qua t 180- 0 tioha ternions e0 sint quiim mat
  92. moductum ex l90a F31. 80, 90a + 4140, 91a +21. 81 = 0 ld non li A (acre 91 a + 481=4 alioqui fieret
  93. 91: 81- 190: 80 sit
  94. retur, 8. 5d sed ne licet facere, qua + 31 40 20 vut qua +. 4180 = 0, alisqui ge novei
  95. retur g0: d t aus has ut decaectio in sutari
  96. Endo rqua vel xxtete
  97. Applicemus ad formutam simplicissimam situe formula talis 10X +.11 facientoque
  98. 10X L H X = 100Z + 101,:, 200Z + 201, fiet
  99. +41. 200Z + 11. 201
  100. ida
  101. aoem
  102. Ergo initio hujus plagulae
  103. imos termitios

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 219v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0434?run=74