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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 62r

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: 0.79.

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. 66v); this page is its right half.

The machine reads it as

  1. lx ratur taane a
  2. t
  3. X+ b = al sorm, vin, vrp) (vAY, vit, utiot
  4. q vfrivet, vtu
  5. , ic, tld
  6. sint m et aequales, item Y et I aequales, praeterea fiat X +b aequalis quadrato, et xtc aequalis quadrato
  7. seu al, v +2aV+ rum vmmH) V + munt
  8. pt 2m en H) 2mnt
  9. q va ri vr fyrbuv + mtt
  10. sietque
  11. at
  12. ErrF
  13. sit (N + sutag) + (vo F r Art)
  14. aequ.
  15. a qu v+ m). (Btnor
  16. sit etiam ven, vet = d
  17. qux+ fv+ ag)-v ratyp aagu
  18. = quadato Ah, qu ( uvris tl x )
  19. substituto C, loco b, pro C ponatur , et pro D poratur Q
  20. at
  21. hsversvras) - (ovrrvert) = O, D
  22. C quadicatus seu
  23. sit vva 2mvrrum ~ ve + hf Xe B) ibq asteritibus
  24. h+ Nba
  25. hribus
  26. fit hf. + + 1) ibq : 2erb9) = m
  27. et aghart 1b4 - mm = qu (hsrltet) ibq
  28. seu c4
  29. h+ibq
  30. h+ Ybg
  31. ahrtu, h + Ibu = qu (hf +(Y+B) Nbq
  32. Hinc habemus m, et g
  33. possunus facere A, B a ratione estante a. cu (Ntnt,) atriado; et B in rtione constrate ad rta, vtt, aneer ad B
  34. itaque tentandum an possint AC: esse niratione constnte et, D: esse in ratione constante
  35. quod si non licet, tentandam an 5 et e possint habere radicem communem
  36. sed hoc provideo lien non posse nam si 6 et G dindantur per ibq, retinebun radicem cemr, Ergo
  37. et summa earum habebit radicem communem, Ergo wetfotague, et vvrroert, habebunt
  38. radicem coem.
  39. Ita etiam O et 5 habebunt radicem communem; et ita radices reliquae
  40. ipsaum D, et D, deberent aequari radicibus reliquis ipsam 8 et D, et quidem decussalum
  41. radix ipsius (3) radici ipsius C radis ipsius 3 radiciipsias B, quod foret coprendrosissimum
  42. loco ipsius vn +sy +ag, scubatur ut e, vek sit e+K = vtr lebet esse
  43. debet esse sed ita fieret aterntia ex ipsis VtY, vel v et, aequalis ipsi v+ n contia hypothesin
  44. taq redemnm ad C: Q in rationi istante et D: f in ratione constante, seu C et G
  45. vel prunt quadrati, et in patone constante, et 9 et erunt in rahione costante ad ven vt
  46. seu cv + Lf + (Y1t) 16qe + hag + rt 1bq ~ veo, hs (11A _q hag. rt ICq = quodato ib um
  47. h + fb4
  48. htibqs
  49. et aubo aequandi quadrato pb. vt M
  50. et similiter
  51. ha Hig
  52. ht h - scq
  53. ex + hf rtc ibus hag- rt ib9 ~ Wup h Hrat) 1q Magt rt teq -v+ n, vat
  54. sba
  55. sit llt +h (rB X H
  56. h=Ybg
  57. h +Cq
  58. h+ scq
  59. (6+L)Gibc
  60. hast h(raibus L hficq () qube -lisis) -hsi re cq tsitus Sisde
  61. d
  62. et sit st) Y et divisis omnibus per hea sit tr+ L - () ob = - ( + t ah) sc
  63. riu. sit F + t - f =d n Et (hag h L 1b9- rtq be) = hhaque -hrt scque (C xt q+ b0
  64. =haq rea
  65. tit (tet hag) (rt - a9) Ab = (a- rt) sc Et sit
  66. haqibe
  67. rt = aq
  68. sed ita e coincidunt vv + fv +ag et Wr+rn+rt ergo etiam
  69. V+F et ven coinciverent, quod non licet.
  70. Ilas exitus non apparet
  71. C vem, Vin, vio
  72. q. vir, vit, WtW
  73. XtC = al (vim. ven, Bp) + cq (xtr, vIL AL)
  74. X. X +b, XtC
  75. Vv + 2uYtrr
  76. vo +2vt LH
  77. inac
  78. ax = B, ax+b = OB arte = D8, fiet OX 9D = 69- ab = D8 - ac, fiat
  79. = OD + ab,: () = OD tac, : D. fit ODD + ab D = O0D F aC
  80. ita res redit ad solutionem hum aequationis dioesanteam 1) = ZVD = ab v + acZ
  81. sit Z2V = ZVV + coYZ = abv -a a3 + cov7 et
  82. et - ZVV = - acZ+ covZ seu - xV = actcoV seu
  83. fit 7Z +eoZ 1, c 7 = 8- c + Y(ab + L Eg
  84. fial. ZZV + CoYZ = ab v, seu 27+ coZ = ab
  85. quo+ ov = ac
  86. et V = - 2 10 + 1C ac + 4 0c0)
  87. Ergo efficiendum esset ut simul coe + 4ac, et coco + 4 ab essent quadratu
  88. posset ut ex aequ. s fieri
  89. ZV = bp = cZ et
  90. et sit bez - be -7y = a Z = ceez
  91. -v = a DC fiet Y = 7- aa - cze:4
  92. abi tollendo Z, omna ficient detenutm b-3
  93. Vitendum an haic aequatio non possit 27V _ - ZrV = ab v - ac non possit reddi rationalis
  94. explicando Z et Y, sed de eo peculiari plagula, ubi pro Q est C, pro V est

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 62r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0123?run=74