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. 386

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: 0.89.

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The machine reads it as

  1. De Fractionum Reductionibus variis. CAP. 44.
  2. Cui denominatores congrui (modo mox ostendendo) alsump-
  3. ei 20, 15, 8, exhibent expolicis 2, 4,E aquales cognomines
  4. 25 325, 25, ee quidem minimum communem denominatorem
  5. habemres. Sic 2, 13, 5; diritis cum 2 _ r0 per communem
  6. MenTuram 23 ProctibunE quociencCS 2, 5; cum iterum 5 (quo-
  7. ciencum jam inrencorum alcero, qui propcerea eciam eliminan-
  8. aus erie, cjalque loconorus per lequenrem divitionem lubsti-
  9. Euendus) S (denominacore tereio) per communem divilo-
  10. rem 5, unde prodibunt quocientes in 2, _ (ex prioribus duo-
  11. Bus) relumendus x, qui in duos communes dirilores 2, 5, Con-
  12. tinue ducti, dant LXE ~ IX 2X5 = 10 communem denomi
  13. nacorem minimum; quibus relpondent denominatores con-
  14. FruI 5, 3, 8; adeoque tractionibus expotcis 2, 103 5, aqua-
  15. Led TunC, cognomines 18, 253 ad. Sic aB
  16. a35
  17. bas caB
  18. reducuneur ad cognomines minimos à B7 A3 à By s’aBys
  19. Invento autem communi denominatore minimo, Numeratores
  20. consrui invenioneur, hoc eAt, Fractiones expolca ad datum De-
  21. nominatorem reducuneur, hoc modo:
  22. Ad darum denominatorem reducirur data Fractio, (Inovus
  23. ad Denomi altumatur Numeracor, qui, ad dacum Denominaeorem, cam
  24. natorem da habeat racionem, quam habee Fractionis daEx numeracor ad
  25. tenneno denominarorem Cuum. (Rario manifecta cA; quoniam dum
  26. Terracur eadem Numeratoris ae Denominacoremracio, eadem
  27. manectractionis quanticas.) Sic sFractionem Z, reducerere.
  28. lim ad aequale eliam, qua denominatorem habeat 10; Guae-
  29. rendus es Numeratur, qui hcad 10, uc eAt x ad 2. Sire, ad
  30. quem, eam hahear racionem 10, quam 2 ad Y. Qnod per au-
  31. ream resuLA PerABIUE: PUta 2. 1:: 10. 9 = =E =5. A-
  32. deoque 15 im Z. Paricer si ad eundem derDminaEOrEM FO, re-
  33. ducere velim Fractionem E, Sumendus est Numeracor 8: (quia
  34. P. 4:: 10. 8.) Adeogue, S = 8 PF propterea (quod ino
  35. Ao diCium erat) Fractiones Z, 16, 5, ad communem denome
  36. nacorem roreduera, erune 15, 10, 20. Eodem modo, tra-
  37. ctiones.:
  38. 20122320: (WVam 2, 2:: 20, 20. ILem 4. 3:: 20, 75.
  39. deem
  40. 8
  41. Fractionis

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. 386. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/826603459:0432?run=74