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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 68v

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: 0.87.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 69r); this page is its left half.

The machine reads it as

  1. 27) Hine patet etiam ib
  2. S1. 113 aqu. p7 aricali 14 et valore 713. 313
  3. 0 et 7112 =0cessare valores ipsarum 73: 313, et binos valores
  4. ipsarum 51: 313, quos quos, alias dedissent aequationes
  5. 11, 12, 13, 14 articuli 18, sed
  6. loco eorum valorem prodere inde ras aequationes quatuore (723 12. 34 = (1mo) rG. 3pe 1712, 123. 312 e
  7. ex 13tia, lire ex IIma 3 1 1723. 112. 323-1712. 123. 312 =0 vel e 28 ve
  8. (1mo) 1723: 1712 = 1230312,:, 112. 323. et ex 13tia, (2d0) 1723: 1712 = 112. 323, :, 123. 312, et ex
  9. 12ma, B3tro) 1723 : 1772 = 523. 712, :, 5121723, et ex 14fa, (4 t0) 1723: 1712 = 812 13 :, . 523.712
  10. Utroque modo colligitur 1723 = (+ C +)) 1712, seu vel summam eorum vel differentiam, nihilo aequari
  11. ut jam habuimus cgrticuli 26 aequatione 9. Cter etsi valor hujus signi ex aliis determinam possit
  12. per inventos jam valores ingredientium ipsius 1723 et 171E. Ex aequ. 1 et 2 huijus, fil 123, 312 = 112. 323.
  13. seu ax aequ. (2 articuli 19 (6t0) 1252. 2372 = 235t. 1272 quae est aequ. 7 articuli, 26.. Et ex aegq. 3 et 4
  14. ot. 122. 729. et substituendo valores ex aegus. initialibus articuli 19, fit utique
  15. hujus fit 523. 7182
  16. 5). 12 (37) 28
  17. 125 seu 1254. 237, :, 235+ 127 = (8v0) 112. 323, : 123. 312 sed per aequ. 2
  18. aes 1 (a) 31E articuli 19 est 115 112. 323, :, 125. 312 = 125. 237:, 235. 127 Ego
  19. ex. aequ. 8 hujus fit 15 295t 1 1252. 237:, 2352+ 127 = 125. 237:, 235, 12. seu 125. 237 = 235, 127, ut
  20. jam habuimus articula oto. Itaque aequationes 3 et 4 nihil dant, quod non jam dederitt aequ. 1 et L
  21. Assumeramus autem ali (aeterum omnis calculus ab aequatio articuli
  22. 18 inclusive huc usque erpori innixus fuit, sed felici, nempe in . 18. qu F aequ. 4
  23. assumti A, 11223. 71223=51273. 31323, quod putarem permutando 1,5 9, 1 et 5 cum 3 et 7
  24. unum ex altero prodire. In quo errami, sed feliciter. Nam hac una hypothesi assumta prodeunt omi
  25. quae malto calculo huc asque indagavi Ae Nam per revera ex aequ. 13 artiuliia et 4 articuli 15, bit
  26. 13. 7 3 et 13 articuli i9 et ar 5 articuli 15 fit. 11223, 71225 = ) 2 15. 37, 125t 25, 17 + 2, 2
  27. 3E, 125 + 235, 117. 2372. Ergo posita, aequ. 1. fit 125 = 235, 127 + 237 = (Gto) 15 4 235, 123 - 299 2
  28. quam aequationem effecibs expliate ponendo fies 15 (125. 12,+ 125. 2372 - 235, 127 (- 235. 237) = (125.128- 25. 233
  29. +95. 117= 235, 237) unde 2 125. 237 = (2), 235. 127 quae est aequ. 7 articuli 26, vel
  30. 297 Rocolligamus jam inventa (1mo) 125. 237 = 235. 127 per aeg. 7 articuli 26, vel jam
  31. aequatio 6 hujus.
  32. + en aequ. 4 artiC. 25 est 112 +512 = 312 + 712 Aa a - (2ho)
  33. seu 323, 112. 123a - 15. 239 2 adot 125, 312. 313 a - 3). 2372 et ex aequ. 6. artic. 25, 113+5 23 = 3134 723
  34. per aequ. 4 articuli 18.
  35. Ecqts 312, _ 112. 122a + 15. 125 . 12 5e. 313a + 37. 12722 jam vero antea ex aequ. 8 articuli 16 vel
  36. aequ. 2 articuli 19 l 1232. 312, :, 112. 323 = (4t0) 235. 127, :, 125: 237.
  37. Accedunt jaem qu ex
  38. ex aeqq. initialibus articuli 29, vel ex aequ (H B. 13. 14 aegg. 9 et 10 articuli 14 itemque aegy. 1. et 2 articuli 15
  39. valores sequentes 5i = (56o) - 15. 235 : 123a et 523 = (6to) 15, 1252: 112 a et 712 = (,mo) ~ 37. 237: 323a
  40. 37. 127: 312a Deinde ex aeq. 17 articuli 19, 513: 113 = (9n0) - 15. 1125. 235, 125 -235,:
  41. et iD 713 313 ex aequ. 6 articuli 15 fit 713: 313 = (10 M0) - 37. 127. 237, 127 - 2373 :1, 312.313, 127 +237. sed
  42. et in q. ex aequ. 10. artic. 16. fit 152. 125t. 2352 :, 372. 127, 2992 Hm0 s A : H H = (+223, Imon;, ester. 123 139 C
  43. et 723 = Bv0)
  44. = (51225. 1L3 100 H 200MM, :, 2 H213. 13 13 id est per a94. 5 et 6 articuli 1(7,
  45. articuli 17, (11E 232 (100l-200 mm, . 113. 513): 31223 (300 nn -200mm, : 313.713). sed per aequ. 14 articuli 14
  46. 2y 112. 123, 125 + 235
  47. or quem valorem inserendo
  48. in valore ipscus IN: AI fet et duos valores aequando, destinitur utrobiue 15,37 et fi R 125. 235, :, 127, 237
  49. et per aequ. 5 articnli 15 est 11223: 312232 = 152, 135 - 235, :, 373 127 -23
  50. = 313.713, 125-2350 (105 - 200mm) :, 113. 513 127 2- 23, (300nn -20d mm) seu fit tandem 313. 713;, 113. 513 = (11 mo
  51. 12) ((125. 235, 125-2371): (127. 237, 125- 2351)) (300 nn -200 nm, :, 100 11- 208 mm) fuide quae scripta pagina aversa articuli 261)
  52. sed ex aequ. 1. hic, sequitur esse 125. 235, 127 - 237 = 127 3377 125- 235 vide calculum peractum
  53. pagina aversa articuli 26. seu est 12720237,:, 1252 235 = 127-237: 1252 - 2392 seu denique
  54. et Z13 per aeq. 9 et 10
  55. et similiter
  56. 113. 513(5 - 15. 115, 125. 235, 125 - 235, 29, 112. 1239125+235 = - 15. 1152, 125, 235, 125- 225 3: 4 112. 123, 125 - 255
  57. et post per aeq. 13 fiet
  58. odnna adonn
  59. 3172. 71s (6 135. 112. 15. 127- 13
  60. 152 313, 3232 125-2354 = 1124
  61. 325 ponendo per aeg. 4, 123. 31 : 112 ert 115 1233:, 315. 325 = 112 5:, 312.seu fiet
  62. ,2s. 277 sobma. vpu d 31 2. . 1. g
  63. ex qui artic. 16 fiet
  64. iults insiquis qu s canticuli 17. fiet 12. S12V + 123. 52)E = 11229 Spoll 2orum, c2. 113. 513), ubi
  65. 1300 nn -200 mm, 15=it. uu
  66. 1t, 12y 522 vatorem per ea 14 articuli 14, et
  67. ratorem ex aqu.15 Exius et ponendo
  68. (275 ergo fit S13: 113 = 15. 125- 238: - 12. 13Irr
  69. et pari modo 713: 1132- 37, 12 - 237:, 312. 323ser et per ( 11, aequ 15 sit as 8 113 51 = 1, 13G 125 155, 12 13
  70. per pro 133 substituem
  71. 125 235 12 +295
  72. q et a est 513: 1Z2 -15. 125. 235. 125-232: 1112. 1231 1
  73. (12, 31Z, 523, 71, 712, 723, consideremus, ex aequ. artic. 3 esse _(m) 213 = 519 + 313 7 13 13
  74. 512 + 312 = (280) 312+112 et 223 = 523 +323 = (3tio) 723+123. Hunc explicando inventos.
  75. et C2 r3: 513, (21) 15 27. 323 i 155
  76. Ias duas aequationes conjungemus cum
  77. 93 235 4 31 213. 323a 37 125, 15 1 1 13 valores iteram ipsarum si, 523, 812, 723
  78. (30) Habilis jam valoribus
  79. prodeunt it pli summa aequs. 1 pro literis 8, quantiratibus 8, seu potius pro rationibus, 7. Quia in ae99. 2 et 3.
  80. et similitur l 212-
  81. uticuli 29, quibus si acceda
  82. erticuli 29 signa sunt apubigua, adeo ex aequ. 2. fvi ibi, facianus 112f + sif = (4to) 312 9 + 7129. posito 9
  83. valores in artic ag fiet
  84. et 3. conjungemus cum tribus aequ.
  85. itatem signo affectam, adeoque gy =1 g, idenque ff =. et ex aequ. 3 ibi faciamque 12yh +513h (sto B2k 1r23A
  86. itidem sunt unitates signis affectae
  87. 512 = 2(2- 312 et 712 = 212 112 substituerdo in aeg. 4, fite
  88. 3EB +9) 2(f-9). Hinc si f et 9 sint sig nondiversorum
  89. odem modo (7mo) 213 = β27 -123) (h+K): (h- K), unde
  90. 112 F, +212F -3l2f = 3129+ 219 - e129 seu 212 ver
  91. conscatit aequationi l’artiali 2g. posito inroe intria ex aequiat u et
  92. 125+ = 235 : 1252 235 2 17 = (12mo) 127- 237: 127. 237 Unde tandem fit (13tro) 313. 13, :, 113. 513= zoonn- 2odinm, :, vooll. 20 en
  93. nisi faciumus 125 23t =0 et n 23X a0 quod minus se jam in hac eu Ex hac aeg. tollamus
  94. et 315. 713 = 37. 3134, 127, 237, 127 - 2574,:, 3122. 3257. 127 - 251. Unde per aequ. 12 o
  95. itemque 115. 5132 = 15. 113+, 125.3359 (25- 2357, :, 112- 123, 125 -235
  96. Z 12N. 127 esC
  97. 100 l - 200 mm, 37
  98. fieret

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 68v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0136?run=74