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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 23r

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: 0.71.

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The machine reads it as

  1. 14
  2. sqb
  3. Rosd pn 2.
  4. a
  5. ib
  6. 01 234567 39 10 11 12 13
  7. d. 1. 9, 1. 9, 1, 0, 1. 0, 1. 0. 1. 0. 1 quata )0.
  8. O1. 2.3,0. 1. 2.3. 0. 1. 2.3.0. 1
  9. 0123456701 2 3 45
  10. 012345678910 11 12. 13
  11. 9
  12. 4
  13. 14 15. 1b 1y _ 19 20 21 295234424925
  14. 1’4’g’ 1b 5 36 496781 100 12y144 69 150 us vl.1 57 4 1 00 4 41 487 519 576 tu. st
  15. 2 2 4 5 6
  16. 00
  17. ∞ 10+
  18. 0
  19. 1 e 1d
  20. 0
  21. 10 11 a 12
  22. 0
  23. 10 1010 10 10 b o
  24. 4 10r 4
  25. 1 4
  26. 10
  27. 01 4 90 9 4 1 0 1 4 9 0
  28. 0
  29. 10101
  30. 0
  31. qo
  32. 1 4 10141 0 1 4 11 4 1014
  33. 9 4 101490 94 1 0 1 49094
  34. 120 1 4 9 1b 25 4 17 0 17 4 25 1b 9 4 1 d 149 16254 17 0 17 4251691
  35. 640 1 4 9 16. 2536 49 0. 17 36 87 16 41 4 3 0334 M 16 5y 3b 17 0 49 3625 1b 9 4
  36. 18 0 1 4 9 16 25 3649 64 81 100 121 16 41 b8 97 03105. 16 57 leo 17 69 3b 8) 16B 4
  37. 0
  38. 65
  39. 61
  40. 63
  41. 1
  42. 10st
  43. 4 9 16 25 36 49 64 8i 100 121 6
  44. 9 i 3 15 17 c9 4 2
  45. 65
  46. (qui suit 12
  47. quaeruntur residui quadratorum per divisorum. primi sunt omnes quadrati infra 128 nempe a 0 usque ad 121
  48. inclusive. a proximo quadralo 144, residuus est 16, is notetur. Ejusdem quadrati differentia a proxime sequent bu
  49. est 25, inde detracto 1, manet 24. is numerus etiam notetur. _ Hiuc dedacemus residuos sequentes hoque modo nempe
  50. erut 16 A, 1 16 + 124 +1 16+2. 24 + 4 ) 16+324 +9 (16 + 4. 24 + 16).61 5, 24 125 1. s. 1 6. 6 165724149
  51. qui faciunt 16
  52. quorum differentiae 2471
  53. 3. 32+9
  54. 105
  55. 05
  56. 41
  57. 4. 31, F 1b
  58. 24,15
  59. 68
  60. 24+3
  61. 16 + 1.402)
  62. 415 9 2447
  63. 16+1
  64. (128)0
  65. 33 69
  66. 249 24H1 24+ 13
  67. 16+ 1958+1
  68. 24+33
  69. ar oro mar 24125
  70. 2Ary 2tg 2421 24+23
  71. 161254 +4
  72. 24+35
  73. Aribo
  74. 24437
  75. C
  76. C9
  77. infdiunaturs bmartuns btngnn sibsq. 2ay,q t sbraune (97
  78. 113. 964
  79. 174396 +9
  80. 24127
  81. (6+ Xit albub )16+r )1b+ 18 2+ B. 18 (16 + 19 24 +1919) 16F2029 + 20. 20 (16+21. 24. + 21. 21
  82. 36+2. 6114
  83. 16
  84. 1
  85. 4+2.60146
  86. 24+39
  87. 656164+1 so+ 16414 96
  88. 24+41
  89. 1gt28
  90. duo secundo assumatur fsiduus primus, auctus sequente impare semel, et primo quadrato 1. pro residuo tertio assumatur residuus primus 128
  91. 29
  92. L1 = 10C
  93. 2E +1 =
  94. e
  95. 2E
  96. Et ita porro donec rursuns eatur ultra diuisorem
  97. 1. (oB = . 2 e atur Rofitui ex quad
  98. l esoy. 2 = 34 essy 100 +1 =b Aequantur residus ex quadratis
  99. Si
  100. 2 - 3
  101. + 1 = 6b = 1
  102. di +C = br =
  103. d
  104. I
  105. deu E1 91 = 2 = gE b+ = I 2 = u 1d L = W A
  106. 1H2
  107. 122
  108. esigagmos esod eso = osit atias
  109. indes
  110. 10
  111. il
  112. 3+
  113. 2
  114. (d + f12)
  115. =
  116. ito
  117. U
  118. : U. P.s i_ = (, 2: I. P.s. H) = + 50 2l: U. P. s3 D qu su H
  119. 147
  120. u
  121. 1+ nC
  122. ul all 2.
  123. =
  124. 143C
  125. -
  126. ui uul caand
  127. quissus esser nos chro DXH. e5dt
  128. vouosur juns vab untomu onp. 50t
  129. ranguribos sineisga ad toeuinul 13
  130. dua
  131. pund 3
  132. nnon ept. B ( F 1) eis
  133. 2
  134. 2
  135. ilust esda pu
  136. no 2 + a + f2 = (uid 5 13
  137. u tD eisaa = tud. egoV
  138. 1+a + 2 = () es my
  139. A + f. E = 22
  140. u . (15da =
  141. a 2150d
  142. cia) oudi ud
  143. a
  144. 45
  145. 2a
  146. ubi residui angen crescerent, ultra divisorem, assumendus est pro primo assumendus est qui superest detracto divisore; proresi e
  147. 4
  148. L1
  149. 3+(3
  150. zo
  151. sicot4 ota
  152. 2
  153. t
  154. Residuis ex residuo quocunque aucto per proximum imparem repetitum
  155. et quadrato numeri ropetitionum
  156. Ex. gr. Exgr. Residuns est quadrato 625 est 13, sumatur alius
  157. residuas quicunque ut Al C 1B proximus impar est 27 fet menum
  158. f 49 + n 2b+ un = 113+ e. 128. qua quad ratus est 625, habetur e, 4
  159. nempe. porro 41 est residnum de quadrato 109 cujqus latus 13
  160. proximus impar est 2. 13 +1 seu 27, hinc numerus 26 etia est duplu
  161. latus ipsius 169.
  162. 625 habet latus 25, et erit n = 25. 13-,
  163. et fit a+ R X _1 + (25- 13) 2. 13 + sq = 113 + 4. 128
  164. A
  165. Ros Retid (15) + (25- 13) 2. 13. +(25 -13) 2) = Refid. ex 252
  166. 41
  167. 312
  168. 144
  169. 4 31 100
  170. d
  171. 1
  172. to
  173. 1
  174. 127
  175. ae
  176. 128
  177. EiS
  178. 04
  179. r
  180. 16
  181. + 0 101018d50+
  182. 2t
  183. Aao
  184. DEB + Resid. 13) + (25 - 13)2. B + (25- 13): C+
  185. 497
  186. f. 128 = 25= C. 128
  187. Ret.io (15) ( 2. 13, 25) (9)131 4 25 (113) - 2. 2413 = 25 + f- e) 128
  188. 128 (P.5
  189. qum
  190. 498 13 - Resid. 13 = ((e s) 1 hhoc per se patet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 23r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0045?run=74