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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 75r

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: 0.93.

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. 74v); this page is its right half.

The machine reads it as

  1. m. mt m m m m m qu.
  2. 2. g. 1. 2. 4 1. 2.
  3. Retid. 1. 3. 2. 6. 4. 5. 1. 3.
  4. 4. 2. 1. 4. 2. 1. 4
  5. c4. 6.
  6. Resid. 1. 6. 1. 6 1. 6. 1. 6.
  7. Repd. 1. d. 0. 0. 0. 0. 8. 0
  8. dlesid. 1. 1. 1. 1. 1. 1. 1. 1.
  9. Obsero. 15. Probari id ita potest: Omne
  10. Numeri in Progressione dgadica
  11. a loro m etr: sunt quaterni Ab
  12. his ergo si auferatur Lvaternus
  13. divisor quoties potest non dani
  14. possut allia residua qua Qvaterna
  15. Quatermarius enim metiens totum
  16. et ablatum metietur e reliquum.
  17. sequitur ut consideremus 28 Divisorem in 0Atodica Progressione Alitae enim
  18. Progressiones loco ejus Critico Unitatem non habent
  19. Sed de eitodica Progressione idem dicendum quod observ. 15 octensum
  20. est, nam d hujus Progressionis omnes Numeri sunt evaterni.
  21. Ergo ipsi 28. in nulla Progressione Charaiter primitivi copetit
  22. Examinetur etiam 21.
  23. Hujus locus Criticus est m Sed m: in sola Progressione senaria residua
  24. habet Unitatem. At hujus Progressiones Numeni omnes sunt terni et Divisa
  25. 21. etia est terng. Ergo omnia ejus Residua erut terna p Observ. 15
  26. Nutlum ergo Residuum Unitas est. Quare ipsi 2. nullo loco Charater
  27. primitivi competet in hac progressione.
  28. sumatur autem etiam Progresio Oitona quae etiam loco m
  29. Critico habet Unitatem
  30. Divisar. 28
  31. m = g. me m m m mt ec: Haec Progressio locis paribus habet
  32. Unitatem imparibus vero octonarium. Ergo mZ habet 8. Non ergo
  33. ipsi 28. in Pogressione ectona Character primitiri competit
  34. sumatur Divisor 21.
  35. m = 8. n m m m etc: Etia ad hunc
  36. Divisorem loca imparia habent Residuam Unitatem
  37. Ergo ipsi Z1 Divisori loco mro Character primitivi com
  38. petit, etsi 21 sit Numerus Compositus
  39. Quare propositus Character Numeri primi, non
  40. est reciprocabilis itaque valde dubito uttrum hic Chara
  41. Aer id quod quaerimus conficiat nec ne
  42. Possemus quidem excipere illum Casum a novam
  43. legem addere ne sumatur Radix progressionis major
  44. ipso subdivisore.
  45. Sed dum Numerum Z1. examino, suppono me
  46. ignorare utrum 21. ullum subdivisorem admittat
  47. Incertum enim adhuc pono utrum 21 primitivus sit
  48. pec ne. Qvare hoc parto nescio utrium 7 sit subd
  49. visor Diviforis 21. nec ne Quare haec lex frastra eris
  50. data quoniam haec lex supponit me nosse quod
  51. primitivus metiens ipsum 21. ut caveam ne D
  52. sumam.
  53. Specialis tamen Regula formari posset, ut examen
  54. subt suscipiatur in solu Progressione Dgadica, sic enim
  55. nunquam continget ut Radicem Progressionis suman
  56. justo majorem.
  57. constat igitur si ad solam Dgadicam Progressi
  58. onem attendamus posito . primitivo, semper loco
  59. y-1 Refiduum esse Unitatem.
  60. Et hoc posito patet omnem Numerum parem
  61. carere charactere Numeri primitivi per Obsesro. 15
  62. Accedimus ergo porro ad ternos Numeros impares
  63. 9. 15. 21. 27. etc:
  64. mo. m= m= m m: m m m = mD in 2 m M M= n2
  65. 1.
  66. 1.
  67. 1.
  68. 2.
  69. 4.
  70. 4.
  71. 4.
  72. 5.
  73. 1.
  74. 2.
  75. 1.
  76. 8. 7.
  77. 8. 1. 2. 4. 8. 1. 2. 4. 8. 1.
  78. 8. 16. 11. X1
  79. 2.
  80. 8. 16. 5, 10 20.
  81. 4. 8. 16, 1.
  82. 22. 5. 10. 20. R
  83. d. 16. 32 19 38. 31. 17. 34. 23. 1.
  84. 8. 16. 32. Y. 14. 28. - 1.
  85. 8. 16. 32. 1.
  86. 2.
  87. 13. (26 - -1) -2. -4. - 8. - 16
  88. B 16. (. = 2f : 24. = 8. = 16 + 4. N. 4.
  89. 8 16. 32. 25. 11.
  90. 8, 16, 32. 13 26.
  91. A.
  92. 4. 8. 161 32. 64. 59, 49 29 58. 47. 20
  93. 13. 2b. 52. etr
  94. Ad D Subdivisor7
  95. n = 2) Resid.
  96. 9 Loco 8 dat 4.
  97. 15. loco 14. dat
  98. 21. loco 20. dat 4
  99. 27. l0co 26. dat 13
  100. 33. loco 32. dat 4.
  101. 39. loco 38. dat 4
  102. 45. loco 44 dat 31.
  103. 51. loco 50. dat 4.
  104. 1.
  105. esid. 1.
  106. Resid. 1.
  107. 63. C0ro 62 dat
  108. ex quibus omnibus parum
  109. certi colligitur.
  110. Divisor 9.
  111. Divisor. 15.
  112. Divisor. 21.
  113. Divisor 27.
  114. Divisor. 37.
  115. Divisor 39.
  116. Divisor 45..
  117. Divisor 51.
  118. Divisor 57.
  119. Divisor 63.
  120. Divisor 69.
  121. 57. loco 56. dat 4
  122. 4.
  123. 8.
  124. 1.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 75r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0149?run=74