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Leibniz-Handschriften zur Mathematik LH 35, 1, 17, fol. 4v

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: 0.77.

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. 7r); this page is its left half.

The machine reads it as

  1. Applocemus hanc constrnctionem ad Paraholam. Casum praesentis problematis Minnas
  2. ex puncto dato ad parabolam ducendae, ubi ex aequatione generali fit haec particularis.
  3. +q
  4. V4
  5. X (+ + 1F) +24fy
  6. +2ga
  7. (+ F) = 2dq a
  8. IB r, d
  9. et divisis omnibus per + 4, fietC aequatio haec: V X (1+ 1+) 2sa (+ +) ada ) 50
  10. ergo lr0. m e (+ ) (+ 4), 2s + 2a n 1 (+ f) id
  11. rpa.
  12. Ergo β A m.
  13. dq
  14. 10
  15. 2mMtb
  16. D B n
  17. -6br + 2mr
  18. Irn
  19. 4mrib
  20. -obesmtmr Fsen
  21. Recta PH
  22. 8. Frn
  23. -nr.
  24. ab) eemel 6
  25. srn
  26. seu = r
  27. + 2a L
  28. (461 qoa
  29. Roc EP 1
  30. -6br +2mY
  31. Veniamus ad lineas quae reapse ducendae sunt, ut appartat constructa
  32. apsius facilitos et difficultas
  33. 2 e =
  34. X 07
  35. EP, 0.
  36. 2m, 1b
  37. PK,
  38. imAtb
  39. +mr sam
  40. 6brSra +2mr 2srn
  41. 6br + 2m + b
  42. S.rn
  43. L radius: ( dungatur recto 2 K. et ex K erigatur perpendicularis
  44. ad eam R H quae possit: Quoniam b in nostro aetbitrio est, ponamus
  45. hic talem, ut 2mrb
  46. 6br sentami
  47. sit B Srn, fiet n b + 2mr S- rn
  48. et erit , L 2n sive erit Gr.
  49. jam
  50. 8-
  51. Rop mo
  52. 2S- ru
  53. e
  54. 2mr +6prin
  55. sin
  56. n. et PK -n (+ 2mrs-ra
  57. Jungatuo recta RI
  58. RCH
  59. 1+1
  60. 2mr +6rS-rn).
  61. S-in mr
  62. 2K et ex puncto R ad eam
  63. rectam normalis erigatur quae possit n rnm
  64. +nr, sive tur + mr
  65. ac centro 4, radio 4 H, destribatur circulus qui parabolam secabit in punctis
  66. , ex quibus demissae in rectam XV indetinitam, axi parallelam perpendiculares
  67. psita
  68. i
  69. d
  70. mr
  71. ur
  72. mY
  73. 2
  74. YV erient _ y quae sitae, quae parabolae axi parabolae ordinatim applicata
  75. puncta sectiois parabolae dabant ad quae ducta recta ex puncto dato
  76. cparabolae perpendicularis est.
  77. applipetur recta
  78. so
  79. mec
  80. Brevissime ergo sicpro paraborae datae
  81. EF i ut ab uxe ejus biseretur ad axi sit normalis et
  82. curvam ottingat utrinque. Ex punctu E dantro intra
  83. i parabalum indefinite ED axi parallela perpendia in IB ultra E continuata, sumatur E K (vel PR.
  84. quia puncta E. et P hic coincidunt) Brevissime sic et sit : linea quaedam, b, cujus vulor
  85. ejus duplum subtrahatur residiai
  86. nra
  87. curvam utrinque attingat in punctis E. et F producatur ultra E, inque ea ita p in ea ultra E producta
  88. sumatur EK (vel PX, nam puncta E. et P. hic coincidunt), quae sit differentia inter supradictam b et n
  89. Rursus ex K retrogradiendo in eadem linea sumatur R S et m
  90. Esn
  91. ex 6 ergatur tucatur vertus ventrem
  92. sive
  93. ergo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 1, 17, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067979:0008?run=39