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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 6r

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: 0.75.

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. 5v); this page is its right half.

The machine reads it as

  1. Hinc jam porra definiemus quod fiet si tras notae vel plures in
  2. unum addendae, ut
  3. p-12
  4. M.
  5. 3n)
  6. 1 (2m) + 0 (2
  7. J. 2 (2)3(2
  8. )1(2
  9. nam- 1) nt
  10. O(P) 1(2P) deba
  11. odeba
  12. 95YD cba
  13. Hic notae in unum adden
  14. habent sedes distantes
  15. binaria
  16. Ex quatuor notis in unum additis oe ip to (2) 1) +0(2 1 (21) +0(22) ip2) fiet
  17. O(.)
  18. )2(
  19. na1)2
  20. 3(2)
  21. ms (nM 1) n+ p-12
  22. jinc si in unum addendae notae tedium e et m et n ft seu
  23. D(2
  24. m)
  25. 1) + 0(1).(2
  26. t
  27. Re
  28. ) En =m)
  29. Duarum notarum proximanu sibti condditio
  30. MaI
  31. simper est O(M) (m) +(m) 2(m) posit i esse numerum
  32. Sidisi teniaet et trium est o(uB 1(n) (mit(m usn an 3
  33. perro psito ne
  34. distaetia
  35. (m-1I
  36. nal)1(2. . 1(2. LC
  37. sedi in min
  38. 2
  39. O
  40. (n in
  41. ne numerium nota insima sedi
  42. noio
  43. ) a0 vel 0 vel ovelo vel 1 vel 1 vel 1 vel I et fit ovelretono veloto Hinc se tres notas inter se addentae, ut O(2) (2
  44. fiet O(2)1(27
  45. nm ( pe
  46. (2
  47. (2
  48. ose
  49. 1)
  50. pro 4 notis; totum hoc affrintur repetatur vicibus (2F) et iderm tantum quolibet numero per
  51. protribus coaddisis notis
  52. vicibus (Z) Et ita porro in infinitum
  53. s Nota per parem designatu, ut per 2, 4, 8, est 0, 0,
  54. n. (9.
  55. Alt 2,3, 4, 5, 6, fant 7, 8 sunt 0, 1, 0, i6 Omnes pares, ut 2,4, 6, u
  56. mo crevopndt
  57. OIZ2312232384 lud semper
  58. dimidm prict in perua exrepetitur
  59. dimidium prius posserictum semper
  60. abeunt in 0; pa impares ut 3,5,7, in 1. sed reliqua (ut im 3, autem dimidium prius et dumdium
  61. posseriu
  62. quod est 11, et 10 et i in 101 rejiciuntur in ulteriora) Similiter uo
  63. si numeri m, n, p, + esse ut B, 2, 2, 4+ omnes exponentes ipsius 2 abirent in t seu
  64. quiqu omnis repetitio non visu duplicatu foret Quod si essent e
  65. p
  66. Bu et
  67. utique prodiret
  68. teb
  69. progressionis Arithmetriae, naturalis seu differrent unultome =ies Obi8 1B2 B28, et lapono
  70. cepto
  71. positio repelitio foret duplicatio, quca
  72. dnuto
  73. bi essit n pllitio ates
  74. ubiquse esset duplicatio, excepta prima repetitione (=m-1)
  75. Acy hoec de
  76. vem notarum multipt additione veniamus ad
  77. M- 1)
  78. veniamus ad notarum multiplicaoem. O(2.
  79. -1q Ca p
  80. O(2) O
  81. m-1p. H. mP-1) Et O (2m 17, ( m - 1)
  82. e
  83. dabit O (2V.) 0(2-) 0(
  84. (n- m- 1))
  85. P-n-1
  86. )1 (2 1) dabit
  87. 1)
  88. Et pro quatuor notis
  89. nu) (qui LM)
  90. O(3n=1) O(,M.H1 (m1) (n1- m) (
  91. Additione notarum tantum opus habemus pro investiganda lege ternariorum
  92. dubitur 0 (.X) 0(2
  93. quinarirum, etc. sed ad multiplicatione quoque pro quadralas
  94. multiplinatio abia Triangulares pyrandote
  95. aliisque figurabi p. sunt summae, et summae pammarum naturatium ab intio. Et es mis simplic additor velde. se
  96. imo etiam ja his evitua fonmandis eoitari
  97. indestigandae et fractiones duadicae expressae
  98. 1 26.1
  99. upieret
  100. tractione et per consin
  101. 3C= Ao2pdotorioro en
  102. Bp non n-M, n- 1=M
  103. upsedp- iB
  104. qi-p
  105. o posterius procrum repetitum dat
  106. tes multiplicatioone
  107. possunt formari
  108. quadrati, cubis

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0011?run=74