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Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 39r

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: 0.79.

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. 40v); this page is its right half.

The machine reads it as

  1. pag. 9. Tabula continaata sotum usque ad cd. Hin.
  2. 3. X3. XV.
  3. 5 X4 XV. X
  4. ua 6.
  5. to generalis tentiata
  6. pro x. y Z. c
  7. sat additraris instructos prodire +2+3++5F +9 +11 +15+ 18 +22
  8. quindecimum
  9. Et ad aequa
  10. +1...... id est totide
  11. 6X. Xy. RG. Xy. XCD. yZ tionem oper simllem multiplicundum potre
  12. 9. XB Xty. XZ. XY. XC. AGZ. y. Z. GGco quad anteoflnum pero adhnc, quia et maximum terminum arbitraria iistsine
  13. licet. Denique ad multiplicandam aequ. 10. per gebis agium pro
  14. 1X? X y. XZ. XV. X. X 1Z. X9. X. XyCo. yZ. formulam Tarbitrariam usquad undecimum gradum inclusive proditi
  15. vunt Arbivariae literae 2tht+ S+B+GutSi
  16. .Z
  17. Ergo summa omnium
  18. V. y2y. Zc.
  19. S 2 2a
  20. 33 X12
  21. 22 45. X
  22. V. +213. b
  23. 1D X
  24. 181 10 37. X
  25. eX
  26. 21) 43 414
  27. 22 _
  28. 1b
  29. CE
  30. nde putet formas tollendas
  31. esse et 276. tollendas
  32. omnes praeter has quatuortres:
  33. 184
  34. 2
  35. b
  36. a. ab. abE tollendae ergo erugt 377.
  37. aut certe
  38. utum
  39. Quoniam autem plures quam lops Elbemus arbitrarias
  40. hini utique patet cuius ex formis. X. X. y. X3. Xy. 9. erc.
  41. posse ascribi arbitra tiam, ac poinde tolli etiam posse
  42. quamvis terminos inutiles.
  43. alerum opus est adhuc ut possimus explicare terminos omnes
  44. ut: N. X. X3. erc. y XI. Ny ore per formuu formas ab a. b. c.
  45. inq eum finem habenda est Tabula in promtu. Eam operae pretium erit calculare
  46. saltem usque ad X inclusive. Quin imo spes est compendium etiam esse
  47. proditurum pro toto aliquo gradud, ut pro toto gradi N V. et pro toto
  48. gradu X. Xy. 7. statum exprimerndo sime calculo per formas ab a. b. c. deu
  49. Etiam pro destructione neculiare se dabit compendium. Denique et pro destrnctionibus
  50. quia omnes termini omnium gradiuum destrumctur praeter anos sata in summa et
  51. ex his unum in summ. Et ores reducetur ad investigationem hujgsmodi aequa
  52. tionum resolvendarum: CC C 1l + 2 m + 3n. . + 4. aequ. 0.
  53. EAl +Dn +Xn, aequ. 0. Gl + jom + 10n + 12 aequ. 0 qutur
  54. quaeritur l.
  55. m. n. fii: laequ 84 - 2m 2n a8 -bu 7
  56. aequ12 tom- en scibatur 15, 9. l + 21 5,9 m + 3,5, 9n + 4, 9, 9. aqu. 0.
  57. 1,5, 9 l =+ 1, 6, 9 m + 1, 7, 9,n. = 1, 8, 9. aequ. 0.
  58. = 1, 5, l + 1, 5, 10m + 1, 5, 11 n + 1, 5, 12. Erg aequ. 0.
  59. Ergo 25,9m = 35, 9n + 4, 5, 9 aequi 1, 6, 9 n + l97, 9n + 1, 8, 9
  60. aequ. 15, 10m + 15, 11 n + 15, 12.
  61. seu
  62. Et rursus omnia inultiplicando
  63. 2,5, 9. m + 35, 9n +4, 5, 9 aqu. 0. 25, 9 mt 35, 9 n 14, 5,9 aqu. 0. 16, 9m +1, 2, 9n +48, 9 u
  64. n
  65. 136, 9
  66. 1,7,9
  67. 1,879
  68. (1) m + (2) n + (2) dig.0
  69. 15,91 1,5, 12
  70. 110 15, b51C
  71. 3) Ci
  72. o
  73. 1,5,10.
  74. (5) m +(6) n + (7) aequo per compendium unde
  75. ad imisationem aequationum 1. 2. 3. pro l. poncndo m, et pro mpopendo n, et pro n ponendo nihil seuo
  76. seu
  77. habebimus aequationem (1)5) m +(2) (5In + (4)6) aqu. 0. (1X) m + (1)(6)n + (1) aequ. 0
  78. 8
  79. Ergo n aequ. (1) C7) -(4) (5) aequ. 2,5, + 1,61 24, 5, 9 + 15, 12 91) - 1,5∞+ 1,89, 2, 5.9, + 115, 10,
  80. seu n ago. 21 4519 + 14B5 6 9 4
  81. 212 415612,-
  82. 2,3,579+ 12, 5,719 + 114, 52, 10+1257 10-2, 3, 5, G - 113,5,6,9- 1, 2, 52, 11 = 127, 5,6, 11
  83. habentur eculo
  84. Hinc patet pro 4 literis. a. b. c. d. vel X. V. Z. Co. formas vel terminos ad qimur
  85. usque gradum inclosive prodire: 1421249 +0+9t+ 15+18+224 26+33+37,43+ 45.
  86. Ad aequationem 5. multiplicaudam per omipessus usue ad dcimum gradum inclusive prodre
  87. ..1.
  88. arbitrariarum erit: 1+ 2 + 3 +546+9 + 11+ 15 + 18 +22923 +2, +26
  89. 28
  90. 1+2+3+5 +6+9
  91. +e
  92. 10 30
  93. 11 108
  94. 155
  95. 168
  96. 3+bIgus
  97. 3
  98. 60
  99. + 40
  100. 92 +26+3313
  101. dem
  102. +45+45
  103. nc
  104. - - . . . . . . - l aqu. 0. et Wo= mpo (013 XB. X. y. X3Z, 42). ~C. X3yZ. L. X (. Xy c0. Xy Zr y c. yY. C0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 39r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0079?run=74