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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 100r

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: 0.88.

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The machine reads it as

  1. Apollonias sectionem nationis quam oveat exposint
  2. peculiari libello, quem nuper restituit Hallerus. Nostra
  3. problema huc redit
  4. x
  5. Ex punctis duobus datis, eductae sint rectae
  6. hatidem posatio infinitae positione datae AB, LM
  7. Et ex punctur aliudatum F educatur recta, quae ex
  8. er
  9. rectis inde a punctis datis abscindat partes AC,
  10. LN, rationis inter se datae.
  11. Hoc problema nostra hodiernae Analyseos more ita attenta
  12. retur. jungantur puncta datap
  13. ex puncto F agatur vcta FG(in ipsam AL, et C AL, CA
  14. rmaltis
  15. Cddo concurrant in 19 cui ipsa CN occurrat in G. Ex ipsis
  16. F, C, N in AL, agantur normales FH, cd, xp
  17. dantur AL, FH, et angulus CAD, et anus NLp
  18. quaeratur GH
  19. sit GH, x FH, H AL, l. ratio AD ad DC sit b: A, et ratio Z
  20. et ratio AC ad LN
  21. ad pN sit iH
  22. sit GH, X i hac ergo Assumta habetur recta FGseu CN:po
  23. punctum C est in duabus rectis AC ABet eN Ob rectam AB erit CD ad
  24. AD ut sa ad b seu CD = HD - AH, CD h: b Aursus ob rectam CN, est Cd: GX dG
  25. = f: X DG autem est GH + HD ergo fit CD= GH + Hd, f: X = Hd - AH, h: b.
  26. Et fiet HB H GH. bf + HD fb = Hd h AHhX. Ergo HD = (B) + AH. H) X :, hX - b f
  27. et Ad = HD = AH. Ergo Ad = bf, AH. hX = AH. L x) + AH. bf, : hx - b f Ergo Ad = bf, X + AN; h
  28. Eodem modo procedemus cum NP, ut cum cd. Nempe punctum N est in
  29. duobus rectis M, et CN. ob rectam LM est Np: PL = n: m, seu est
  30. N p = HP = LH, h: m. Rirsus ob rectam (N, est NP: pG = f: X est autem PG = GH = HP
  31. Ergo tit Np = GH - HP, f: x. Ergo sit Y sed rp et n sed supra Np = Hp - LH h: m
  32. Ergo fiet GH. mf =HPnf = HPhX = LH. hX seu HB = G mst LH. hx, chx+ nf
  33. sed LP = Ht p LH. Ergo fit in fx(+ LH = LH h∞ = LH nf,: hx + mf = L P, seu
  34. (P= af, X LH; tix um mfE X - LH: tx + inf = LP.
  35. AD: AC = b: s(bb +hh).
  36. jam Lp: L N =
  37. Ergo fiet jam
  38. AC: LN =, Et AC: LN = Y si Y dato rationi Ergo fiet
  39. et
  40. m: Amm+hh)
  41. itaque AC = (Y (bb +hh) C: D) Of, XF AH, :, lx - bf
  42. LN = C Semmelh) (: M) rf, X - LH, :, hx + nf
  43. , aex, hxamf
  44. =2 , UX, hx- bf
  45. Et eodem modo
  46. jam AC: LN = g. r rationi datae
  47. et compendi Abb +hh) =C et Noumthh) = n
  48. 4
  49. et AH, a et LH, L
  50. ng: CY = 5: t
  51. aD, a + X.:, hx - bf
  52. seu fiet (a +X, X + m. )5): (l - X, X - (b. h) 5) = s. +. Unde tandem
  53. SEm. h) rat -st (b.h -ls X + as A(m :h) + (5 5 (b. h)
  54. 5+ +
  55. Unde jam more Cartesiano facile deriva
  56. 5+ t
  57. n(B X. : hx+ inf
  58. Ergosiet
  59. FXX +Am: h) GX +m .t A5 = C sia XX =
  60. eeta
  61. +5 XX Sib: h) fX + 5(b. 4) (f
  62. porrosed assumta constructiore Aptolloniana poterimus
  63. a3aX
  64. pitur constructio
  65. ad hoc problema reducere ea omnia, ubi rectangulam duo sunt aequalia
  66. quorum quaelibet latera sunt ut e iX + K
  67. si non ratio ipsem rectarum AC, LN data sit sed rectanentum videtur
  68. eodem pene res redit, si heerc nostram Analus sin sequare, musatis fautum
  69. mutandis. Daulo difficilior res videtur, q si summa aut differentia sit data
  70. 10

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 100r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0199?run=74