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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 120v

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: 0.81.

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. 119r); this page is its left half.

The machine reads it as

  1. Xydx + Xx hy = dexty Xyydx + Xx ybu = dxxyy
  2. Sae xdx ANa = L nx rar
  3. AK, Y ABZ BC, y.
  4. 5= Sex Pellereree sxyax + sun y Xy
  5. (xxdus asse dus -sygay er saay- : sedus xy- sydx. Ergo
  6. Ergo ex 7 per A, 5 fii sxgax = xg nky + 2r Syax + : yd
  7. seu (xyta = 2Y syda -2= (x Sipe. Xu
  8. quaenitur sipinter XX Sirx Xxd = g xxyAx (xxyax + sxdus = xy. jam
  9. Xdy = (er IrXX du = Xyyduys 2YXdy = (per 1 arrX dys - gryydy
  10. yy r ly =.
  11. du fr- fx, ex, : YY. Ergo Xyyes? x ,) rxy Xxgdx a X. r. X. yax = rXyaE - XXydx
  12. Ergo per 1o et reliqua fit (Exxude = Xy - 4 rrsedu + Erydy Arspydx (axydx. Ergo nihil hinc
  13. a sit a arco, t tangens sa = RY rad fit a = (a: rrtH sinu verts X, rectus y fit
  14. Aliter Xdy y ahat:
  15. sector = ra Syax = ira - cy r g: F : c: 4Y Ergo gy: ec = H: YY
  16. yy = 2rX -XX CC = H -2rX +XX
  17. AT, B 2Y = X, : y: r: B seu 2Y-X : EY- XX Xrr: BB fit 2Y -X,: X:: rr: DB seu Zx: X = rr+ BB: BB seu X - 2rbB: m a
  18. 3dx = ; vati rr+ H = LC dy _(- ydc:) ydx
  19. Xdb = 2ydu SBaq = 2sy dx - xy SBa = sxa +B - sxdB. Ergo 2 sydx -xy = xB - sx dE. seu Sydx = x yB - ( aB
  20. Lvidet ad hoc praestari aliquid posse diffrentiando, verb. gr D multi per X. fit DX = X sb et differem
  21. tiaudo d DX, fit Pr. X + X. AX. s+bX. =, ubi quilibet ipsus ) trminus diviitur per x, et per nto
  22. vel per entr omisso. et ita B. +X
  23. 123.+ 5b er sit VIbX X haoc spries maltiplicabitur per X se
  24. Alius usus serici infiatae pro provehendis quadraturis:
  25. dath +
  26. it IX+ b. Xut - + 8
  27. Sx+b. X de = 1. ot2
  28. (X SixbX ad
  29. + en + Co FY T poterunt addi, sed video jam
  30. enrco, sed 1par o prelcudi pt im A, et rin β. Ergo nil nobi hire
  31. nec haec juvare quin en +0r7 = 1= ent
  32. TItbX = L +
  33. 5.2
  34. s
  35. 1. 2 b. X.
  36. 2n 1. 3. 5
  37. nth 1.3
  38. b. 222F2 13.
  39. intcoC
  40. .Xa
  41. (4 n +5
  42. 1 etc = es
  43. 1.23. 4. 16; 4u +3
  44. Bentto 135 b. ed erc = D (4
  45. = 12 3, 8. 3n+ C
  46. 1. 2. 34, 16; 4n +Cd
  47. .2it red
  48. b
  49. ris p2j4; An +to
  50. quivis terminus ectum, quorum seres infinita facit O, vocetur W, et quivis terminus quectum
  51. quorum series infinita facit D vocetur H
  52. fit O = su et D = si pt - W
  53. ergo similiter se si X ejusdem est gtadus cum 1d 1 - 1. 3.5 etc se enti et eodem
  54. .. Ergo 1p x et 1 sunt ejisdem gradus quoad X, scribamus
  55. 1.2. 3 et, 2. en+ W
  56. Ix = 8 fiet Yb = 9. videamus an hec duo possimus ita multplicare per constantes in
  57. g entcd
  58. tota ferie, ut ex ipsis conjunctis vriab
  59. sed e est valiabilis; sed tamen ipsius us
  60. dus co
  61. Et primum majoris simplicitatis lausa sit Cd = D ubi x= (it quod places g)
  62. quia alioqui si melhodus universaliter succedeet haberetur setragonismi sircularis reductio d quadratur
  63. absolutam, qualis plarabolae, quod absurdum.
  64. 1d per On + A. et addamus poducta sit pnas
  65. Ergo si Y o sucedit depressio
  66. ergo V+X s seu L mult. per β3n. +), et
  67. entt quod - eenn + ejn + Z), :, ea, en +
  68. eDnn + C
  69. idditorim fuisset nihil
  70. slsans
  71. facitrims V = = βn, procedet duplex depressio, sed hoc non licet
  72. si faciamus ) = 0. d pressio quidem fit, sed secundum n, se non secundu
  73. uni ex prioubus it jam inde id agi, ut secundum e potius de primamus
  74. ildeamus an
  75. en + 3 cividere possit nominattore, inultiplicando per _n, fit
  76. e Mn +3 ( = e pun+ dunt rn tAn + 3 en + 2Y fit m = Bn + Y
  77. effici possit, ut
  78. e + s
  79. entco Cn+
  80. et addamque in unu
  81. et videamus an numerator divisibilis e
  82. Ergo recurramus ad
  83. Cen + 3 + e Aen + 1C
  84. entco, ent3
  85. fine e ent In + 3+ 1C = pn C + C
  86. fiet en t an = pun seu β+ A = en
  87. sed ita raisus nic lacramur
  88. 3C + 2c = Zβ + ZA. Ergo c0 = 3
  89. frit een +Nen prsr en neenn + n eM + 3B; entco, ent2
  90. eenntvey +2a
  91. quia ed desomisset asse integer
  92. HCo + (2 H) = (2 + B + A. seu β3 = nCo - LA- a
  93. ergo (Z, HC0) - 2 = E. A +. cos + Nco + ZH = (2 NC0) sed mdm audeon hiberefidem
  94. ferro + L + H. (- Cen + ZB+
  95. A=- B, et co = 3 quo facto nit latramur. sed quod si ceapco + d + H = e M sed e hoc
  96. += 0 sit B ee qu + Crn C 1X + A Zu e + Z en A = -+ 19. n B rn 2 69. : , 2n + con
  97. nihil quiae B simmul sumi possunt
  98. H. in e2)e Xeo qu. Co enH
  99. Nam Qpotet esse certa telcuminata, quae vubbit si QCon + Brd. 1 +co 43 C. ACo Z, = 2E+ Nco Z: -2Cd
  100. proquodrandis multis n
  101. = = 3+X qcoZ9: 3 + Co3
  102. (3 C ZA +c. β + (Z ( 110) 3+1
  103. + qeomasit sid eu eet integuis.
  104. tX 2 40 quod videtur procedere
  105. jevansi

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 120v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0240?run=74