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Leibniz-Handschriften zur Philosophie LH 4, 7B, 2, fol. 68r

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: 0.93.

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. 67v); this page is its right half.

The machine reads it as

  1. TAt
  2. TH EOR.
  3. 1V
  4. Contentum contenti est contentum continentis
  5. seu si id cui aliud inest, inset tertio, id quod ei inest eidem tertio
  6. inerit vel si A est in B et B est in C, etiam A erit in C.
  7. Nam A est in B, (ex hyp.) Ergo A + L ∞ B (per def. 3. et charact 3)
  8. Ergo est aliquod L tale, ut sit A+ L ∞ B (per def. 3. t vel
  9. charact. 3) similiter quia B est in C (ex hyp) erit B+ M ∞ C
  10. in qua assertione pro B ponendo A + L (quae coincidere ostendimus)
  11. fiet A+ L + M ∞ C. Jam pro L+ M ponendo N (per postul. 1)
  12. fiet A + N ∞ C Ergo A est in C (per def. 3) Q. E. Dem.
  13. TH EOR. V.
  14. cui singula insunt etiam ex ipsis constitutum in est
  15. tiam
  16. si M est Si A est in C et B est in C, erit A + B nC (constitutum ex A et Bdes. 4) erit in C
  17. possit fieri
  18. Nam quia A est in C erit aliquod M tale, ut A +M ∞ C (per def. 3)
  19. similiter quia B est in C erit poterit d fieri B+ N ∞ C
  20. quae conjungendo (per coroll. Theorematis 3) fiet A+ M +B+ N ∞ et C
  21. Ergo jam C+ C ∞ C (per AXiom+) Ergo A + M + B + N ∞ C
  22. a
  23. Et proinde A+ (per def. 3.) A+ B est in C. Q. E. Dem.
  24. THEOR. VI
  25. Constitutum ex contentis inest constituto ex continentibus
  26. Si A est in M et B est in N erit A+ B in M + N.
  27. Nam A est in M (ex hyp.) et M est in M + N (per def. 3.)
  28. Ergo A est in M+ N (per theor. 4) similiter B est in N (ex hyp.)
  29. et N est in M + N (per def. 3) Ergo B est in M + N. (per th. 4)
  30. jam si A est in M + N, et B est in M + N, etiam (per th. 5.)
  31. A +B erit erit A + B in M + N. Q. E. Dem.
  32. THEOR. VII. pa.
  33. siBerit si qu
  34. si quid additur ei cui inest, nil constituitur novi
  35. seu si B est in A erit A +B ∞ A. Nam si B est in A potest fieri
  36. +C∞ BFC∞A (def. 3.). Ergo A+B ∞ A+ Ergo (per th. 3) B+B+C
  37. B+ C + B ∞ A+ B ergo A+B ∞ B+ C+ B, ∞ B + C (per axiomius
  38. proris praecedentis
  39. t per dicta hic) Q. E. Dem. Par 2,
  40. conversam
  41. Si quid addendo alteri nit constituitur novi, ipsum alteri inest
  42. EORemalI
  43. A conversum T)
  44. Si A+ B ∞ A tunc B erit in A, nam B est in A + B (def. 3.) et A+ B∞A
  45. Cex hyp) Ergo B est in A. q. E. dem.
  46. cui nomen
  47. imponemus
  48. intermscendus
  49. familians simo
  50. cui juncendae
  51. demonstra
  52. hoves
  53. expressione
  54. propositionum
  55. smitiares
  56. illustrande
  57. exemplis
  58. + (per insertum
  59. inter th. 2 et)

Cite

Leibniz-Handschriften zur Philosophie LH 4, 7B, 2, fol. 68r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068646:0135?run=74