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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 72r

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: 0.81.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 65v); this page is its right half.

The machine reads it as

  1. Extractione igituo fucta ex aequ. articuli 12 sejundum articulm B3, fiet
  2. 12. 512V + 129. 523Z= Sir23 ((11223CU - mm.) I. p (1213. 12913)). seu per compendium
  3. H2. S12V + 128. 323Z + 109. 100 a =0. Et pari jure ob 8, p- 0 fit, 312.712D + 323. 723Z + 200. 200 a0
  4. quae duae aequationes debent multiplicata ut debent coincidentiari, ne per eas reperiatur
  5. Y vel Z, vel veZ. et fiet 112. 512. 200 aV = 123,523. 290 a2 100. 100 a 40 quam aequatio
  6. nem jam identicam reddendo, fit 20: 105 3121712. Mp et 208. 100= 323,733,:, n35 Unde
  7. 15) Omnia ergo rducta sunt ad aequationes 5 et 6 arsiculi hujus, itemque 3 et 4.
  8. 1. 2, 3 g articuli q
  9. vgrte tamen adhuc se imstendia quaedam
  10. et semper let u3 vel siem T1213, S12B, (1413, 52313 solum
  11. comptendia
  12. tantum extra haec t occurrit 13. 5C3 in valore lationali MI3C iC. 313 + 13OSAZ et 1X5B. 2
  13. qud seli et ieatoribus P,
  14. e . et H2B i si3 n sI. sit mBsB = I S) an ergo praestat tollere 113513
  15. quam caetera. Nempe 11213 = 112. 513 + 1γ. 512 et 1213 = 125B- 113.512 ergo addeado
  16. 11213 F51213, :2) =. 513 = 123(3 +52313; 2 2. 123 Hinc 123, 112I3 +H3. SnB = 112. 123 Gru2My
  17. 1213 - 51213, 2. 512 = 113 = 12X13 - 52313; 2. 523AIc C5. 11213, 52.51213 = 5I2 NN , 5yV
  18. monisin
  19. quod si velimus tractare eodem modo fiet:
  20. mess meneurs erdussus
  21. 1213 = spH + (231 - si5 - 11. S13 = + 3. 523. (27- 195711215 2. 8. m B
  22. 4112. 512. 1532 112. 12. 52313)
  23. et Rationalis aequatio destructis irrationalibus erit
  24. utim ( us ib videguns an aequationes 4 articuli 9 possint
  25. u
  26. jam
  27. Ex aequ 1. s fiat - 112. 513 + 13. 512-
  28. -312. 7B3 + 313.712
  29. fit 12. S13 + 113. se2 - 571
  30. -123. 513 + 113. 523 - 1323
  31. 1312. Ex a9. fit 2, 3 73t313 723 3123
  32. B pro 1, sit 1 a + r2bl. L 0 pro 2 sib ad 2a
  33. 129. 511 F 13. 522 - 5 23
  34. pra dsic Matp = 3 pro
  35. pro 4 sit na- nd 21 40
  36. Ex isit na + 12b = 10 (1d + 14). Et ex 3 est na - 12b = 30 (13d - 140) Erg. 2. na = ( d 312C)
  37. deniqu pro 3 sit 4la atrb 3 30
  38. 2. 21a = 29 (22d 1249) + te su d un BC)
  39. Et eodem int ex aequ. 2 et 4. fiet Et eoder
  40. 2. 12b 2 (0 (1d +14C) - 30 (13d -14 e)
  41. 222b (23d1240) - 48 (3d-24e)
  42. similiter suburendo ab aeq.). sustichendo aeq. 6. fit
  43. et ex aeqq. 2 et A pari jure
  44. Ex 7 et 8 fiet: (12 13, + f 13, 22 24, 40 23d) d = (2 te 14. + 28 14, + 2 14, - 4e24) e 80
  45. Et eodem mod ex getiosis (2. B n - (3e 1u- renn +. 40 21) d = (- 1∞3. 1472 4 0, 4. 22 + 28 1412 + 20. 24 12) e
  46. Eiqu ex 11 et 12 fil (10. 1 2) + 30.13 21 - 2a. 1125 - 40 241) (- 1014 2 - 2 19 21 + 20. 24. 12 + 40 24 12)
  47. 1apat - 30. 1722 - 20. 1712 , 40 11 n (- 10 1 4 21 + 30 14 21. + 20. 241 - 40. 4 1)
  48. prasabit Addantur in unum egus et c2 jam 2+ 2 = sar 123B
  49. 11223.51225 (inise
  50. 2. 11213. 2313
  51. et deni
  52. Et subtrahendo
  53. =11223.51225, 52312 (l mon)
  54. = 312. 712. 1001. - 323.723. 106.. = 100,. 200ad
  55. etiam 112. 512. 323.723= 123.523. 312. 712 seu 12. 512:, 123.523 = 312.712:, 323. 723
  56. x articuli B3. aq3 et 4 quaecamus 51: 113, et 713: 313. Nempe ex aeg. 1. fit 51 F 4 Scus 5i + 4. 5u s.
  57. 4. 1123. 125. 512. 525- 11. 123,. 512 625. 1225. seu
  58. ((12 a mte (4. s 51s
  59. u2. 125. S1C. 325 = 112. 123. C. 312. 512. 123=Z
  60. 112, 123
  61. determinatione consequamur
  62. 11223, 112. 123( to) 112. 125, 512. 523 H: aa piet
  63. seu (4to). 112. 113. 312. 5(3 = 11225f. ) atih- H
  64. faciamus 4.113. 123. 5123, 523-112. 123. 312. 523. 112257
  65. 4. 112. 123. 5p b23 11223 = 112, 123. 513.523f.tah
  66. et fiet SeZ= (112. 123. n2. 513 0(f. 2H) f seu =) 512. 51Z (f - 24). Et ob G, F-C pari
  67. Mg. 12. 13t 31223 a: +ka -99 et (7mo) 713 = X1. 724g- 219.
  68. turc fiet (670) 312. 323. 312. 123=
  69. dum tamen res pentus ad rationales redacta est quia 12 173, Si2. 523 latent in 1122
  70. 112. 123512523(4aa - B) ~ 112. 52374 123. 512,2. 112. 123. 512. 523XA. Unde transponendo
  71. fit. f112. 123, 312. 523ff = (9n0) 112. 525 aa + 123: SIkR = 2. 112. 143 512. sB Hk, ergto
  72. tandem fit f f- 112. 113. 512. 523 ffi12. 523la 4- 123. 512h =4 51223k.
  73. Si faceremus () aha -Y = 0 seu f= -2R. quia ob eg. 5. non
  74. licet
  75. Ergus faciamus b, aAA- fs, Cd, = M. 523A + 123. 3. ita nulla fit nova determinatio
  76. et x asg. 9 fiet 112. 123. 512. 52317 (112. 523 ab + 123. 512 ab seu =) 11223tb seu per n et 12
  77. un fit B. 123. 512. 52 = (1310) bb, 4aa - f. Ergo res reducta est ad aegq. 5, et, 11 et 13. quod
  78. jam seto com jam bb, ata- s compendio vocemus B Nam majus esse debet quam ata seu
  79. d ps quel. 10 113. 123. 512. 527 est quantitas
  80. au atoremjam ex aequ. 1 sit B = B
  81. 112. 525 ab + 112. 52B ab B) B 112. 515 + (P. lb) 112. 523 + B8. as bb
  82. 30 + 4 aabb3: 4habb. seu 12. 523 ub (B 2ab) ( (+ aalbb - β: etb
  83. sergo ex 4 et 18
  84. jam 3β2 b SB. qua et B aabb dabb sbb et B b fona _, ergo fief
  85. tanb
  86. a ia oses it siasit e s
  87. sis reduci potest ad rationates
  88. uie art asnse

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 72r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0143?run=74