Leibniz Legible

Machine transcription of the Leibniz Nachlass

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Ps. 2, fol. 30

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: 0.90.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. 30
  2. P R L H. C I P L it
  3. nacorem reducere, ica ec opus sic, quanticates lurdas, si diverta (i
  4. onaradicalia habuerine, reducere ad idem signum radicale. Ouod
  5. Hc, li ad numeros, a quibus radices denOIINAnEUE, minimuS ip.
  6. veniatur numerus, qui per ipsos sine reliquo dividi possic. CIE ad
  7. reducendum V aq (eu Y (2 ag & V C. 4 ag Peu V 3) aag ad idem
  8. Tigtum radicale: Quaero ad. 2 _ 3 (numeros d quibus Y O a V C
  9. denominantur) minimum numerum, qui per ipsos linc reliquo
  10. diridi pocest, qui est 6. Jam cum 6 dirilo per 2 Oriatur 3, et per
  11. 3 dirilo oriatur 23 hinc ag mulciplicandum erit in le cubice, et
  12. anquequadrates tienique sub eodem lignorOC. a3 43 (CuV 6) a39
  13. X V 2C. at 49 Ceu V (6 at 49. Sic de V ab a VV a3 b - F ab3 fub
  14. eodem signo radicali CruNE YV a abb _ VV a3 b - F ab3.
  15. Hluc reter cum quancitas aliqua rationalis per mulciplicatio-
  16. nem in se reducitur ad aliquod signum radicale. Exempli gracia,
  17. ad reducendum a 4 b ad idem lignum radicis cum V a a F bb:
  18. oportet multiplicare a L b in se quadrate, ec Fic V a a F 2 ab. L. bb.
  19. Non secus si mulciplicetur a - L b in se cubice, Het
  20. VC. a- = 3aab + 3 abb. + b3 sub eodem (igno cum V C. 43 - b3- f abb.
  21. Et sic de aliis.
  22. Deinde sciendum, quancitates surdas non raro ad simpliciores
  23. reduciporse, tollendo ex signo radicali quic quid est rationale:
  24. nimirum, diridendo quancitares sub eodem signor comprehenlas
  25. per aliquod Duadratum, vel Cubum, ecc. per quod mulciplica-
  26. cione tuerint producta. IIEV 75 a a reduci potest ad5 a V 3: naim
  27. 75 aa producitur ex mulciplicatione 25 a a per 3, quarum radi-
  28. ces lunc 5 a de V 3; aded uc, li 75 aa diridatur per quadeatum
  29. 25aa, sub higno radicali tantum scribendum sic 3, hoc modo:
  30. 5aY 3. Id quod monstrat s a, hoc est, V 25 aa, mulciplicatum
  31. esse Per Y 3:
  32. Fodem modo cIm 43 b - F a ab b airidi posie per quadratum
  33. aa, ec oriatur ab - bb; Hc uE pIO V a3 b - + a a b b Ccribi queac
  34. a V ab - - bb.
  35. Similiter quoniam a3 b - a a b b - 2 a a bc - a bcc - a b3- 7
  36. bb6c 2 b3c b+ dividi potest per quadratu a a- 2 a c +
  37. Cc 2ab - 2be bb, cujus radix est a. t 5- b, ee quoriens elt ab. bb;
  38. hinc

Cite

Ps. 2, fol. 30. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175906937X:0054?run=74