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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 92v

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: 0.75.

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The machine reads it as

  1. unt
  2. Aranitur exxetabus Ax+aC) dX ay dx, formula summa riondita rtioali
  3. siat X: a = sO + D,: VZ, jam dsC = d0: 210. et similiter in d SD et a VE
  4. erit t lx: a = 18 +C: 10 - 10 de: H +BaD: s-(Dd8 14 :28
  5. Sit y = aQ + f+DP: Q, patet ydx non continere rat irationalem trimam, et proinde
  6. pendere a quadratura rationalis, si duo ipsiusy valores sidentificentur. Quod ita tentubimus
  7. Ryy = x tab, 22 tac - a 8 + b8 + 2a 1OD, ad + cQ + 2arD a an 82 + AOD + 2afG 1OD
  8. te
  9. aa
  10. per compendium sit 0+8 =k. et fiet
  11. autiq +ab + bcB8 + iaatu 10D + 4au BD) = aa ZQ + HOD + 2af4 (OD
  12. AC
  13. +2ab28. . compradio sit Aaa -H = ag et b+c =C
  14. ut jam identiticentur irrationales, erit 4aatue + 2a Z = 2at Q seu 58 =2at + e Z
  15. nicd
  16. Et ut identificentur rationales, substituto valore ipsius f) fiet
  17. a
  18. 2
  19. aahh + aetr Z +bc 8 + ag0D, ff = 4 ag H99=) 2a +4aetr Q ee
  20. 5E
  21. 4
  22. seu aephh + aaegte + (aa e bSf) ZY agfOD = o rt, agee = bs Hsit F a h
  23. th. ahg D-t.
  24. 88 + eg. t8 + ees th = ee gghit - gatraoh h + 4htOHCD
  25. C
  26. 4aatitr
  27. Itaque ut procedat extractio utrobique, faciamus eegqe- 4agh = -ontif seu reg9
  28. fiet
  29. X
  30. an T Anaph
  31. seu eeg t 4aah 3: h et seu et ontrando sit h fict et seu ueque ds
  32. seu eeaque. 4aeh --aliss, et ulcando pet 4
  33. seu et seu eeg a ceu- taah=- hH, sen eeq = hag et ee = ah.
  34. et seu aa ee = ah = anee bcff, seduta fint baff = o, quod est absurdum,
  35. Ergo non licet hoc modo procurare extrahibilitatem ipsius numeratoris in perte latere
  36. dextro, ut C) et D nantant simil vgiantes. Auligo Itaque opus crit ut faciamus
  37. D constantem, A et pro D substituamus est erit B = C+ l et OD = 10
  38. et tZ = 00 + 2l0 + I, habemus (ee99- 4 aahus) (9O + 2lO +U) + ahg fflC
  39. sed nec hoc prodest. An explicamus 3). per 10O + na, erit O+ D = (00 +10) O F1a =h
  40. itaque ex seegu -gaahqs t + at gff0D fict (elug- taahis) (20 00 + 2. 70. na O + i1 a) tahgffioetru
  41. ubi ut tillutur DC fiet ubi ut procuretum ormphibititur, sul et ordingudo
  42. compendio M OC Y CAnaC+ paa, seu
  43. d- 2. 20. +ghg + 4 1ihia ff.) a0)
  44. egai
  45. (+ (regus gaahus) ita
  46. jam mn OD + MnaC +mpaa, ut sit extrahibide debet esse um = 2tm M D tal
  47. mn= 2m imp, et n = 2simp, seu nn = +m
  48. iid
  49. seu gu quigg qu (20e59 20. 4 dah + 2hff)=
  50. n
  51. 20 C99-, 20 a eegt -4, 20 Cgh ff
  52. +20. 66a B) = (5). 20. qui H t ( t f4
  53. es
  54. 8
  55. mmoaet orpaa
  56. +2mimp a0
  57. roeeg-490 aah + 4. 1olff eegu auh
  58. (20g420 ahec 1ol trus H
  59. =E eegauti (+ 4. 20 ahhs (. acclilit
  60. e
  61. fiet 2. 1 ee Ha
  62. 2 2020) g = 6. 26 a h +2 (4. 20 - 10) aasph; + 2hf
  63. seu (2. 10 + 20 eB 4aa- ee +4) = C, 6. 20 a 2 (420- 10) ff. + 252) (a bct f)
  64. loupendios elgg. qaagh = acgq, siit tiz + A fff C3G - AhtsOC) fiat - 8+ 31a,
  65. el
  66. Kesser 21+20200
  67. firt 9030. O0 + 230. 31 ap + 31. Haa + 4 l.B
  68. aa
  69. aaque
  70. eaaque
  71. 00. 3000 + 4hH. ao. 3t a0 + hf6B
  72. aaque
  73. fiat 22 + AbH RD. 30aq F 4hHf. 00. 30 = Ahff0d
  74. =O et R. 30. 31 aa9 + 4hff. 00. 31
  75. fit 30 =. 2. 00hf: aaque et fit 0ff8100. 200R ag- 65. 00 aaq f. aff = 3aa9
  76. seu ahs= 30q seu nae- bc54
  77. l day= ac caih fraee + pe hcet
  78. tet 4aa ee= 12 2a bc = bc B
  79. Chragauus tercabets

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 92v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0184?run=74