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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 56v

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. 55r); this page is its left half.

The machine reads it as

  1. Vedeamus an non transformatione aliqua effici posst
  2. formula in qua duo termini suimm vel altimi tollibiles
  3. sunt qualuor factores
  4. e m +ysa m- ysa m+y m - y. seud in ponanusta
  5. fent mst mhy m-hy ntus m-y. qui a ducti in se invicem
  6. debent producere quadratum vst
  7. La2
  8. et
  9. sit mahus = sv ioZ et m- hy = spo ZCo et nty = + moga t
  10. pro ducentes
  11. .
  12. et fiet mahius st V im hy s
  13. 2
  14. Engus 2m = stv + stoz
  15. communem
  16. quatrat
  17. 3 a. et fiet quadpitum (SsEt vxuroZZCoc
  18. 5.: s. ... .. + v M+ hy = stv m - hy 2 spoZ
  19. u.-
  20. . z
  21. L
  22. se im + y tloco m. 1= vzco
  23. .- co
  24. (∞)
  25. = FWco + vZco et 2hy = stv - sZ = 2htWco hoq
  26. solvendae ergo ae quationes b,7, 9, ut obtinentur aeq. 8. post illas. Ex 8quo est
  27. (62)
  28. + + s 2m: lv +WZ= (ex q) M CDONCo, W +VZ: tv+noZ= se 1) to so- v2
  29. v2
  30. E = ubi ut inveniomus s vsi per aeq. lo. resolvamus aeq vationes H et c2. vatores V et 12
  31. idi aquemus cun vatire 10. fit 2m = cotevW + torZ+ thoWZ + VWZZ seu
  32. co=n: trW + tuviot tuW Z+ vuZZ sei c 1d
  33. a + et similiter co m. Hov -W10ZZ: a, tW pqe Exvalire id et 72.
  34. 1+ 1
  35. i V ujam duos. ipsins Cd valores 13 et 14 inter se aequando fiet
  36. At
  37. 83E 2h. 2v + WZ. tW-BZ = m. +vtoZ. t
  38. 700.
  39. papc es S Cee 2M: evau2 eB ritou
  40. es
  41. + et ex aeq7 est 5= Cd, tW + vZ:, +V+ WWZ et ex aq. 9, s 2hco, tW -vZ tv - W Z
  42. 11 de 2
  43. (14)
  44. oc = et denique ex 1 et 12 fiet: 2h, tW - vZ tv + WoZ = t W + v7, tv- WZ
  45. de
  46. es faciendo multiplicationem actu ipso sac 2hFLWB + LHWZ - vozt - vWZZ= FWV-tw Z1 vV, t v1 2
  47. is
  48. SC
  49. seu 2_ AVV
  50. 2h - 1, vWv, Et -Z2
  51. C
  52. 2h + 1, +Z, v -w1 ubi saltem eo casu
  53. quo poneretur h= L facilis prodivet solutio, fieret enim vv- W010 = 6, seu
  54. seu
  55. li v = =D = W: quod si v = 1o fieret co = 5 = 2m: B, L +Z
  56. et ∞= per 8 fieret y = 5B, t-. Z seu y = B 2 mB, t. Z.: fp, L1Z
  57. ergo saltem illo cusu Hyperbolae vel Ellipseos haberetur solutio, et
  58. quadrali latus soret am: (B E+ Z on tZ(VD seu ammtz:, F +Z2
  59. Sed stemus in generalibus, et sit v = 10X + 1 et W = 20X + 21
  60. et t = 30 X + 31 et = 40 X + 4) fit vd v0 = 10. 10 X+ 2. 10. UX L 1. 11
  61. et (WWW = 20. 20XX + 2. 20. 21X + 21. 2) et tF = 3a 30 XX +2. 30. 3IX F 31. 31
  62. et _ZZ = 40. 40. XX + 2. 40. 41X + 41. 41
  63. et VW = 10. 2OXX + 10. 2) X = 1. 21 et tZ= 30. 40Xx + 30. 41X + 31. 41
  64. + 11. 20 X
  65. et tE. Z2 vWV = 10. 20. 30. 30 X F 10. 21 7 3. 30 X3 + 11. 21. 30. 30 XX,
  66. 11. 20
  67. 2. 10. 20. 30. 31 X) + (10. 2 j2 2.31 xX F 2. 11. 21. 30.31 X
  68. + 31. 40 X
  69. = 10. 20. 31. 3IXX + 10. 21731. 31 X = 11. 21, 31. 31
  70. ed ante quam in calculi prolixiore pergamus 1.
  71. considerandum est
  72. posse aequationem 16 ita divelli in duas, ut sit
  73. 2h 1, +F- Z2 e2) BtZ
  74. et βVW 2h+ 1, v-wW, quae divulsio
  75. quod summe notandum fit sine suppositione, quia B est quae cunque
  76. ex aeq. 17. fit H- B ZF + B
  77. sit (3: 2h- 1 =B si 3. 1 42 - B +
  78. Z= ( +Bh-27. seu t R
  79. Eb122
  80. seu 1 - D4Z + = BB, = 472+ 8837. 4 seu fiet
  81. F= LByt 1a2Et 06 seu t e E2t: Z B+ 54+ BB. et eodem modo, si faciamus
  82. 22)
  83. MF 3: 9 2h+1 = A. fiet vY D vv- Ay W= WW seu vV - AW P+ SW - WX, A1X
  84. quia antem
  85. seu v- = AW = 12d 1, 4 +X seu 20: W= S + 14+ M. ubi si β adeoque et D est
  86. habeauus pro constantibus non opus est ulteriori aliquo pro aequuationitus 21 et 24
  87. his positis v: Wd est constans _ +: Z
  88. copans. fariamus B.I
  89. ii valoribus
  90. 1d, 5, et y, aequationum 13, 10, et 8, fiet co= em: t ; et S Em: it enat, et denique
  91. erit 2hy = 2m: 1+ N. 1 (. sed ita fiet y constans contra intentionem itaque nihil actum est, nise
  92. sutlo
  93. faciamus (3 esse indeterqusam 3: 2= 6, it . = iea res in arctum contrusa est

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 56v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0112?run=73