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Leibniz-Handschriften zur Mathematik LH 35, 3 A 27, fol. 2v

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: 0.85.

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. 1r); this page is its left half.

The machine reads it as

  1. . 1. 2. 3. 4. 5 6. 7. 8. 9
  2. posito bra fit: 11d+ 2F 24d
  3. er tecda esile) o.
  4. 2+ 3. ponita jam 4, quoque f7 1
  5. posito divsore 1 fit:
  6. nempe residui erunt : 1. 0. 1, 0. 1. 0. 1. 0 etc.
  7. s 8. 1. 0. 1. 0. 1. 0 ese multipheati per 1. seeurs
  8. per 3. dant residuos: 0. 1. 2. 0. 1. 2, 0. 1. 2. 0. etc., per 4 dant 0 2. 2. 3. etc.
  9. Multiplicati per 2, sunt. 0 2. 4. 6. 610. 12. 14. 16. 18. 20., divisi per 1, dant 000 per 2, dant 0,0. 0. per 3, dant. 4 2+
  10. 0. 2. 1. 0. d. per 4 dart, 0. 2. 4. 2. 0, 2. 0. per 5 dant 0. 2, 4. 1. 3. per 6, dant 0. 2. 4.0. 2. 4 d et per 2d
  11. per 8 dart.. 0. 2. 4. 6. 0 per 9: dant. 0. 2. 4. 6. 8. 1. 3. 5. 7, per 10 dant 6. 1. 2. 4. 6. 8.
  12. Multiplicati per 3. sunt: 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. qui divisi per 1 dant residuos: 0-0- 0.
  13. per 4 dant: 0. 3. 2. 1. 9. per 5 deliaquant: 0. 3. 1. 4, 2. 0
  14. per 7. dant 0. 2. 4. 6. 1. 3. 5.
  15. per , dant relinquunt: 0. 3. _ 3. 0. etc.. per 7. relinpoint: 0. 3. 6. 2. 5, 1. 4. d. per 8. velingmut: 8. 3, 6, 1. 4. 7. 2. 5. 0
  16. per 2, relinquunt 0, 1. 0. 1. 0. 1. 0. etc. per 3, dant.. 0. 0.
  17. et 10 relinquunt: 0. 3. 6. 9. 2. 5. 8. 1. 4. 7. 0 per 11, retinquunt 0. 3. 6. 9. 1. 4. 3. 10, 2. 5, 8. 0
  18. Multiu ocati per 4 dart: 0. 4. 8. 12. 16. 20. 24, 28. 32. 36. 40, qui diusi per 1 dant 0. d et
  19. per 2. dant 3. 0. per 3 dent rclinquand 0. 1. 2. 0. per 4 70 3t per 5. relirqouit 0. 4. 3. 2. 10. per 6, rel. 4. 2. 0, per 7 rel.
  20. 9 relinysunt: 0. 3, 6. 0. 1
  21. 4. 1. 5. = 26. 30. per 8. rel. 10, 4. 0. etc. per 9. rel. 0. 4. 8. 3. 7. 26.1. 5. 0 - per 10., n: 0. 4. 8. 12. 6. 0.
  22. Multipl. per 5, dant, 0. G. 10. 15. 20. 25. 30 35. 40, 45. 50
  23. et it veltiquiit: 0. 3. 6. 9. 0
  24. dividper. 1 rel. 0. per 2 relinge. 0. 5. I. per 3, rel s. 10. a 0. 5. l. 0. per 4, vel. 8. D. 3 3. per 5, 6. 1. 9. per d vel. 5. 4. 3. 2. 1. 8
  25. rel
  26. per 11 rel. v. 4. 8. 15.9. 2. 6. 10 3.70 per 12., vel p. 4. 8. 0.
  27. 0. 5. 3.1 - 642- 0. per 8, rel. 0. 5. 2. 7. 4. 1. 6. 3. 0 Per 9. rel. 9. 5. -1. . 8t. fh 10;
  28. per 11 rel. 0. 5. 10. 4. 9. 3 82.31. 6.. per 12. ccl. 0. 5. 10. 3. 816. 4, 9. 2. 7. 0. pr 1, 23. 520. 2. 7. 1. 4. 9. 1. 6. 1 5. 80
  29. per 7. de rcl.
  30. Aegula ergo Gegeralis
  31. p resis aterum et terum
  32. isit. sed quando id a quo sutrohendum est, subtahendo minus esst, diferentia inter divisorem est,
  33. Y Numri natuciles, muultiplicati per 1. addito 1 F
  34. quam inde duco haec est: prim asiuorum sub tra hitur a des
  35. primm pesiduum ep diffentia in sublucta a quolibet Residuo relinquit sequentem residuum nodo sa quo subtrahendum est,
  36. subtratendu minor est, divisore augeatur. Ita 13 C H 8 5 pe 14.. rel. 0. 5 10. 1. 611. 2. - . 123. 8. 13. 4. 9
  37. etque ita continue honec uiste
  38. Regulam ergo generatem hanc observo
  39. in sege multiplorum, pltinum duorsore minorem, ab eo, tubtrahe, residuum a primo subtractum, dabit primum ortiorum a secundo nattio
  40. 0. 5. 10. 0.
  41. v. 5 10, 15. 4. 9. 14. 3. 8 3. 2. P 12. 1. 6, 11
  42. data subtrahendo minorem, divisore augendum esse. Igitur omnsum
  43. acundum ortivorum et ita porro, modo nolerur ortronatiosioos residuot, sed et habeas factitios, anxortrvos dixisore ei poductum
  44. diide per differentiam inter divisorem et minimum ortivurus, residuacrunt quaesa fuctitii deruceps.
  45. brevius omnes multiplos divisore minores, auge ipso, dant
  46. pmo, residuus additus primo, et penultimus additus Do, et antexenultimus tertio, etc. dant diisorem
  47. uod si ergo Multplum ilum mnon dati quaerunus qui per dotum divisus relin quar datum. Sic agendum est; ante omnia vide an
  48. ste int qui its, ad est
  49. id est quaere duoru
  50. relinguat 0. seu quaero
  51. quaere numerum natira tem, qui
  52. odictue u duitoris dabit sumer
  53. quod si is o non arte verit, alio est, quam communis omnetiplus (non est aliu quam
  54. produlcat altrum datum
  55. nrabobis, dividendo numerm datum per divisores altius cati
  56. minora est possibilium
  57. iduo s tet
  58. dinicurum Residuorum aptorum
  59. 0, statim enim apparet
  60. incipienda a maximis.
  61. pulloma est possibile in ommibus imcica
  62. et videtur possibilis in iis tantum
  63. quod si duo numeri sint primi inter
  64. numerus minor unitate
  65. ca lcutado facile
  66. a angendi proponuntur
  67. esidmum si epe
  68. diviti per 1 el. 8. 0. per 2
  69. minoribus dato; sier nunque tunc longe
  70. idem, qui duos datos divisorem et
  71. onis u, cui hasono
  72. ops unde jam proporito retituo aliquo sic agemus
  73. suuisorem et sume refidumtus;
  74. hoc Residio eodem modo; incides tandem in uul
  75. ns repete quosu hoc dcendum ex qrisitius complectetaur, injus scilicet Mulape
  76. P. 2. 3. 4. 5. 0. vel. 2. 9. 1. A. per 4 2. 3.0
  77. 4. 5. 6. 5. 8. 9. 10. 1. 12. 13. divisi per 1. relinysbunt. 9. 0. per 2 2etinpunt: 1. 0. per 2
  78. 2. rlinquunt. 0. 1.0. per
  79. at 13. 15 17. 19. 21 diviti per
  80. 3. 4. 0. 1. 2. M 1. 3.5. 7.
  81. men cum atesset angmentam
  82. et summae per divitorem datu
  83. multiplicentur per E
  84. t li
  85. 6.78. 9.10. 11 divisi per 1. relinquunt 0. 0. 0. exc. divisi per 2. relinquind 10. 1. 0. sse X
  86. locum monies.
  87. oi d tant
  88. li 2. dant. 24. 6. 810 1214. 6. 18. 20. 2
  89. tantum augmentum eti
  90. dividatur per B. residuaque ordine scribantur
  91. ducto addatur, 9. sum ioc primum appare
  92. si decedatur per 12,
  93. iduum 14 sit multiplus
  94. es seroentur
  95. sp renoglads
  96. criors detendum est exerplobes
  97. semper autem ultii 42 - 6
  98. Nunc enim divisor est ipsemed est multiplus quaesitus. deinde a divicori residudatum aufer
  99. Rrasionus datus, sit inter ipsus multiples; si non ita quere illam ex multiplis minimum
  100. metiuntur ide 3.
  101. a divisre, si asiluus est multiplus tunc
  102. merumus itorem uni
  103. qui ex ipsis fuctia
  104. multiplicandum
  105. x
  106. sie frunt residui:
  107. f. 2. 3. 49. 1. pr b. H. 3. 0. 1. 2
  108. Multiflicati per 21 _ 2. 4. 6. 1. 18. 12. 16
  109. unt ergo sident qui supra
  110. ili 3. rel. 1. 8. per 4. F rel. 1. 3i reling. 0. 0. 0
  111. multiplorum etiam
  112. is igisi Numeri naturale
  113. jurdisferenti
  114. lesin an VLlti
  115. requiritur, minod q
  116. es siciles per p erp. 13. b 15.
  117. c’unde res sie sals fecile perficitur tentan
  118. tempim litib. a
  119. Verit quaesitus: mimorum ioc
  120. post + Be a quacudus
  121. =1C, n aise exp
  122. sed Adtiaras. S. 2
  123. qu ntlgtus er datum, alti
  124. t ese au t tam s. a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 27, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068240:0004?run=74