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Leibniz-Handschriften zur Mathematik LH 35, 7, 18, fol. 9v

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: 0.85.

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. 10r); this page is its left half.

The machine reads it as

  1. et
  2. id est, ut tres abscissa, veltres applicatao correspondentes punctis interse
  3. Mrerum fianl aquales et secundum methodum (crtesi prodibit equatio quae rela
  4. sionem ostendit inter AH et HG, et proinde nafuram survs quam desiginnt
  5. puncta screntorum osculantium. Operatio est alis qu. BG_-qu. Bp
  6. - qu. HG = rect ang. 2BF. HG = qu. F ( id est vn - qy - 2yt =
  7. (5 = 25X + xX _ vel Xx + yy -25X + 2ty + 5s + H -vv = 0. ope aqualia
  8. curo 6 tellatur X velu ut se curva sibstarabola, ubi x = yy:a fiet
  9. y4 + aagy + raaty55)
  10. =2a5y G
  11. ve
  12. 20 si ergotres radice saequales
  13. comparonda hoecaequabii cum
  14. producto ex y- e, y- e, y-e, y-f undef
  15. comparanda haec aequabro it - 3ey + 5Cegy - 3 Chy + e2f =0
  16. L 3
  17. 3efusys -zeefy
  18. quam aequationem priri aequando fit. -3C f20 Hec + 3ex 2aa -2a)
  19. C3- 3eef = 2af et e3f (5 +H-v) aa perprimam F= - 3C, ande
  20. in 2da6ee =aa -2as. Et in 3tia erit 80= raat unde juptu illudes
  21. e= 1(2a5 - aa): 6 et juxta hoc C= 2V raaf. Quas duos valores
  22. quando f et ponendo, 5 = Y+ a, fiet ar = raat set
  23. 16Y3 7aH. Unde patet curva naturam, in quam cadunt centra
  24. circulorum parabolam senlanbium esssem parabota cubicali secunda
  25. cujqus parimeter est 27: 16)a, et cujus vertex distat a vertile para bolee
  26. data quantitate La, quoniar s+ a = it si raditem eB quoque inve-
  27. nire libeat, tantum supram saequ. 4ta ef - (55+ H- vv) aa substituatur
  28. valor ipsius f et e fiet =3C(5s+ tt - VV) aa et quia ee = (2a5- aa): 6 =
  29. ar: 3 eut = (aarr: 3) F id est - 39. 7 = (55 F id est rr+ a+ + aa) ett - vn) in ad
  30. et reducta e aquatione invenitur Vv seu qu. G0) = Z rY + ar 1 aa
  31. +H. Hinc si r = 0 erit F20 et v=ha. id est centrum circuli oscudtantis
  32. parabolam in vertie dipatcenro quara ab eodem vertice quantitate ta
  33. similiterfaciendum in omnibus curois Algebrinicis, sed quia sartespanaG eo
  34. pietiase ad Transcendetes nonextendit, quomodo Cago centro lirculorm
  35. seulantium inveniantur ex calculo differentiatium nyllo negotro ostendi poest
  36. non osculantium centra qatuntus
  37. osterdimus ea esse in concursibus duarum perpepdiculariam Bd, od infinte pam
  38. sit ergo cupua data, ABdenius cu
  39. ap antitate distantium imcenenda enjoest longitudo, sd ex abscissa AE, et ordinata B
  40. ducatur Be parallela ipsi AG, et dF perpendrcularis ad BC silt
  41. 2X, EB,
  42. AF dx. F0, dy. erit FC = a dy: dx, et BG dxdx + dydy3: ex et quia .
  43. di +
  44. ydiidu cujus differentiare posito dax =D es
  45. HG quia autem BC: HG = Bd: dH auldevidendo
  46. ACHGi BC = BH: Bd, i ess- Yadys ddx dp + dy dus) = G H(d Z ext dyduy eli
  47. F. F0 = AE. EH eus EH
  48. des dy + y ddy): dx=
  49. ad B, d Ergo Bd = (dx ax+ aydis: adue in Cdx dx + dy dys):
  50. demaliter inveniri potuisset dicendo B0: BF = HG: LG. ergo LG erit
  51. dedx + dy dy + y ddi:, S (dxdx + dydy). Nunc B0-LG, : B0 = BL
  52. per alios adhuc
  53. dem provenit quod aute.
  54. (vel BH) 2Bd pro quo ad cognitionem rectae B3d. dacantur nempefius q
  55. dats tangentes pM BN, et arculus vel perpendicularis MM erit
  56. rerfferentlalis ippus AM et quia B0. OF = NM. MP. aabetitur Mp.
  57. modos peroenri potest
  58. eoM et Bdo sunt trpiasula similia fociendum ut p M ad
  59. del adhocaliter ducatur perpendicularis
  60. AG eut Se disferentialis ipsius AS, et quia B0: BF = 59. sR, ets R: B0
  61. 20, ita AO adBd quaesitam.
  62. quia ante
  63. =DS: Bd, inveniri potenit Bd, quae semper erit (dxdx idydus,: cidus) t
  64. in Scaxdx + dydus): dudx. in qua quanltate so subestituatur vator.
  65. nont natura curvae requirit, proveniet seu pers Bd
  66. in quantitalibus ti ordinariis et absque differentialibus. Monstremus
  67. ipsius axvel dy
  68. 7 obi AB, AE
  69. BEy = F ax, et gni Talore
  70. st autem in farabola,
  71. dy = adx: 2 lap. proinde dydy = adx do: 4x et ddu = adc ax
  72. excuplo paribalo
  73. oclor dus et adus.
  74. axtax. Ergo fit Bd = a + 4X sa + 4x,: 4 a) sit jam A sed more
  75. Bd dicto substituendus
  76. Cartesi sit sit jam AL, s. et Ld, t. quia EH= ia erit BH
  77. ob BH :EH, = Bd: Et fit Et = 2
  78. axi. =aq
  79. a + 2X et AL = 2 a +3x= et sit
  80. =3X vel X = L Y et sic 4X: 4) sax
  81. qu e: 3) HaT: 3) = + et reducta aequatione 1673 -27 af ut supra
  82. al supraposuimus (= 2a +Y erit Y
  83. in parabolucabicali prima parameter a AE,X. BE, 7= Baax
  84. dy = adxe: 3Yax fit tandem Bd = (aa X= YY aaxX): 2aYa
  85. saa +gr saa: gxYaax. in Hypibola diapneter ex panmettib
  86. AEX. EB,) = (aa X + axX,: b) unde facile habetur Bd. sit
  87. AB Cycloestalis linea, AGH Erculus Gentor (fig. 8) AE x. EB, y= EGrAG
  88. = Rax - +x) +s: Et dy = (a dx - Xdx : (2ax - XV) - ds = quia
  89. ratx-xdx: EaY -x. et aly = -adx dx: XHeaxa
  90. Ladys.
  91. c1( ax- 7. P
  92. atran s
  93. epera pretum ert ostendere particulariter quo pacto percom
  94. s
  95. un
  96. F2 ag = 2 ax)=
  97. renum inveniri possit distantia a vertice centri circuli qui curvam
  98. d
  99. osculatur in vertice. Sit AB euva data cujus Ayus AC

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 18, fol. 9v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068089:0018?run=73