Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus, fol. 325

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: 0.87.

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The machine reads it as

  1. C AP. 35.
  2. Elementi quini Euclidis declaratio.
  3. 29 Si sit MI toia ad toram, sic ablata ad ablaram; erit e reliqua au
  4. religuam ut tora ad totam. P. A0 enim e + e
  5. a =R. Prit ica-
  6. que cum AZ B = R in a +6 =R a F R6, cum A = R a. 2-
  7. deoque e residuum B =- R 6. PC
  8. urrinque aequalirer dividendo)
  9. B
  10. 6 = R = a t B FAque HaC
  11. propolicio unirertalis ad prop. 5.
  12. a +B = Ka 16
  13. a -
  14. Fuclides illam sic demonstrat. Ouonsam ue A F B. a +6:: A. _C
  15. erit alterne (Ceu permucando) A FB. A :: a +6. a. Pc divi-
  16. dendo (sire per divitionem rationis) B. R : : 6. a. iterumq5
  17. permucando, B. 6:: A. a:: A + B, a + 6.
  18. Acque colligie hoc nesux leu corollarium, Si compositae mac-
  19. nitudines sint proportionales; e per conversionem rationis proportionales
  20. erunt. Cum enim ostenderit A + B, a + 6:: B. 6. FC permutan.
  21. d0 A F B. B:: a F 6, 6- GUX TMnE qLanCIEaCeS COmPOLICR PEO-
  22. portionales. Sed _ octentum eAt A F B. a F 6: : R. a. adc09:
  23. permucando A + B. A:: a F6. a. gux es convertio ratio-
  24. nis. Ouippe 26d5 definitur Conversio rationis (araspoen noge
  25. sumprio antecedentis ad excessum, quo antecedens ipsam consequentem su
  26. Perat.
  27. Clarius hanc demonstrarionem improbat, propter achibi.
  28. tam alcernationem, quae in Tolis homogeneis obcinet, cum ea-
  29. men convertio racionis eciam ubi bina binis (unt hecerogenea
  30. locum habetu adeogne hanc (ubstitmic. Si A F B. B :: a F 6. C. CrIE
  31. (dividendo) a. B :: a. 6, _ (invertendo) B. A:: 6. a. _ tan-
  32. dem (componendo) At B. A: : a 4 6. 8. quae eAt convertiora-
  33. rionis. Nempe siuc coca prima ad sui parcem ablacam, sIC FOTa
  34. Secunda ad Cui ablatam; erie uc coca prima ad lui reliquam, (C
  35. eora secunda ad lui religuam. Vel brerius, E uc cora ad abla-
  36. eam, sic eora ad ablacam; erit _ coca ad religuam; ut toca ad
  37. reliquam.
  38. MorenouroC deulonuab et
  39. 6 +
  40. derit
  41. 6 3 a
  42. 82

Cite

Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus, fol. 325. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/826603459:0371?run=74