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Leibniz-Handschriften zur Mathematik LH 35, 3 A 27, fol. 4v

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. 3r); this page is its left half.

The machine reads it as

  1. tiagnem
  2. Aeq. (7)
  3. + 2
  4. 33
  5. t al sus inbis sim a intregra. quia ex duobus mimulus semper par.
  6. uHinc a dussi chriangulares a + al. a quidus anferantur al nuneri natuates decinceps ab mtite
  7. restant quadiata a a a.
  8. aq. (5)
  9. .L Ex aq. 4. fit: Lb- Ne p ca - da.
  10. Et quoniam L, et N debent esse integri, substimamus pro ipsis eorum valores ultem pro uno
  11. fit X sed ita, ut quosdam arbitarios, At aut saltem pro uno sed ita ut ex ipsis valorit
  12. quoque appareat integro esse, fiet: nemper pro L, substitmamus: Jsm + str
  13. smb
  14. in +h
  15. 4
  16. Aeq(8
  17. in+h m+h tcy.7
  18. m+ B ga fiet neu mn inga +hga ohib
  19. snb - Nc B ga. ponamus sub
  20. in +h
  21. Ae (10)
  22. et Na Nem + Nch sb 1.
  23. fiet ex eq. 9, hoc aeg. (12)
  24. (11
  25. pro priore ponamus l p 49a,
  26. in + 48 H 5. g b. Quo valore ipsius m,
  27. integris invento p in aeq. 10 substituto fier. (1) Nc Af(- Nc _9 +N .49a)
  28. a
  29. aaequatione 5. Arrgo cresse aoque siticet psi etium darc cutorem
  30. A ergo fractio integum faciens ud satis suit composita Muteruus: (Z co - Hb Acob - hb - NC e ga
  31. stone libm
  32. c- m H
  33. fier C A s Il e _ sb m + m.
  34. b sive expercanda h, et l, fiet. col g4.
  35. H VA A D. SL. E. xt. n
  36. jam pona
  37. Restabir. cob - nb +
  38. quaeritr Multilus
  39. 1
  40. cole - ga BC
  41. 5
  42. sb
  43. A
  44. redi
  45. leob
  46. 11 ed
  47. Lb - Nc +g ega.
  48. 17
  49. A -D
  50. ar
  51. m
  52. =1
  53. Restier cbi lib Ccols N
  54. n. le
  55. TNc. Jam pontumus C0p C54 + 98
  56. fit n
  57. 1) Nc, ade Explicatok en m fier:
  58. lea
  59. ad
  60. e
  61. 1s- gat
  62. a 2 NCd
  63. pone + C. et Le M+d. fier
  64. Mb a et _ P ga inde fieri potest: Mb - Pc a
  65. Quaeruntur ergo duo integri, ita uno multiplicato
  66. per numeraem, datum, et alio per alium datum differentia inter productot sit Unitas.
  67. 4
  68. sed quia hoc semper fieri in integris non potest, ergo nec methodus isa succedit
  69. eo casu, quando autem sucredit,
  70. e. g. 3. et 4.
  71. 307 H 21.
  72. 45 20.
  73. solulum ae problema. Non semper succedere ex eo patet, quin e. g. omnes multipli
  74. denarii teminantur in 0. et omnes multipli quinarii in s alt impossibile est
  75. diffeore eos unitate. Quam sm b et in genere multiptos ab in si b. et c. sint primi
  76. inter se impossibice est eos differre unitate. siit 1. et 2 nisi
  77. v.g. multiplum a 3 et mallipum a 6. estae possibile differre unitate
  78. omnes multipli a senario terminaotur in 6
  79. Mb - PC = a. ponc Cp D c p d - a. et l1
  80. inus exosis sit 1
  81. si sum sit MCcsb. - Pc p 1 ficret 5b - 1 . Ergo sb. non foret
  82. c - 1
  83. integer nisi PC - 1. sit teger 1. seu PCB2. a 70E Or
  84. Quid si 1 sic: Mab - MF Mtc a. patet M. esse imntile seu B.. Hinc
  85. concluditur tam M quam hoc sensu col debere M esse numeros primos inter seore
  86. mo Lb, et Nc fore primos inter se. id est L. et N uti b. et C.
  87. ponrc
  88. bp bp c + d. tei ME + Md - Pc a, fict
  89. Dc
  90. M
  91. Haira ataram arareu e
  92. Multiplus dati numeri
  93. MB PCrahigo M A PC + a. Utque f quantitas fractio esst, tantum quae.
  94. C + d 1
  95. gutur, quomodo ex ipsis queat compori
  96. Numerum et nt Namerum invenore, qui mullisa datum, addita unitate dividi possit
  97. per alium datum.
  98. vig.
  99. dividi possit per 7 is et
  100. vel pro E ponento d, fier
  101. b Numerum invenires qui unteliplic abus per 4, et motate
  102. 4+
  103. VPn5,
  104. cp+
  105. b et C +1
  106. cp 2d., et b p 3d + 1. unde 2Pa +1. Unde:
  107. ue qunit
  108. u
  109. a b, cuict
  110. ques mulliplo
  111. a c, unitate
  112. aucto
  113. 212 β.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 27, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068240:0008?run=74