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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 207v

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: 0.80.

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. 208r); this page is its left half.

The machine reads it as

  1. Loto X pinatur 7. in hoc catculo
  2. 10V + iea 20 20X F2Ia = 0 (50. 20X) + 11. 20a 1-0
  3. X + 1t ax. + 12 aa = 0
  4. 2077+ 21: H + 22 aa =0
  5. -20. 10 a) 21. 10a5
  6. +10. 21H. 11. 21a =0
  7. 20. IH = 2IH a)
  8. 10. 20, + 11. 20(a)H +12 20a ( (3) Fu. Z2L11. 1a (+ 12. 22a4 4
  9. 20. 189-1. 10 (aY - 2210 a( , 20. 12 = 21. 12a 22. 12445
  10. videamus an duo hi valores ipsius X coincidant, quando du ae aequationeshabent divisodm
  11. communem. Sit 30H + 31a et 407r4la multiplicantur hae duae aequationes pe
  12. od + 3051 ag + 31 s1a a Eet e 40. 50 4 y +. 41 50, a9 + 41 514
  13. 50x. +51 a fiet 30. 50b + 31. 50aY
  14. fiet 10 = 3050 11 = 31.50 42 =31.51 20 =2 4050 21 = 41. 50 27. = 41. 51
  15. et fiet L. 31. 50. 40(G0)
  16. agato
  17. 210. 51. 30.60)
  18. 30.50, 41 (51) 7
  19. = 31 (51, 40. 50
  20. + 31.81. 4060) a
  21. 3150.
  22. 31 (5)) 41.50)
  23. = 31. 51. 1f0. 61)
  24. I diso. ises X +21150 ile
  25. quae binae aequationes
  26. coincidunt inter se, quando
  27. scilicet datur communis ouojor
  28. utonque nempe 50 + si a
  29. nam p duisa per 31. 40 - 30. Cx t oat 50X 1 51 a
  30. Hc nempe methodo etiam determinatur divisores communes, cujuscunque gradus
  31. sunt hae duae aequationes 9X + Da =0 et 6X + 8a, debet esse utiue
  32. ettque 3+ 2a - communis aequationis divisor eutus 2
  33. Si 10xX auat +2
  34. hadem methodo inter tollendum eit
  35. o habeant dommune
  36. mcoris sepressionabus
  37. et habentur divisores communes aequationum
  38. Prgamus in c 3, moste notae sinistrae sunt dextrae sunt l. D in Hy
  39. 2. 0 in a,
  40. Tanxio cs aen. 3 A. 4
  41. in aeg. e notae dextrae sunt 5. 2 in FY et 112 in a
  42. +12. 20, 10. 22 - 11. 22012010 semp 1220, 10. 22 = 11. 72. 11. 20
  43. posset etiam aliter RCsE +. E9. 12. 22.
  44. ordinari sil pt
  45. nabo baaa abab laba
  46. baal abb
  47. italim enunture ormis 20
  48. qua 20 poni potest = 0. si aequatio
  49. autera sit primi gradus, et fier
  50. explicando
  51. IL. 10- 20. 12 4 11, 22. 21. 10.
  52. p0rg. 1 d H0. 21. 11. 22
  53. +10.2t H. 1a Sc
  54. -10. H. 21, 22
  55. notarum aptem sinistrarm in 12. 20. 10. 22 sint tantum vata
  56. parere, sed ex binionibus horum sequentium 1. 2 et 1. 2. et. 2. 15t. 31
  57. seu exbinionibus ipsorum a, a, b, b et harum transposit onitns
  58. quae sunt aa, bb ab, ba seu 1.2; 6. 2 2.1 2.l 125 24, 2 1; lo2
  59. 13 est -10. 22. I2. 10 + 10. 21. 1. 220 caeserae combinatione exeluduntur, eo ipso quod
  60. iho gx gr ape o can maysuas 2 vurga
  61. itaque hac jam videor ad clavem pervenisse harum variationum.
  62. 10γ3 + et aHY ,. 12 adY + 13a =0 (+10, 20N3 H. 2otX , 12. 2eX 1 15
  63. vel exquatuor pariparibus
  64. seu =10. 21. 11.2 1) + 18.21,. 12. 234 =8
  65. 3D. 2281625) du (∞. 23)
  66. Extense +10. 21. 11. 23 Y 4 10. 21. 12. 23a (5)
  67. = 10, 21.21. 13 = 10. 21. 22 13 1
  68. -201I. 1. 23 - 20 11 12.27
  69. LeN X
  70. 11021. 12. 23Y + 10. 27. 14 3a0
  71. +10. 21. 12. 23H + 10. 2E, 12. 23 a 7 (6)
  72. +20. 112. 13 +20. 150. 23 k) X. XVI -
  73. Et explicate fie
  74. Idem cum oimen Des si giuihiabet onemtinur, quod ex io sit
  75. transpositione nitarum sinistrarum simplice, triplice, quintuplice, etc inimpari
  76. opposit. Ain suu embro signum habet aliad membrum quaod exillosit
  77. transpositione notarum sinisrarum duple quadmplice, sextuplice etc.
  78. Ab solvatur adhuc tok p. Na FLa aX 13 ax rc
  79. et 20d 21 Laax 3aX 124a 20
  80. il Hotae aptro se haber ad V, ita notae retmo ad a, hinc in ullima ag. ubi
  81. eornescit u ut a habent se eodem modo
  82. is alterias
  83. Hoc unius sequationis se habent.
  84. erm i utor ni e otalitu et iet pant
  85. Deniqe onplipaitia. vtiam institui potest 1er efli 10. 21. 1 23,9 4 10. 21. B. 23a 20
  86. oalisene cum coetti–
  87. 21. ll. 23 10
  88. 1+..
  89. nemp. 10. 11. 51. 24. 10. 22. 13. 24, et 1021. 11. 24 1023. 4. 24.
  90. +10. 20. P: ad F 11. 20Y + 12. 20aH + 13. 20aa 120 +0. 23HH + 1. 23at +12. 23aa (+ 13. 23 a. X) 7= 0
  91. 20, seu 10, 21. H. 23
  92. ti
  93. 10. 2. 11. 349 10. 2r. 13. 24, 10. 4. 11. 24, 13. 15447
  94. veldemque ex dutibus parpat ponions
  95. tronssi quo mo paria essesil coltatata)
  96. -29, 13 = 2. 13 - 32. 13
  97. compendio 26. 10 + 2a 2o a 1 lona = 10. 29 hy + 11 ay + 12. 13 os
  98. -20. 10. . a) 2 21. 10
  99. unde
  100. a - 12. 20
  101. transpositiones quatuor, hinc patet rem non ab earum hanspositionoti
  102. -10. 22. 22. 10 + 10. 21. 11. 22 =
  103. 20Y + 21 axy +224a) + 23a3 2 20 104 4qod v nu 25. a
  104. 2
  105. citdibus teminer
  106. aatefas
  107. Ex functiim insino ))
  108. .... 20. 12 14
  109. . H. 13 Eit

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 207v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0410?run=74