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Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2, fol. 112v

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: 0.84.

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. 111r); this page is its left half.

The machine reads it as

  1. seu Ad BE
  2. ponatur XF, y. fiet. CZ C, ZV,, e+ h, e h
  3. rit G et h, c-h
  4. Sit ADe d BEB f
  5. erit ECe c- Z.
  6. DBHkZ D WC c.
  7. et fiet: d +Z B AB H e.
  8. et f2+ C + Z-2cZ BCph.
  9. quae debet esse minima
  10. fet t (d +G + c5C+Z nZomnium possibilium
  11. minima: erit ponatur
  12. M
  13. nn
  14. N
  15. n
  16. sitque curva cujus ordinata B absust e M sit y. et absis
  17. DB sit Z. Quaeritur ileut punctum M in quo minima
  18. haec sit
  19. est curvae lalitudo, seu ut sit BM omnium aliarum
  20. minima. Patet tangensem in M. fore axi parallelum,
  21. adeoque fore dus 10. est autem dus.
  22. Est autem dus
  23. 2tZ, W0, (Z- tc
  24. LLat XYf +C+ Z 202
  25. fiet. Ve 5C+L= 2Z
  26. d12
  27. r seu
  28. S52CF - 21Z 10, Bc.7
  29. id
  30. 1o 7+ C- 2C3
  31. P
  32. Cl
  33. f222
  34. id est Bevs BC debet esse ad A BA, in composita ratione ex EC ad DB
  35. et ex 2 ad T.
  36. Producatur BC in F ut fiat BF aequ. BA. et per
  37. F ducta FGparallela CE producatur BE dum ei occurrat in G.
  38. erit FB seu AB: CB:: F G: EC. at spra
  39. at paulo ante AB: CB:: BD in T: EC im -2
  40. Ergo FG: EC:: Bd in T: EC in -2. et FG: Bd:: BZ
  41. refractionis
  42. erit ad
  43. Rteuti
  44. i
  45. Bd Sinum anguli incidentiae in reciproca ratione densitatis mediorum, id est
  46. incidens in medium rarius ideoque at radius incidens in medium densius
  47. esin
  48. incidens in medium rarius reflectitur perpendiculari, simu aucto.
  49. Brevius sic concludemus: ex superioribus: AB: BF: : io compos. ex Bd: FG1t
  50. et T. 2
  51. est autem ratio AB: BF aequalitatis, ex constructione, ergo composita
  52. ratio ex BD: FG et T: u est ratio aequalitatis, Ergo ratio Bd: FG est
  53. rationis T. reciprioca, seu BD: FG2: 2.F sive sinus angulorum sunt in
  54. ratione reciproca resistentiae mediorum.
  55. e
  56. Fper meam
  57. methodum
  58. tangentium
  59. imo videq id non
  60. licere sic enim
  61. mroblema jam
  62. heterminamue
  63. ieque amplius datis
  64. punctis ob. C
  65. in potestate est
  66. Quaerere B.
  67. datur intersectione
  68. circulorous ex centris
  69. C et A
  70. radis
  71. CB. Ap descudsitom

Cite

Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2, fol. 112v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068531:0224?run=74