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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. 229

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: 0.91.

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The machine reads it as

  1. C AP. 25.
  2. Duoad Disseremiam, es quoad Rationem.
  3. 3. 5. 7. 9. _C. eE COnETa 9. 7. 5. 3. _C.
  4. 229
  5. Progressio Ccometrica, ubi plures numeri (alixere quanci
  6. cates invicem homogenea) eadem (vel aequali) rarione (re Procressio
  7. proporcione proBreciunEuT. IC 2. 4. 8, 16. 32. &C. e 3. 9. Geometrica
  8. 27, 8T. 243. _C. _8, 12, 28. 27. _C. _ COnETA 32, 16, 8, 49
  9. _c. e Paricer in similibus. Uc enim progrectio Rrichmerica.
  10. aequalicacem Difterentiarum spectat; sic Creomecrica, Racio-
  11. num hre aequalicarem sire identicacem dicas: IInde illic com-
  12. munis excessus tire differentia, hric communis ratio Cive proporrio, peo-
  13. frectionis speciem decerminat.
  14. Ilarum aucem Progressionum verags (cum Arichmerica cum
  15. Geometrica) eAt vel Continua, rel Disjuneta, (Tive dilerera, dif. Proeressio est
  16. Continua, inccrruPTa;) IIla, ubi quancitares concirue palicae _- vel continna
  17. qualibus auc differenciis aue rarionibus ubiq; procedunt. HXC, vel aisjun-
  18. eibi eadem quidem differentia auc racio idencidem redie, sed cta.
  19. non concinue. In illa, quilibet cerminus incermedius cum an-
  20. cecedens est cum consequens, communis Cive differencia Cive
  21. racionis; Inhac, non icem. Sic 3, 537, 8, T2, vel 22,9,7, 5, 3.
  22. Cune in progressione arichmetica concinua (vel, Si libet, Arith-
  23. metice proportionales concinue,) quia quilibet numerus illic
  24. ancecedencem, hic consequentem, binario luperat. AF 3,5;9, 1F.
  25. vel 9, T135,7. Cunc in progressione arichmecica diljuncta live
  26. interrupta constituci; nam eodem excessu secundus primum, de
  27. quarcus cerrium superee, at non icem certius secundum. Ec pa-
  28. ricer 5, 3; TT99; 17, 153 19, 27. Tunt in eadem progrectio-
  29. pe arichmeriea, sed incerrupca. Eodem modo, 2. 4. 8. 16. 32.
  30. _C. vel 32. 26, 8. 4. ec. Tunc in progrettione Geometrica
  31. concinuas quippe illic numerus conlequens ancecedenti (uo cA
  32. ubique in ratione dupla, hic dimidia sire Cubdupla. AC
  33. 2. 4: 33. 6:: 4. 8. lune quidem in eadem progrestione Geo-
  34. mecrica. Ced incerrupta; quippe secundus primum, et quarrus
  35. cerrium, et lextus quincum eadem racione superane; Ced non
  36. irem cercius secundum, vel quincus quarcum. Similicer, de
  37. 4. L: : 12. 3. dicendum ett, qui quidem numeri sunt geomen
  38. erice proporcionales, sed non contine.
  39. Ec quidem (quod semel dictum eAo) hujulmodi sive numen Proportiona-
  40. rorum sire quanticalum desienacio A. B:: C. D, in lequenci- lium noratio.
  41. bus saepissime incelligacur quancicares designare proportionales
  42. Geomerrice inellisc) Talrem discontinue; nempe quaratio
  43. nC

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. 229. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/826603459:0275?run=74