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Leibniz-Handschriften zur Mathematik LH 35, 4, 17, fol. 8v

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: 0.76.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The same scan is also registered as fol. 9r; its text is given once, here.

The machine reads it as

  1. si numerus propositus sit impar. Sumatur
  2. ejus duplus. 2Z.
  3. a
  4. 14Y 2 _B aequ 1 + 2Z + + 27. 9-1.
  5. 1
  6. et 2Z- 2 aequ divisib. per Z. Si Z sit primitivus.
  7. 2Z. 27, 1. 27-2
  8. 1. 2.3
  9. Hinc a + c + eequ aequ. b + d+ f etc nec coincidunt
  10. ut in impare. ecu
  11. a+ c+e ecc - 1 (est divisibilis per Z. si Z est primitivus potet
  12. seu b+d + fet-v,
  13. Cb7 d + f erc = 1 est etiam divisib. per Z. patet etiam ex
  14. ex terminis
  15. terminis posito Z esse primitivum
  16. Unde e0 casu sunt condioisibiles si y non est primitivus
  17. 2, 2 aequ. f + Z0 2- 1 + Z. Z- 1. 7-2
  18. i
  19. 1.2.
  20. 1. 2.3
  21. et (. + Zete
  22. Si jam Z non est premitivus, quaeritur an possit esse
  23. ponatur ita
  24. esse, et sit 2 - 2 divisib. per g. erit etiam 2- 2 - Z
  25. 1. 2
  26. 1. 2. 3
  27. etc.
  28. 1.2.3
  29. P
  30. Z. 1. Z-2. 2.3 Ck.
  31. 1. 2. 3.4
  32. 2
  33. D
  34. 1. 2. 3.
  35. Auferatur prior a posteriore, fiet:
  36. etiam integer
  37. 1. y - 1
  38. Ergo
  39. 1. 2
  40. q- 1
  41. 2
  42. + 2, 3- 1. Z-2
  43. 1. 2.3
  44. Z - 1. 7-2
  45. 123
  46. +
  47. si Z- 1 est par seu si Z impar erit
  48. e Z.t di 8 divisibilis per Z
  49. ergo 2
  50. 2 - 1, Z + 22-20 Z, =C
  51. seu 7- 2 +2 Z. 2. 9.3 erc. erit in leger
  52. se 28 a d anferatur restabit integer
  53. L
  54. et
  55. q integer
  56. MEC
  57. nl1111
  58. Dec 1111IF 111
  59. t
  60. 1 etc +I
  61. 1. etch.
  62. 3. 2- 1.Z- 2.Z3 integer
  63. 1. 2. 3. 4
  64. Z. 1. Z. 2. Z-3 integer
  65. 1.294
  66. 7-1etc.
  67. Z- 1. exc. 7- h
  68. Dy - 1 + Z- 1. 7 - 2 + Z- 1. Z- 2. Z.3 etc +
  69. ert integer.
  70. Jam 2
  71. a
  72. divisio ergo omnibus per Z. euit quotitus
  73. integer, ac proinde
  74. 7-1 + Z- 1. Z-2 +
  75. 112
  76. etne
  77. posito D aequ. Z 2. Ergo si Z primitivus erit 2. 2 primitivus
  78. ac proinde et q -1 primitivis.
  79. 92 esse divisibilis per Z.
  80. y. 3-
  81. divisib. per Z. sive L +
  82. erit
  83. a
  84. +
  85. . 2.
  86. 111
  87. 250
  88. 2
  89. 14 d
  90. Onnus Numerus progessionis
  91. duplae unitate minutae
  92. 2 - 1 est integer
  93. si z est primitivus.
  94. Omnis Numerus aliquem
  95. numerum prodhessionis
  96. Geometriet duplae unitate
  97. minutum, dividit
  98. ratio patet ex periodis
  99. Ls cuet
  100. factionum oluior sur
  101. duo dantur numeri enidem
  102. numerum progressionis
  103. ss cometisco duplae divi
  104. dentes, seu qdivisores
  105. com sive confactores potrs
  106. 1046
  107. 1+9
  108. 11
  109. e
  110. 1. 22
  111. 1. 35.531
  112. 2 B 28 307056288. 1 A1 2835.
  113. 35M 1 9 36 841261684. 36.91(3,12. 8. 12
  114. Diore 11045 1201115116.
  115. f2orB 1 N 55 165370462. 412. 34)1. 5. 15. 30. 72
  116. 4096 1 12 66 120 2 792. 914t
  117. e
  118. est 48198 .B B286 1151. 16 1. P. 22 1599. 131
  119. 93-5 93- 12 0
  120. 1x2f 29
  121. 1
  122. a A99 dypt 13E 207
  123. uxp
  124. prt1.
  125. i
  126. VC
  127. e
  128. G0
  129. 7b
  130. 32
  131. 300
  132. 307L2 eut
  133. Axil 308f28
  134. 18761 ccil
  135. 16
  136. 5
  137. si numerus in progre propressoone trimali binos numeror
  138. UII crc exaste dividit necessus est duos illos
  139. esse periodicos ut si exacte dividet III etiam exarte
  140. dividet 1III. item 1IIaHI. et ita ponomonasos
  141. et generalitur sinumer quod inprimis utele a vimali
  142. proressione.
  143. in Brimali gcessione
  144. 111 1 1 11 1
  145. 1011
  146. 0
  147. 11
  148. 1
  149. lloci
  150. le
  151. 11
  152. 2501
  153. 1. 3 3
  154. s
  155. +
  156. 22
  157. 69
  158. 128
  159. 1Y L 35 217c
  160. 1 ∞ 10 10 5 1
  161. 2 6 1520 156
  162. 16
  163. pot
  164. Aobs )315
  165. ti
  166. p
  167. 11Ce11
  168. 100000001
  169. 1
  170. ∞
  171. ees
  172. agu aeq
  173. aequ = + 6 +5 e
  174. u

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 17, fol. 8v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068014:0016?run=73