Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 77v

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: 0.86.

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. 76r); this page is its left half.

The machine reads it as

  1. abula valorum punctatorum ad Casum Maximum
  2. Pre II. Nominibus
  3. Pro III. Nominibus
  4. a potterim esfecta
  5. Ergo pro 1 Nominibus
  6. Z= c. Ergo Z-
  7. Pro 1V. Nominibus
  8. tabulai hi lalores ad1B
  9. fam Valores punctatos
  10. Fuit O+p -280 = (())
  11. Ergo (6)- C = a -20
  12. abcd - 5. abc = 10 ab. -10
  13. 2b. - y =0. Ergo y -0
  14. a OD+PD -210 D = (0D)
  15. . - 2. 10 44. (0 -8. 5. +Z. 1. = 1.
  16. Ergo ad vlenm
  17. F-9 - a 4-7 -0 ad ,
  18. Pro V. Hominibus a - b ab -15
  19. abcd = 15. abcde =b abedet=
  20. a -2ab. + 4 abe - dabe t 116 abede - x abides -0
  21. 102 - 150 +80 - x = 0 182 -1
  22. ProZ. ad VI. Nomina abcd-aubede +Z abidet - 1.
  23. Atque haec Methodus etiam expeditior videtur priere Methodo. Sunt tamen utrique
  24. suae seorsim commoditates d Praerogativae
  25. Tertia Methodus est quae Columnas invenit independenter a toto systemate Columnarum
  26. de tantum dependenter ab una vel paucis columnis, quam Verbis Leibnitianis ita explie
  27. Sit O = n a + 12 ab + 13 abc + 14 a bc d + 15 abcde
  28. 2. H. a +2. 12 ab + 2. 13. abc. + 2. 19 abed + 2. 15 abcde et =0
  29. Ergo 11 = 2. 12 = - 2.11. 13. = -2. 12 14 = -2. 17
  30. Huic seriei si addaz Ap. +12 a p +13aba
  31. venit Valor (() ad unum Nomen ampli
  32. PTheor: II. Ergo (8 C-n Hira Hhab
  33. d inde EOR 1. Coefficiens Membri cusquis in Colu
  34. Ergo 0= 1a 2ab. + 4 abc -8abed etc: etc:
  35. una elis duplus est praecede
  36. tis Coefficientis cum Signo contrario.
  37. D) = 22a + 23 ab + 24 abe +25 abcd + 26abe de +27 abcdet) (03)- D - 122a + 123 ab H2gabe +12s abel H2balud
  38. +20D = 2. 12E ab +3. 123r4 + 2. 124, + 2. 125, 4 +2. 126 a a
  39. fit D - D = p D - p0
  40. Ergo 30- D = 9 -6
  41. C = =1a + 2 ab- 4 abc + 8abed -16 abede + 32 abcdef
  42. 22 - 4. ) 23+2t22 - - 2 (24 +2. 123 - 4 (25. +2. 124 - -8
  43. +207 = + 2. 122 1 1 + Z. 12311, + 2. 124 111 + 21
  44. D= 4 - 2E ab = C3 abc =29 abed 425 um
  45. 2.122 = =23 +22. 123 =4, -24.) 2. 124 = -8 -25 2.125 = 116-26.
  46. N 122 -0. (2. 122, = 22. 4 1 23] 2123, 23 -129. 2. 124 - 29. 125
  47. et 2.= q 2 f 1]- g, 8. 25 per 5 20 = +16- 16
  48. P∞0 - + - 123 per H2 - 23 -124 P, 1t9- 24
  49. Ergo 125 = 1. Z
  50. Ia per saltus alternos utrigque, Dnae odnae coefficientes ordine nt
  51. CD: p = 122 a + 123 ab + 124 ab5 + 125 abcd +126 alu de)
  52. D.P = , - 22 e = 23 ab - 24 abc - 25 abcd - 26 abe
  53. Haec ultima Aequatio identificatur in singulis menibris
  54. ja - 2 ab +4 abc -8 abid tibabedo (=0. Inveniendi autem Valores 2. 172. 2. 123. 2. 124. 2125.
  55. = D = a 2ab - 23 abc-24 abccl - 25 abide
  56. Excalculo ad dextram fit THEOREM A II.
  57. Coefficiens D fit si summa duorum Coefficien
  58. tium proxime praecedentium duplicata
  59. statuatur affici signo contrario
  60. ut pro D incipio oa + x ab sunma Coefficc: est a.
  61. duplicatur cum Signo - Fac. - Z abc
  62. tam ex hac Aq Aequatione quam ex priore DX
  63. sic. 2. 1227-23 2l _Z. 127 = +2. 24, 2.
  64. Hom Z. 123 = -24 +4
  65. _ Z. 123= +2. 23+ 22. +2.22
  66. ergo - 2414 = 2. 23 +4+2. 32. facit 24 = - (2. 2212. 23
  67. Hem 2. 124-= : 25- 8.
  68. 2.124 = + 2. 24 -8 +2. 23 Fac. 25 = - (2. 23+2. 24)
  69. Pergo 1 ab - Zabc Suma 1- 2 = - 1. Duplicata cu Signo contr. fit +Z.
  70. Pergo -2 abe + 2abcd Suma Coessice = 0. Facit - 0. abc de
  71. Pergo +rabe d = 0 abede Suma Coeffucc = 2. Facit - 4. abedet
  72. Pergo vabede abcdef sua Coefficc = - 4. Fac. +8 e sic porro
  73. Et sic porro 26 - - (2. 24 + 2.25) 27 = - (2. 25 +2. 26) et
  74. Ita jam Columna Dna ex se ipsa elabo
  75. rabitur per Theorema Il. in calculo
  76. Pro Columna OD ex se ipsa inveniendâ. Capio - 123 = 2. 122- 22 ex Aequatione V2
  77. THEDREMA III.
  78. Coefficientes Columnae sal fiunt ita: Duo proximi
  79. coefficientes additi et duplati hanc summam subtra,
  80. 5]-8- 0 10D Seu 000 -8 - 8D - 0
  81. =08- 2028
  82. Explico 1ZZ. ex WX = a. fit - 123 = 2. 122-1
  83. fit Hem. 124 = 1 23 eBZ. Seu 123 = 1-2.122.
  84. Explico - 23 ex VX fit - 124 = 2. 123+212
  85. Htem ex V2 125-= 24-2. 124.
  86. hunt a Coefficiente Columaae Solis que Minori additorum respondet.
  87. . 5 por. 202s. Calculus pro He
  88. (OD -S
  89. Ergo x - 32. & - x - -3
  90. e Sit D - 22 ab. + 23 abc +24 abed + 25 abede +2o abede f etc: sit OD - 122 ab + 123 abc 4 es abdl 412s abido
  91. (0 -03: p. +20D - D-0
  92. Pone (0) -0 =0
  93. 4. -2.6. + 4. q = X. 1. =0, fi
  94. a, 20. -12 -X =0
  95. (1) - C +20 - 1. = 0 Ergo (1)- 0,: p = 1. + 12a + 13 ab + 14 abc + 15 abid +16 abede etc
  96. Fuit D +pO - 2p0 D- (D
  97. Ergo (D) - D +26D-0-
  98. d
  99. Explico +24 ex VN fit 125 = 4. -2. 123. -2. 124 etc.
  100. Inde fit THEOR: III.
  101. Sit 8- 44 abed +45 abeder a 6 ab. f et 50D - 1247 abedesgue +124V abunh eti:
  102. Ergo OD5: p = 1247 ab . f +1248 ab ag +1249 ab h.)
  103. Op oi ee abe
  104. 000 - 5D - 8D-80) = Hrab a asab. udl B rsale xirabf a quabig +g abucta 20
  105. 00+. 00.0. 0 00
  106. Sece 12g= -2, 2. 1E,. 2. 1
  107. (+0D = 123 abc + 129 ab, d +125 ab, e +126 ab f + 127 ab. 1g + 128 abuh
  108. SD9D = a n 246 abif 127 ab. 9 + H ab H.)
  109. Aujus autem calculi prosecutio inopinatam prolixitatem offert
  110. pro Columnâ otis ex solo ore de OD continuanda
  111. fali Theoremate 2 49 = 2. 129 + 3 121 + 2. ei + eM unde Regulam non ausim
  112. Ergo hic labor in altioribus colamnis nondum succefit
  113. 2. 410 - 3. 411 - 2. 41E - L 413
  114. Pro V. Nominibus
  115. Effectusyabede. + Zabia
  116. ab -2abc + 2abca =G abcdef - 2.
  117. Proy. ad VI. Nomina - 15 + 2 - 1. Ergo Z - 16.
  118. Systema ad VI. Nomina

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 77v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0154?run=74