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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 145v

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. 144r); this page is its left half.

The machine reads it as

  1. et apparebit si q sit major quam a, fre aequationem ipsarum PO, axi ordinatum applicatarum
  2. fore ad Hyperbolam Ellipsin; sin minus ad Hyperbolam, adeoque superficies Sphaerolidis Motigi pendet a quadratura
  3. , superficises spherocidis lati a quadratura Eli Huperbolae. Quae jam et ab Hugenio inventa
  4. videamus jam an adhuc aliud curvae Elliptiiae momentum exalia quadam recta
  5. determinata habere liceat. Jungatur VT. et ex puncto in cura . ducatur in VT. ordinata NC
  6. sunt.
  7. sit VAHX H AOH Trax - 2 X ut ante VNNZ. NONW
  8. Anto omnia VAHX,
  9. quAc
  10. Tagrier
  11. Ergo AB, XYaq. et BO, y - XYaq
  12. et X VBr SXer Naq H X SIt a. et BNB Z- X S1+
  13. H et NONCor = 2 yx Yaa (+ X 4) - Z - x (X a) - 27x Yi1 9
  14. rursus VB
  15. reca
  16. 1 1 ∞ - X saq acit y -r saq Zsira - + 2B
  17. Z= YF1+ 2
  18. sive V4 ⊓ 9Z 5. +29 IX. et XC Z s+ + - y et Y ( ZSi r2 -Y
  19. sive. X adg, ut quem valorem inserendo in equatione co fes:
  20. 2v age fia + 29= Z Z + 229 Fi y
  21. Ulnde in aeq. superiore, explueando y. fiet
  22. rax - aX, - 2ZX SiF aqu + 2X saq., - Z1 - X - 2ZX Y1+ cor
  23. ursus quia y HZ +Z4, + X, - 2 12. 1 + 4 5 cax - 2 +
  24. va + (7ZX S1 +q B -1ZXSira Saq
  25. fier Z + x - 2aX + a X + ( 2aX - 2
  26. et sed his non est opus. sufficit habere nos Y+XeZ. Unde 4 ut
  27. omne
  28. obiter dicam, sequitur Z. semper haberi posse.
  29. Sit2
  30. Caeterum rectius videmur factari si gene alier calculemus: sit
  31. sinq
  32. Aequatio est A aq a vt. pone 91 V et Praa a x. Et perpendiculoris sp ae
  33. sive VH eag- 2 v. (et S seu quad. a perpendiculari
  34. reritar
  35. 2 +, y 1 (a) + a9 - a ∞ (= a) 4 a v
  36. sive SH aq + 124∞) in aeq. 5( aq - a V. pro y ponatur _ + - bco. et pro vfias st eb +b Z + aco
  37. ad -cYeeb
  38. se +bd
  39. a 2. adeot percompendim Ve +b rocetur d. et eb - cra metur f. fe. Ve rbo
  40. et valoribus pro y et v substitutis, sier. E + 26Z - 20bc0, + eZ- 2ebZC0 + bC0 daq, - af- 2a flz- 2 ao,
  41. (4 baZ 2b a c0Z P a3co, sive +e2 y + b co -2eb ZCo + 2eZ- 206c0 + e+
  42. +b2 +a. +2ab..
  43. +2afb. +2af.
  44. -d249
  45. +acis
  46. A Quae est
  47. aequatio ad Ellipsin aut si 4. quanlitas vgativa su, Hyperbolius quam maxine variata. Compendti causa secrilamus
  48. 9Z + h + lZco + mZ n Cd + p B0 quam ad tangentes ordinando scribemus.
  49. 29Zt + lEd + + mt p - 2hco - elZc0 - nco
  50. . Porro co p P. et co +co s fiet
  51. A aE coC AS jam ejqs i literas arbitiarias
  52. mempe e. b. c. ita explicare tentemus, ut omnium s. per Z. explicatarum haberi possit summa. sicenim
  53. novum curtae vel Ellipticae vel Hyperbolice momentum habebitur. Est autem t -2hco2- 12co nco. Ergo erit
  54. Co H 6297C0 + lco + nco
  55. =2hco - 1Z - n
  56. pon CoH 32 - 1ZCo- m Z= nco- P Y
  57. ponamus -9Z - lco- m H Y. per trachy logiam, et fier : - 4Z- nco -p,
  58. c + 1Z co + pr
  59. 1
  60. vide sec. fig. Li
  61. a -
  62. + 8 22
  63. +B: la Z
  64. 1 n
  65. m.
  66. 2
  67. 1g
  68. sed culculus paulo prolixior
  69. 292. + 1c0 + m
  70. S1 N SigEco Uo mco +1
  71. sa
  72. 2tco 1Zn
  73. etico- 1Z n +
  74. AcoplZ +)V Z atatn Z + n
  75. -24
  76. amus
  77. -+pg
  78. t punctum in cunva E inde ordinata CB. verlex Ellippos A abscissi Axis AB Y erit
  79. CBriSZar = a r2. ipsa C9. sediameter sit b CHIg- 219 +r +2ar - a
  80. into in curca puncto O. ducatur ad diametrum Cy. adinatur (tangenti paralleta) OD quae et posita CD pZ
  81. alere recto respondente diametro 24. fiet OD( Y26X - bZV producatur usque in E, ula perpendiculari CP. occurat
  82. in calculo superiore essent G. et nejo; foret co 29Z + m. e+ co F1 - Z- niZ= P et SM Sg2+mrI Z
  83. Enor in praecedentibus inde a signo quod sureseron Codco +2. curm debeat scribi co 1. Est autem +, co ( 2t - 17.
  84. cortoem
  85. 2t- 1Z n 3 = si, Yoiir YI S. Unde poncndo l to frerci 29Z + m Y S5- 1. Quae est aequalio 32 + co tm
  86. ad Hyperbolam, quod si ergo fieri potest 0 et nullus est error incalculo, haberemus momentum quoddam curvae lonico ex quad.
  87. aequi, 9 aq + a9 +1 v = in typ +. in cir. etEll. -
  88. sit in Hyp. aequilatera: vaequ. s bF + 2by t
  89. 12 + y conferendum priori,
  90. fec. Mro res non procedit
  91. Ergoer ll
  92. hypertio le. ut autem sit 10. fiet C⊓ a
  93. aquatio ad curvam conicicae Etementur
  94. pater triangula si esset er. sed haec quoque puto inutilia
  95. mullipticato elemento per

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 145v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0292?run=74