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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 135r

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. 134v); this page is its right half.

The machine reads it as

  1. Quaritur modus efficiendi, ut productum ex 10 ~V + 12 et 20VD + 22 aequetur Bto
  2. Cipse r= 31e 4 32e + 93, :, 40e+ 2. 40 4e + 45. fiet 1F= 1St 02SI Net OI
  3. asa Eodemmodo licebil explicare 3ovrt 12.
  4. porro ut nt prvtentus ext plicationis ae
  5. XId ZL. SEEECXBIIEHOS
  6. fiet 10b0+12 - 11 4 q ebqo Cr p V E. Heip. qi
  7. 408+4. 1d4 e + 6 40 2i e 1 4. 90 n C 41
  8. Ut ae ergo productum ex dectis aequetur qu Eodem modo explicabimus 200 + 22
  9. Ut ergo prodactum ex duohus sic explicatis aequitur quadrato, oportelit numeratore,
  10. in se juricem ductos aequari quadrato; svia
  11. finge v= 30 e + 31C+ 32, :40C+ 41 e r 42, siot Nam irrationalitas ista non nocet, cum caeteris
  12. peractis resolvi possit
  13. + 10. 31. 318 F10. 2. 31. 32C +10 3232 : 405 + 41C +42
  14. Bd 10. 31. 30C + 00. 2. 31. 31 e2 + 10. 2. 34 32C
  15. et fiet 10VP+12=
  16. + 12. 400 + 12. 41C + 12. 42
  17. pastemus si jim C (valoris i ipsius 10vV +12, aequetur quadrato, idemque fiat cum nlore ipsius
  18. Ntn spator
  19. utique productum valorum aequaevitar quadrato, quia
  20. netrobique neminator est idem videamus primum compendii causa, an liceat quaesitum
  21. nulmeratore valoris ipsius 20B + 2
  22. assequi ponendo 30 =0 in aeq. 2. ita 10. 31. 31 e +2. 10. 31. 52 C 4032 32 aquabitur Ctr
  23. 100 eC + 101 C + 102
  24. a C + 2a+ bb
  25. a = 100 b∞ f102
  26. ab 2 (100. 0d = 101
  27. 12 40 D 12. 41
  28. et fiet 4. 10. 31. 31, 10. 32. 32 = (2) 2 10.31 32
  29. 12. 40 .n 12. 42
  30. 12. 41
  31. 12. 42
  32. et fiet 40 = F.): 10. 3,. 32 +1. 42 = 4. 10r31. 31,, 4. 12
  33. (6
  34. Sed similiter 402 (D 2. 20. 51. 32 + 22. 4) - 4. ~. 31. 31 20. 32. 32+ 22. 927:, 4. 22. 1. 5l. 51
  35. (2) 2 10(3r. 3r4 12. 41 = ( 2. 10. 31. 32 +12. 91 - 4. 18251. 31 10. 32. 32 + 4. 20 31. 31. 20. 312
  36. quos duos valores aequando fit
  37. 4. 10. 12. 31. 31 = 4. 29. 22. 31. 31
  38. quod si compendii adhuc majoris causa, quia sic licet, cocissemus ad huc 41 = 0,
  39. =
  40. fivet 40 = (4. 10. 31. 35 = 4. 10. 31. 32) (4) 10(62) 31. 42,: (4 12)
  41. quid si compendii ad huc majoris causa (quia ita videtur licere) sccissemus aDhuc 41 = 0
  42. fieret 40 = (4. 10. 21. 32 = 4. 10. 313 32) -(4. 10 (12) 31. 429:5 (4. 12)10. 324 12. 42
  43. seu 40 = - 10. 31. 42,: 10. 322 + 12. 42 et rursus 40 = - 20. 31.42,:, 20. 35 12. 42
  44. s
  45. quos duos valores aquando, fieret 10 20. F 10. 20. 32 + 10.22. 42 = 10. 20. 32 +12. 20. 42
  46. sed ita autetrem non licere, fieret enim 10 - 20 10.22 = 12. 20
  47. quid si 42 fecissemus 0, fieret 40 = (410. 352 32) + 4, 10. 1231. 32. 41 4 132 41( 410. 31. 32)- 4. 10. 12. 31. M2, :, 4. 1012. 32
  48. et rursys 40 = 4. 20. 22. 31. 324 12. 417 - 4. 2022. 31. 42,:, 4. 2022. 32
  49. quos duos valores aequando
  50. fieret (4, 10. 12. 20. 22 52. 4D1 10. 122 41 4. 10 12 20 2 31. 32. 41)- 201 0
  51. 4. 10. 12. 20. 22. 31. 32. 41 + 12, 20. 2X. 41 - 4. 10. 12. 20. 21. 31 42
  52. c 4, 10. 12. 20, 22. 31. 32.41 + 10. 12. 27.45 = 4. 10. 12. 20. 22. 31. 42
  53. fiere
  54. C10. 22 = 12. 20
  55. Ergo rursus esset 3 =20
  56. Quid si in aeq. 6 et 7. faciamus 32 =0 fiet 40 = 12. 41 4. 10 3i 35 - 4. 10. 12. 31. 42,:, 4. 12, 42
  57. aequ.
  58. et rursquse qu = 22. 41 (488235 52 = 4. 20, 22. 35 92 : 4. 25. 42, quibus aequalis fiet 10. 12. 22 = 12. 20. 21
  59. : 4 10. 12. 32 + 4. 12. 42. = 22. 41:, 4. 20. 2232+ 4 23. 42
  60. ubi eursus 12. 20 = 10.27
  61. quod nonlicet
  62. seu fieret 10. 22 = 12. 20, quod minus adhuc procedit,
  63. adeoque A. 12. 20. 22. 38 (44. 122. 22242) = 4. 10.12. 22 324 4. 12. 22. 42
  64. fecissomus 40 = 0
  65. feret (4. 10 31. 324 4. 10. n. 31. 32. 41 + 12. 41(= 4. 15 35 327 - 4. 10, n. 31. 42 = 0. seu
  66. sed potius licet facere 10 = 20 adeoque 41 vel 42 farere = 0
  67. 22 = 12. 41 + 4. 10 31. 32. 415: 4. 10. 31 = 22. 4,2+ 4. 20. 31.32. 417:, 4. 20. 312 quibus aequatis,
  68. id est 10. 20 = 12. 22 ut semper
  69. ethoc faciunt ut arbitrer idem generalite futurum ex aeu. 6 et 7 adeoque eas non procedere
  70. fier, 12. 29. 41 + 4. 10. 20. 31. 32 = 10. 22.41 + 4. 10. 20. 31. 32
  71. sed ujus tammen experiendium.
  72. non procederet recarre retinenda esset quantilas 30, qu sed quea tunc
  73. retur ad quadrati quadtalum faere
  74. 1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 135r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0269?run=74