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Leibniz-Handschriften zur Mathematik LH 35, 4, 16, fol. 2v

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: 0.85.

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. 1r); this page is its left half.

The machine reads it as

  1. dota dividendi ratio reducitur ad sublationem incognitarum simpli-
  2. cium, tanquam casus geer specialis ad Generalem. Exhibeamus rem in exemplo, ut
  3. sit Divisor 10X + IIX + 12
  4. Dividendus 20X + 21X + 22X + 23X + 24
  5. Erit Operatio contracta 30 X + 31 X + 32X + 33 X + 34
  6. Quotiens purus 30X +31X + 32,: 10
  7. Fractio adhaerens
  8. cujus numerator
  9. est Residuus
  10. Nominat
  11. X +34
  12. est Divisor:. .. 10X + 11X + 12
  13. Lexoperationis
  14. 10.20= 10. 30
  15. 10. 21 = 10. 31 + 11. 30
  16. 10. 22 = 10. 32+ 11. 31 + 12.30
  17. ete
  18. IL
  19. etc
  20. Unde tollendo ordine incognitas 30, 31 etc
  21. habetur cujusque ex his incognitis valor, et ex
  22. his quetiens pariter ac Residuus.
  23. valorem quotientis ac Residui, itemque
  24. Super est ut demonstremus (aequationes in Lege operationis contentas. Itaque
  25. tota exempli operatio ex explicita exhibeatur, ordinatione tali quae
  26. commodissima visa est:
  27. ORDINATO DIVISIONS
  28. CHARACTERIS TICA
  29. +37
  30. 20 ac
  31. ouidenis 20+21, +22. . t 23.
  32. c 1ud) = 1t.2B,
  33. ((= 10. 11. 21 10. 12. 2
  34. 1. 1o F 112 20,
  35. Hic 30 = 20. 31 = r21, - 11. 208
  36. 10. 10. 11. 22 = 10. 10. 12. 22
  37. + 10. 11. 12. 20 + 10. 12. 12. 20.
  38. + 10. II. II. 21 4 10. 11. 12. 217.
  39. = 11. 1L. 1. 20 = 11. 11. 12. 20.
  40. 10. 12. 20
  41. = 10. 11. 21
  42. +11. . 20
  43. 32 = 22, = 2, 20_ - 10. 11. 21 + 11. 11. 20
  44. B Rm XD e3AX
  45. 33= 23 + X
  46. +
  47. lic DY VS
  48. ∞10. 12. 21+11. 12. 20 = 10. 10, 11.22+ 10, 11. 12. 20+10. 11. 11.21 - 11. 11. 11. 20
  49. 102
  50. 10
  51. = 10. 10. 12, 22F10. 12,12, 20+10. 11. 12. 21 -11. 11. 12.20
  52. stellulae replendae forent, sini (quae loca vacua designant) si divisor esset
  53. 10
  54. 34 = 24+ X + X +
  55. altior, et in eo esset etiam 13; si scilitet esset 10X3 + UIX + 12X +13.
  56. jam valores ipsarum 30, 31, 32, 33, 84 consideremus. 30 = 20. 31 = 21 = 11. 26
  57. seu 3t = 21 - 1, 3B seu 19,21 = 10. 31 11. 30. e
  58. 31= 21 - 11. 20 seu 31 = 21 - 15. 30 seu , 21 = 10. 31 + 11. 30
  59. 32 = 22 - 12.30 - 11. 31 seu 10. 22 = 10. 32 + 11. 31 + 12. 30
  60. 33 = _n 234X - 12. 31 - 11. 32 seu 10. 23 = 10. 33 + 11. 32 + 12. 31. E vanescait hic 13. 30
  61. via 13 ab est
  62. Et ita porro habemus ergo aequationes in Lege operationis continentas.
  63. Apparet etiam ex nuda inspectione valores R Quotientis et Residui
  64. uoniam ergo Aequationes in Lege operationum contentae simplici
  65. esse quales assignavimus.
  66. admodum regularitate procedum, h et earum incognitae sunt simplicis gradus.
  67. hinc regula aequationum reducitur ad regulam ad regulam jam a me
  68. inventam tollendi simplices incognitas, ejusque harmoniis suas proprias seu
  69. visionum
  70. speciales addit. Sed placet ad jicere modum inveniendi valores temminorum
  71. operationis, 30, 31, Ck, maxime proprium et Axalysi converientem, qui cous
  72. comparatione succetsus cum quaesito. Nempe 30XF 3X +DZ multiplicabimus per
  73. empe Quotientis partem pulam 30X2 + 31X + 32 multi plicabimus per divisorem
  74. producto ad damus residuum 33X+ 34, et proveniet formula coincidem
  75. atum divitendo 20X +21X+ 22X + 23Y +24. Unde habebuntur aequationes comparatitis
  76. Uni fiunt aequationes copanempe easdem quas ante 10. 20 = 10. 30 10. 2 = 10. 31 + 11. 30
  77. 1020(+ 10 21 t 10. 32X +IO2YH034 2t 10. 22 = 10152 +11.31 + 1. 30 10. 2) = ,0 33 + 12 32 L 12.31 et 1024 = 1 a)4 + X + 12. 32.
  78. ubi ex natura residui in ultima aequatione contingit hiatus per stellulam expressus
  79. neupe abest 11. 33. cujus rei ratio est, quod ultimi germini operationus, qui residi
  80. istituunt, non nisi inne hoc loco 33 et 34 non nisi per 10 multiplicaatur
  81. non vero pes 11 et 12. se cus fuisset, si continuata fuisset divisco. in calculi exeem
  82. esset 11. 33. ascriberdo ei notam seu includendo, ut regularitas melius servetur
  83. otienre
  84. divisione. Item inquisitio
  85. 34 = 40X + _, .B3, +
  86. e
  87. quationit
  88. sine Residuo eont
  89. +10. 1. 22
  90. 20X taX +2X +23XF24
  91. 10x +
  92. + 1
  93. Qvonens totus
  94. equ. IOX +uXFC
  95. 30X +31X 132, 10X ux+12, F3X13
  96. con ronauxter
  97. 30X2+ 31X + 32 (.10
  98. 10X2 + 11X +1
  99. 10. 30X7 10. 31 X3 +10. 32X H1O. 33X1
  100. + 11. 30. +11. 31. + 11.32X X
  101. +13. 30. +12. 31 (ri 10 Xt + 11X + 12
  102. 40X + 4 1(: 32
  103. B3X + 3
  104. 33. 40X43
  106. 10. 35X + 11. 337(+ 12. 33
  107. ox ruxr
  108. 13X + 34
  109. ost as.
  110. his etam aaebitur sories insine
  111. com
  112. jui
  113. dasper
  114. uti WX FIX + R,
  115. pensura, siquitur subtalia
  116. lnis in tad laita
  117. dibunt omnes e4
  118. r. 313a iams at sec lolos trctatioum uiterarum
  119. aequ.
  120. EoX + 31X+32 + 2+
  121. tione fingere licebit pst etia

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 16, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068013:0004?run=73