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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 317v

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: 0.82.

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The machine reads it as

  1. habebitur aequata 4 quae de2 formula aequationis 14 quae
  2. debet coincidere datae forta a ib, ubi a, et b sunt fa formula
  3. datae ex y et x ravaliter integreque formatae
  4. (17
  5. Remlicebat statum ab initro sic facere: dx: dus = a: b
  6. do v: v + dz. X: + dc co: cd Ct O posto v, 3, cd, dari per X et y
  7. jam de= =V dx + dv du et du= Z dx + dZ du et deo dco ax + X dus
  8. fiet de v + dq ZV a + dcocov Z:, dv. VZ c+ dVdo
  9. Eet -dy: dx) = -b: a. latus autem suistrum aequavis. E vel exhibeamur
  10. aectus ipso ponendo formationes per Xiis esse rationalis e integras, et numeros
  11. 4, 5, 6, 78 significare contidem foatee formulas rationales integras. Monamus
  12. p 10X + 26y + 1 et Z= 30X +40y+ 91 et cd = 5oX +60y + 51 erit d v = 10
  13. et Xv = 2 et dZ = 30 et dZ = 31 et a c0 =50 et d0 = 6 et V = 70+ 71
  14. et = 50 81 et R- 40Z + 91 et 23 = 1002+ xF 10) et co =10 11
  15. et 108 = 12O4 + 121, et fit ex 84. 6: 10. 70. I0XF goy1BI +71. 100. 3OXH0y1 31 4 01
  16. 120. 50X + 60y +5) + 121 + 30. (80. 10X+ 20yKII +81 90. 20X+40
  17. 16. 50X +60y151 F
  18. 450. 80. TOx +20y+1I. +8]. 100. 30X + 40y + 31. = 10) : 20, 70.10X et 8100. et 20
  19. +10. 80. 10X.: 9030X.. 170,50X = 60. 8010X, 100. 30X. 11050X.. = - b: a
  20. unde perinde est ac si parbamus 10 E 150X16B 170~9 11OXG +151X (1 161 y
  21. +17+ yX + 152X + 162y + 153 et,, 430, in 190X + Ly CM, +50 in 230124
  22. indivis. per 20, in 130X) eu + 40 in 90X + eu, +60, in 230X + et,
  23. vel Tubi -b: a alcendat
  24. dB. . Ryeux. py ea
  25. E
  26. in immentore et numeratore eunt prii numentor stae ipsi ae quandae aequetur
  27. edus non sulori, Tabemusue literas conpartioes intrliendas decem
  28. iseum fiat s in numeratorem compatatio, non
  29. pec
  30. que fia
  31. biunl litere
  32. e
  33. a
  34. , b bia
  35. sit inferior, poterit multiplicando Pattollilad p. dele in habeautersit
  36. liferae conpantitiae. Nota: NZodet e 190 et 100, iem 10 et red finsti
  37. noniunsuntur sufficit hotum nagna sed et 1 st abjici possint, et pro tis poni mutas
  38. terns iier padfecturae sindt 15
  39. xperopretium etit prosequi quont s hac
  40. smplici positione, multiplicare fecta adendorm mogrdilliaat
  41. proxinni est ut V, Zvela ex et y ormentur Hormula integra rationat adrasica
  42. sed ipsae 3 56,78 significent autum somalicas formaoes ubi musidebine
  43. e quousus racinave proficiptua nostieno videbim quid fiat si utem modis
  44. stimand si quadratic soel estiam ost sint altiores aequales aut
  45. in aequailes Et haec vietur compendiosissima ratio tractandi hanet
  46. minam inde siiliter plegeuad differentiales formutas
  47. irratomales.
  48. uquollies s cb
  49. dod imaloeissimis manesa quosties quol tatemu literas ut v, Z co, toties
  50. EKhabemut E larbitrarias proficiente
  51. ec literarum. jan in quovis quadu o sunt
  52. . Et ad Tradum ascendimeus aequale numtro
  53. ant termin
  54. n+I nt 2,: 2 posito n numero
  55. gradus seu ex pomento, et arbihariae sun sunt 5n. quibus D
  56. tns
  57. alius gradus ipferior pe
  58. epantio itaque numeu terurigore
  59. SM +
  60. verum bis instituenda est
  61. debet este n+ l. net de un
  62. +1. pF2: 2 dee essae nf1. diFE posito n. p = gradii
  63. a daule exaltioe sed pet sme exsitratione dato gradu a, et gradu b,
  64. n,vel salle
  65. et ex hiis ndiginio (4, siet ntqt 1. nq non major n, et dato 9. qutur na

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 317v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0630?run=74