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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 186v

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.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 185r); this page is its left half.

The machine reads it as

  1. fiat 20. 100 +02 300 + 11. 100.300 = 402. ubi 2 in fine ob duos 1 otales
  2. 10. 100 + O1. 30=8
  3. Et 2. 20. 100. 101 +2
  4. 10. 101+01. 301 = 00, 411. (4 30101+02. 30 4 11. 101. 301 = 00, 912
  5. scilicet permutatio interm, et.. O inhrinetalib
  6. et aequando valores 2402. 201 + 411. 402 = 2 4012. 200 + 401. 201. 200 + 401. 4012 + 40,2 201
  7. Ergo 200 = 12. 4 401) 201 + 411. 402 - 401. 4012,: 9012 +401. 201 qui tersins valor
  8. si aequetur secundo, habebitur aequatio in qua 201 assurget ad gradum secundum. Sed videarum
  9. an r deprimere liceat sed deprimere dem licet melius hoc modo: Sint duae aequationes
  10. 00. 200 + 00. 40]. 200 +004920
  11. 205 + 401. 201 + 413 20
  12. 2.00200. 201 + (929 00. 401. 200 +90. 4012 =0
  13. ba 00. 9I1. 201
  14. ubi aeqq. 12 oriuntur ex destructionibus terminorum
  15. auserendo aequ. 2, a summa aequationum ieth fiet
  16. (
  17. sae
  18. 200 +201 2200. 201 = 4012- 402 seu 200 - 201
  19. (5) CB - 401 + 1(401. 401 - 4. 402) sd si conjungamus aegqu. 4, 5, 6
  20. habemus solum duas
  21. 2
  22. 20) et 26) - 1. 411 + 1 Y(4 11. 411 - 4. 4 12)
  23. 200 + 201 vocando et 2001, fiet
  24. se d sint interventus irratio seid a
  25. Addendo aequ 1 et 2 et 3
  26. 20 et 4uo 4 200. C + 401. 200 4, 4: 201 + (2. 401. 411. 2011 201 = 4. 200. 201 + 4012 + 2. 2 e
  27. eu -401 (401. 200 +402) 4411 (411. 201 + 412) (- 401. 411 (401. 200 +411. 201 4 4012), aequ.
  28. (D (401. 4u (200. 2101) + (20, an. 200 + 402. 412) + 4012 4. 4017 (401. 200 + 2 1. 201 + 4012)
  29. ita res omnis reducta ad 200 ut 201. non nis
  30. simpricem gradum facientes. Nam ordinando
  31. 401. 200 +401 402 qu. 2. 401. 411. 200 + 2. 401. 211. pu12
  32. 2. 401. 4112. 201
  33. 40B. 200 2. 401. 41. 200 + 4. 401. 912. 200 = 4. 4012. 401. 200 + 40 (. 402 = 4. 401. 4u. ton + 4 402 112 ( 4013 - ( pon
  34. 4113. 201 4912. 412
  35. 413. 201 - 2. 401. 412.201 4. 411. 903. 201 - 4. 4012. 411. 201 4 411441
  36. compendio inde fiat 830. 200 +840. 201 +801 =0 et 690 200 1640 201 + 601 = 0
  37. et loco aequationis 0- 200 - 201 - 1 (4012 - (402+ 412)) scibatur 200 - 201 = 152, = 0 vel
  38. generalius 630. 200 + 640. 201 + (60) = 0. unde fit - 200 =+540. 201 + 501, : 530 = 640. 201 +601, 63
  39. ergo 540. 69D. 201 + 501. 630- = 530. 640. 201+ 530. 601. Et 20 = 501. 630- 530. 601, :, 530. 640 - 540. 630
  40. Et pari jare 200 permulando. 4. et a3. fiet 200 = -501. 640 +540. 601, :. - 540. 680 +530.640
  41. ubi jam explicationefacta et pro 630, 640, 601, ponendo +1, - 1, - X2, fiet iunde ut
  42. 200 = 501- 540152, :, - 530 -540 pt 201 = 501453015E, :. - 530-540 quos duos
  43. C + qu (530+540)4012
  44. 6= 2. 501. 501 + 501. 5301522530. 540. 52 A (570+ 540) 501 (401 4 91) - (BB 0n 20) (210530 - 401. 340) 152 7
  45. valores substituendo in aequatione rda, fiet
  46. ubi magnum habevitur compendium, si destnatur 152, quid fiet
  47. si faciamus 2.501.530 - 2. 501. 540 = (530+ 840) (411. 530 - 401. 540)
  48. 2501. 540 152
  49. atque adeo 2. 501. 501 - 2. 530,540 (9012 - 402 - 412) = (530+540) 501 (4014 411) + qu (530+540)4017 =0
  50. sed haec omnia forte brevius consequemur, utendo Canone ilum a me posito pro tollendis literis ex duabus
  51. aequationibus secundi gradus Redeamus ergo ad aequationes 1,2 et 3. Et per aequ. 2. erit
  52. 261 = - 401 . 200 - 4012,: 2. 200 +411. quo valore substituto in 0g. 3. fiet
  53. + 401. 401. 200. 200 + 2. 401. 4012. 200 +40121. 4012
  54. = 2. 411. 4012
  55. + 4. 411. 412
  56. Unde ex canone alibia me reperto fit.
  57. =0 seu compendii causa 00 + 8t. 200 + 82 = 0
  58. cui conjungende aequationem primam, quam umfor
  59. mitatis causa sic scribemus 70. 20047. 200 +7
  60. 80. 10. 82. 82 + 70. 7. 31. 8 -10H. _ =0 ubi res plurima
  61. +72, 12. 30. 80
  62. 71. 71. 80. 32 =71. 17. 80.
  63. = 20. h. 81. 82 =0 sed fortasse
  64. 2. 70. R. 80. tantum +70. 72818
  65. H. n. Ve. B fiet s
  66. coptraheretur, si fieret 1B. et - 7280 =0. restaret
  67. et optimum quidem videtur
  68. aq ita foret 412 = + L 401 41 - = 40i, ob 20 = 0
  69. fatis ert ad contrahendum facere 82 vel 80 =0
  70. 82i GI = + 11 + 11.71 - 4. 70.72),: 2.10 seu 8 g = 401 + Y(401. 401 = 4. 402),: 2
  71. 401 + 3 (40i - 2409)
  72. 70. 82. 32+ 72. 81. 81 = b1. 81. 82 = 0
  73. 4012. 4012 - 4112. 401284112 (2401. 411 - 4401
  74. 2. 401. 4012 - 2. 411. 4112-401. 4112+ 4 (.3, 401. 411 - 405)
  75. 401+ S(40- 4. 402)
  76. seu 4012 = 4112. 4012 - L 411.401 + L 411.401
  77. Hinc aequatione plana habebitur 4012 N llideamus j 411. quae cum 4012 sola ex ha cinculum radicale est
  78. Aia = 2. 401.9012 - 2. 411. 4012 (= 401. 413+ (2) 401. 4112 - 41. 401
  79. bendit ad cubum, quodest sisto altius
  80. sed videndum an ex ipsis 402, 401, 411, , 4012 possitit inveniri quantitates 100,300, 10130
  81. Nam 20 = (00 . 81) 461 - (10: B1)100 301 = (00. 1) 411 - (D: () 101 sid musus
  82. et quidem plane. Et apparet rem succidere
  83. Ex qua et unde 2. 20. 100. 101 + 2. 02. qu (oN: 31) 401. 411 + (00. 10: 012) (101. 401 + 100. 411) + H1. 100 00: 01 ) 41 br1. 100 (10. 8,) 101
  84. per et
  85. nteg adhibitas ubi pro 100, 101, substiturndo valores fit relatio inter ipsas
  86. assimulas 401, 411, 402, 4012 nam sufficientes adsunt siliceret facere
  87. Si liceret facere 902 =0, diretur 300: 100 ex datis et fiet 200 = - 401
  88. esset aequationi I. Hinc ex aeq. 2 fieret - 2. 401. 20) - 40, + 411. 201 + 4012. Unde fiet
  89. 201 = 4012 - 40i,:- 41 + 2401 = - 411 + Y (411 - 4. 412),: 2
  90. ex 402 et 412 habetur
  91. hons satis factum 300 + per 100, ita
  92. quod si faceremus
  93. et ficet tandem
  94. habentur 20, et 30
  95. 101. sed praeteren
  96. 4V- 4. 412 =0 duretur haberetur 301: 101 ex datis
  97. 4012 -, 401 = 4112 + 2. 401. 41 sex A6 q0c qui q gr unde elici
  98. poterit ratio 14 ad 101 ad 100. sed intis Haec succedent modo ne fiat 300: 100, ut 301 ad 101
  99. vel 301 ad 100, ut 200 ad 100. Et primum si sit 402 = 0 f et
  100. di
  101. 2; 100 = - 11 + H(1 2- 4. o 20.02), : 2. 02. porro ob 415 - 412 = 0 fiet 10. 10124 01. 30 i + 2.10. 01. 101 301 2
  102. 4. 10. 1012 +402. 305+ 4. 11. 101.301 sit 4. 20- 10 = 3 Et 4. 02 -0 = 39 Et 4 . 1= 2. 10. 01 = 2. 31. atque it
  103. neque fiat 101ad 100
  104. g in 31. 1012 4 33, 301 +, 313. 101. 301. unde 201. 161A = _ = 373 + YC3132 - 31. 33)
  105. nisi egitis cesibus
  106. 100 sit 301 = 112 101:
  107. semper in fallor niabilibus coincidit cum
  108. bre substituto, . 000. 1 100
  109. +2. 401. 411. fro1310. 10d. 100. 101 +2. 62. 112. 102. 100. 10141
  110. e ea a ui is

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 186v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0372?run=74