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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 133r

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: 0.78.

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. 132v); this page is its right half.

The machine reads it as

  1. (4
  2. 140)
  3. seu trilineum AE BF A ag trap ei AHBE. trilim AHBFA. sed Trap AABC= Emper 15B Ex hilamus 4G
  4. et traper AGBE = volanus AB _ (seu Xy) - trianus AGH (seu gy: 2) et trianus BHG p Z7:2
  5. Ergo fiet denum Tuilin. AEBF A6q. Xy - gy: 2 + 72. 2 - frilin. AHBFA et pro trilineo AEBFA substituendo
  6. valorem ex aq. 18 fiet pilin. AABFA = 2 nX . y - = X: yy - xy + 9y: 2-27:2 est autem
  7. Xy C (per 20. 21) +6177- vv, : 2 ergo = xy = 22. 2 (= _ - 7Z + vv. 2 et yy, = 2 1V + vV. 2. adeoque
  8. =Xy + 9y: 2 - Z2: 2 2) (- 77 + vr: 2 + Z7: 4 - Zv: 2 + vr: 4 -) 322: 4 + 3vv. 4 - Zv. 2
  9. Z AXy8- ZX: gy = 2n L. v EtV: iq, + Z∞ + 6Zv gZV + vF: 8, : Z. yvrvv; 2
  10. seu 2nxy- Lx : gu ~ 1en Z7. vr Z+V + =84ZV+6ZV +ZV+ V,: 4. 22. 230 + W Ergo
  11. trilineum AHBFA fief 16n 97. vv. ZFD + Z4 4ZV+ BZEBVH V, V B. 3 ( WV L 2V - 2ZV _1ZV,: , 4 - v
  12. examinis probationis causa
  13. Sed nunc his omissis saltem calculum ese prioem insistendo ipsis er reassemamus
  14. (4
  15. u
  16. 352
  17. sed hoc prolxius ut verear ne in calculo sit eiratum.
  18. X+ G = nxy sit G = xv:n fiet X + xV. D = n Xxv:n seu rXeX = nV seu x = nv: n+V
  19. et per 2 et 4 fiet y = (v: n NV:, n’ + V =) nV:, n + v. et dx = v + N, Ndv, - n v 3Vdo,: EV
  20. = ( PaV) + n dB = dv: ( v + M= dx. Ego per Set 6 fil Gax = nd v a - 2 nv v7:, (L V + _. Cujusqueritur
  21. summa. Quod ut fiat commodius, ponatur V4+ 13 = co et pier 3Vd a seu v co- n et 3Vav deo seu
  22. v du = deo: 3. Ergo per 9 et 11 ex ag. 7 fiet : ydx = = n deo - 2 n co - 13 de, : co = 3 n deo C - Z clleo + 31 la,: c0
  23. = nd dco: C5 - 2ndeo: 3coco= ydx jam (ac: coco Fisco Ergo Et pro co in aeq. B substituendo
  24. adesque pro deo, ponendo 2do, fit S2odo: ct = - 1: 0c adeoque Sdco: a = - 1: 2cdc. Ergo ex aeqe 12
  25. fit (ydx A = nb A- n: 2c0c + 2n. 3co Assumta nb tanquam adjectione
  26. summationis ex propessu determinanda. set jam cosseu n3+ v) = n v: X ex aeg. +. et v Z ny: x ex .
  27. Ergo ex 16e117 fit co = nt y: Xx. Unde ex aep. s fit syx = ab - n X. e y +2n X: 3nty se tbdem
  28. seu sydx nb - X: 2yy _ + 2nXX: 3y. jam si X = 0 fit etiam y -0 ex ag. 1. et Sydx = 0.
  29. Itaque eo casu ex aeq. 19 fil 0 = nb - 6 00: 2 _ + 2n0: 3 seu 0 = nb. Ergo b = adeoque connesis,
  30. et filt denique sydx = 2nXX: 3y - X. 2yy Ut supra. Huic ergo calculo fide potest
  31. vider non esse necesse po C Ctolli Epli
  32. Generalior fieri potest inquisitio. sit, 22+CV Inxy posito c esse numerum quentum
  33. sit xo: n fiei nX + C Vx = n v. seu x = nEr: n’+ CV fiei y = nV., ut cv
  34. et et dx = (Cp + n3, nav , =no3Cvdv (2 P + h =) ndo - 2 Vdo,: (2 ((V + R. Ergo
  35. sit Cv+ n= co fit v = co:c - n:C
  36. et 3Cv dv = deo fit v du deo: 3C et ex org. 7 fit n deo: 3c - 2C n. . C - n C devis
  37. yIx Z n vao - 2en v d, : (3) CV + n3
  38. = ydx = (n deo: 3Cco = 2n: 3cct +2n: 3cc =) ndeo: cc , - 2n: 3cc ade oq fiet
  39. jam co = nV: X et v= hy: v. Ergo co= nt y: XX
  40. adeoque syax = e, 2nX: 3Cy = X. 27y Hinc si c- 2 fei sydx = nN: 3y - x: 4y
  41. (12
  42. Cydx=
  43. -n3: 2C c02 +2n5: 3CC
  44. Aluud problema iihi ab Hugeuio in eadem Epistota propositum
  45. .cuius
  46. invenire lineam cartesio a Beaunio sropositam Ept. 79. voluminis 3 artesii
  47. subtangens sit yy -xy: a, aut dx: du = + posito t: y = dx: du ~ y - xB: a. fiet
  48. dy = 1DdqZe F u dv et Fydy = _ 10 2dZ f u v dB F 10. 1 Zdv. + 10. 1. vd z 410. na d Z +. 1. 2av 117)
  49. adx = ydy = x dy sit y = 10~ + 11 V + 1a
  50. - xdy = - 10. 20Z 4Z - 11. 21 viv - 11. 202 .1v - 10. 21 vtZ 11o. 22 a d z - 11. 2a dv
  51. c
  52. = 20 adz -21 a dv
  53. alatu fiat 10. 11 - 11. 20 = 10. 11 = 10. 21 et summabilis crit aquatio 7. Ex fit 11. 20 = 10. 2)
  54. =adx=
  55. C
  56. non procedit, quic fieret X = 21y - 1a + 22a quod absurdum. jam enim haberetur lineu
  57. ub si fiat H = 1 et 20 = 1. 2t. fieret y = 10Z + v 4 12
  58. ante applicaoem ad problema. Hinc nec licet tollere Zdo et naqu nam et sic earum coetticem
  59. ferent aequales inte, se, aclae solicet ipsi a. Tollemus ergi si licet terminos in quibus sunt es
  60. sne y vel V. et fiet 6. 12 - 10. 22 - 20=0 et 11. 12 - 1122 -21 20
  61. Erg
  62. 20 = 10. 12 - 10. 22, et jam 22 12 - 21: 1 et fiet 20 = to. 12, 10. 1112 + 10. 21, : 11
  63. e Et et ex 10 et 11, fet 202 (10. 12 - 10. 12) + 10. 21: 1I et fiet y = 10Z + IIV+ 12a et f- 1B9. 27 + 21B + 2. 1
  64. sit = 1 et =- 1 et 13 = 0 et fiet sed vi sed video rarsus rem non procedere nam fit
  65. sit X = _ 10 + u y + 121 + 13 13 + 14 1t fiet ad . = a1 + 2. 1298 + 3. 127 4 4. 140 el sit 10-8 et l -0
  66. a
  67. -
  68. 1 - 12 - 13 et
  69. fit X = 29 22 217: 11 = 1 2a + 12-
  70. yd=
  71. 14 = 1: 23. 4 eu
  72. oidutu it ie te, st sti ee su desteti
  73. 4d
  74. et fiet X= _ y + 21 + 2740
  75. Edgat

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 133r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0265?run=74