Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 242

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.

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

The machine reads it as

  1. V P P L E NE F N X V M
  2. DROPOSTFTO III.
  3. aucem exterior primae lic proportionalis uet palemeleeccuta
  4. ee partem interiorem ejuldem: crit quoque pars exterior lecunda PlOPOi-
  5. tionalis inter partem exteriorem primae ex partem interiorem ejuldem.
  6. Sub A cenrro descriprum circulum, secene duxe linex rectae ab eodem B puncto ex
  7. era circulum sumpro, eductae. Vna in punctis C, D; alcera in punctis F, P; unde parres
  8. exteriores secancium
  9. sInEBC, BE; incerio.
  10. TeS C D, E F: Citaurem
  11. BF proporrionalis in-
  12. ter BC, CD. DicoBC
  13. FOre quOquE PFOPOE
  14. cionalem inter BF, P F.
  15. Ouoniam enim ab c0-
  16. dem B pancco cireu-
  17. Iam SecanEBCD, BEF:
  18. ideo csturBF ad BC.
  19. ica BD ad BF. L.X hy-
  20. Pocheli aurem eAt CD
  21. ad BE, uEBF ad BC.
  22. Ouare est CD ad
  23. BE, Sicur BD ad BF,
  24. ex per lubductionem
  25. eAt C D ad BL, BCHL
  26. BC ad F. F: COHI-
  27. guenter ur C D ad BC, ita est BF. ad BC, d ira B C ad F. F: Ieaque BC proporriona
  28. lis estinter BF, B F. Ouod crat ostendendum.
  29. PROPOSY FTO IV
  30. Si dux linex rectae a puncto exera circulum eductae iplum sccent, quo
  31. aucem sic lub partibus exterioribus eductarum, ae quale sic ei quod AE sub
  32. InECTIOTIbUS: EXICLIOTES PAFLCS PCTUTaTIM LUIIPEX, CrUMECONtinuCpid
  33. pPortionales intEI ParteS InTeTIOTCS.
  34. Sub A cenro deleriprum circulum, secene dux linex re ctae ab eodem B puncto exte
  35. circulum sumpro, eductxe. Vnaquidem in punctis C, D; alcera in punctis E, F: une
  36. parres exteriores lecantium (unEBC, B F; interiores C D, L F: quod aucem Aic sub BC
  37. BE, aequale sicei quod sc sub DC, E F. DicO inter D C. P. F esse continue proporcc
  38. pales BC, BE, eas adsumendo permurarim; ur videlicer interiorem partem primX Le
  39. cancis lequatur pars excerior secantis se cunde; vel incerioreim secundae pars exteriorpes
  40. mae: nempe cAen D C ad B F, ita B F adB C, e ita B C adF F.
  41. Ouoniam enim id quod Hc tub CD, E F, aequale es ex hypothesi ei quod Ec sub BC
  42. BE: ideo eAur C D ad BE, ita B C ad F. F; per synaerelin, ut C D ad BF, ita B D adt B
  43. Sed exratione constructionis estBF. ad BC, sicur BD ad BF. Ergo CAtuL C D ad BLV
  44. ita BE ad BC, e ira consequenter BC ad E. F. Ouod crac demonstrandum.
  45. P R O P OS F F F O V.
  46. Daris duabus lineisrectis, inrenire incer casdem duas medias Continue
  47. proportionales.
  48. Sine darae dux linea reCXZ, X. Oporcexinvenire inter Z. e X duus medias conci
  49. nue proportionales. SicZ. major, Lminor.
  50. LCl
  51. Si dux linex rectae a puncto exera circulum eductae ipsum secent, pars
  52. C
  53. iX

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 242. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0248?run=74