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Leibniz-Handschriften zur Mathematik LH 35, 4, 10, 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: 0.86.

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. 7v); this page is its right half.

The machine reads it as

  1. Regulam
  2. Inventio communis Mensurae, eique connexa
  3. sublatio literae ope duarum aequationum.
  4. aotigationem communis mensurae
  5. investigationita communis mensurae
  6. Quod fit perdicisiones replicatas
  7. sit dividendus 10 + IIX + 12 X + 13 X + 14 X + 15 X3 + 16X
  8. Divisor 20+ 21X + 22 X +23 X
  9. Zetens sntus
  10. Operatio 30+ 3IX+32 X + 33. X3+ 34 X +35 X + 36X
  11. Quetielis p 3B ro
  12. Residuus 30+3IX + 32X
  13. Quotiens purus 33 +haX + 35 X H6X, : 16
  14. Vel ad huc altius asfurgendo
  15. s
  16. ex operationis
  17. 1. 16.23 = 36. 23
  18. 15. 23= 35. 23 +26. 22
  19. 14.23 = 39. 23+25. 22+3621
  20. 13. 23 = 33. 23+34. 22+3
  21. d. 5=
  22. 32. 23
  23. 2
  24. Sit dividendus: 10 + uX + 12X + 13X +14X + 15 X + 16X +17X + 18X + 19X
  25. Divisor 20t uX FuX + 13XXtX , 6X
  26. Residuus 30 + 3IX +32X +33X +GAX 135N + 36X +37X7
  27. 36. 20
  28. 10.26 = 30. 2B + 31. 27 +32. 26+33. 25+34. 29+35. 2) + 36. 22 +37, 21 +38. 20
  29. 11. 28= 31. 28 + 32. 23 +33. 26+34. 25 +35. 29. + 35. 27 +37. 28 + 38. 21 + 39. 20
  30. 12. 28 = 32. 28+ 13. 28+ 34, 26+35. 25+ 36. 22+ 37. 2+ 38. 2a + 39, 21
  31. 13. 28 = 33. 28+ 39. 27+35. 26+ 36. 25+37. 24 +38. 9+ 39. 29
  32. 24. +39). 23
  33. tio= 14. = 3 28 + 35. 27 + 36. 26+37135+3
  34. 15. 18 = 25, 28+ 36. 2 + 37. 26+38, 25+3929
  35. 16. 2 = 36. 2 + 37, 37 + 3Y. 26+39. 25
  36. 19. 8- 39. 2
  37. 9. 26
  38. jam rursus it
  39. prins chisor sensemu dividendus 20+ UX tuX LXtRHSX +isx Z 27X +18X
  40. prifisitus sen seundus divisor 30+3IXLZIXY3X B ,35XS +3BX + 37X
  41. secundus Residuus 40 LAXtAIE +4IR tAnX HASX + 4bX
  42. 20. 37 = 40. 37+41.36 +42. 35+43. 34+49. 33+45.32 + 96. 31 + 47. 30
  43. 1. 37 = 41. 37+43. 36+ 43. 35 + 44. 39Y 45. 33 +4b. 3st + 47. 31 +48. 30
  44. 12. 37 = 42. 37 + 13. 3br 47. 3 + 45. 34 + 96. 33 + 47. 31 + 48. 31
  45. 24. 27 a 44 27+45. 36+ 4b. 3
  46. f. 3) = 45 43
  47. 6
  48. 8. 11
  49. .= 4 3 ab 3b
  50. 28. 37= 18
  51. . 34+48. B
  52. 47. 35+48. 3
  53. 45. 35
  54. Et tertiavice
  55. primus ralituus sen digsni sen snus Dividendus 30 + 31X132X +35X +aX + 18X +36X 137X
  56. 3tius Residuus SOtSIX FSix H SSXHsX +SIX
  57. 30.46=50. 46+51. 45+5244+53, 93+ 54. 42+ 55. 41 +5640
  58. 31. 46 = 51. 46 +52. 45 +53. 49 +54. 48+ 55. 42 + 5b. 41 +57. 40
  59. 32. ab = 52. 46 + 53. 95+54. 44 +55 11+ 5b. 42 + 57. 41
  60. 33. 4b = 53. 96 + 54. 45+ 55, 49 +36. 13+ 57. 42
  61. 2 46 = 14. 46 + 55. 4 156. 44 +57. 8
  62. 35. 46 = 55.
  63. +56. 45+ 57. 44
  64. 16. 46 = 5b. 46 +57. 45
  65. 3. 9b = 57. 4b
  66. et quarta vice
  67. Edgresitu en 3tiusomtaseu atque dividendlis40 +AIX tAX 143X 1 AX L4X bX
  68. 50 + SI X +5IX +53X+54X 155X
  69. 60+61X +62 4 63 X 6qX 1
  70. 90. 55 = 60. 55 +61. 54 + G653t (2. 52 169. 51 +65: 50
  71. 41. 55 = 1. 55+62. 54+653+64. 52 +65. 51 +66. 50
  72. G2. 55 = 62. 35+ 63. 34 +6)53+65. 51 +06. s
  73. 42. 55 = 61. 55 +5454+ 45. 53+ 46. 51
  74. 44055 = 64. 35 +5. 54 +66. 53
  75. 4c. 55 = 45. 53 + (b. 54
  76. Et ita pergendum est ad huc vicibus quatuor; et ita omnino instituendae sunt operationes
  77. 46. 5 = 66. si
  78. seu divisiones octo. Quia regulariter seu generubler, residuns est uno gradu inferio.
  79. divisore, ideo ut residuus ultimus sit gradus nullius, seu ut litera sit sublata
  80. oportet divistones fieri 8. Nam primus est gradus ymi secundus gratus sexti etc. ergo
  81. octavus est gradus nullius. Tot ergo opas est divisionibus, quot graduum est divisor
  82. In aequationibus duabus ejusdem literae, sem peus reperiri potest communis divisor, cujuscunque gradus;
  83. imo plures. Itaque hiac eadem Methodo datis duabus aequationibus ejusdem literae
  84. possumus tertiam lavenire ejusdem literae inferiorem fe ambabus, quae sit dat gradus;
  85. adem et valorem literae, qui est comndi aequasio infima literam continens. Data una
  86. aequatione licet invenire ab huc aliam per inversionem turarum, pro X substituendo y = L
  87. idem est calculus; tartum ex nutis primis fiuut novissim et, pene primis, penultimae ete
  88. oguit
  89. a
  90. jam
  91. se imiem ducartur, sed inveninntur ordti
  92. ita lalrus s asi catmt abat sa aqeatires qua se sratutum si inalicatione
  93. Quotieas hic negligitur,
  94. quia non pertinet
  95. ad replicatas
  96. divisiones
  97. qua-
  98. nes
  99. ssse 2y resitussenHius Divisor 40+ 41X + 42X +43X + 44X 145X + 4bX
  100. atus Residuus
  101. 3tiis residussenatus Divisor
  102. HIC potius scripsi 10 + IX+ nX etc
  103. ut residum divisore mutato in
  104. in dividendum, residuoque in divisorem
  105. novum idem temper literarum
  106. progressus se notarum servetur
  107. continuatis licet replicationibus
  108. Etsi Residuus non contineat
  109. notas omnes sui ordinis, nempe 37, 38
  110. tamen concurrunt ea ad reliquarum
  111. ejusdem ordinis inventionem, quippe
  112. ingredientes operationem anteceda
  113. nec ad inventionem residui;
  114. nam constituunt quotientem
  115. ste
  116. cujus inventioni infa
  117. Pior est inventio
  118. ui Etsi
  119. igitur ipso quotiente non utamm
  120. tanec utiuur ejus ingredientibus.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 10, fol. 6r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068007:0011?run=73